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| calculus with matlab: MATLAB Differential and Integral Calculus Cesar Lopez, 2014-10-01 MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Differential and Integral Calculus introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving a short introduction to the MATLAB environment and MATLAB programming, this book provides all the material needed to work with ease in differential and integral calculus in one and several variables. Among other core topics of calculus, you will use MATLAB to investigate convergence, find limits of sequences and series and, for the purpose of exploring continuity, limits of functions. Various kinds of local approximations of functions are introduced, including Taylor and Laurent series. Symbolic and numerical techniques of differentiation and integration are covered with numerous examples, including applications to finding maxima and minima, areas, arc lengths, surface areas and volumes. You will also see how MATLAB can be used to solve problems in vector calculus and how to solve differential and difference equations. |
| calculus with matlab: Calculus for Scientists and Engineers Martin Brokate, Pammy Manchanda, Abul Hasan Siddiqi, 2019-08-03 This book presents the basic concepts of calculus and its relevance to real-world problems, covering the standard topics in their conventional order. By focusing on applications, it allows readers to view mathematics in a practical and relevant setting. Organized into 12 chapters, this book includes numerous interesting, relevant and up-to date applications that are drawn from the fields of business, economics, social and behavioural sciences, life sciences, physical sciences, and other fields of general interest. It also features MATLAB, which is used to solve a number of problems. The book is ideal as a first course in calculus for mathematics and engineering students. It is also useful for students of other sciences who are interested in learning calculus. |
| calculus with matlab: Multivariable Calculus with MATLAB® Ronald L. Lipsman, Jonathan M. Rosenberg, 2017-12-18 This comprehensive treatment of multivariable calculus focuses on the numerous tools that MATLAB® brings to the subject, as it presents introductions to geometry, mathematical physics, and kinematics. Covering simple calculations with MATLAB®, relevant plots, integration, and optimization, the numerous problem sets encourage practice with newly learned skills that cultivate the reader’s understanding of the material. Significant examples illustrate each topic, and fundamental physical applications such as Kepler’s Law, electromagnetism, fluid flow, and energy estimation are brought to prominent position. Perfect for use as a supplement to any standard multivariable calculus text, a “mathematical methods in physics or engineering” class, for independent study, or even as the class text in an “honors” multivariable calculus course, this textbook will appeal to mathematics, engineering, and physical science students. MATLAB® is tightly integrated into every portion of this book, and its graphical capabilities are used to present vibrant pictures of curves and surfaces. Readers benefit from the deep connections made between mathematics and science while learning more about the intrinsic geometry of curves and surfaces. With serious yet elementary explanation of various numerical algorithms, this textbook enlivens the teaching of multivariable calculus and mathematical methods courses for scientists and engineers. |
| calculus with matlab: Multivariable and Vector Calculus Sarhan M. Musa, 2023-02-08 This book is designed primarily for undergraduates in mathematics, engineering, and the physical sciences. Rather than concentrating on technical skills, it focuses on a deeper understanding of the subject by providing many unusual and challenging examples. The basic topics of vector geometry, differentiation and integration in several variables are explored. Furthermore, it can be used to impower the mathematical knowledge for Artificial Intelligence (AI) concepts. It also provides numerous computer illustrations and tutorials using MATLAB® and Maple®, that bridge the gap between analysis and computation. Partial solutions and instructor ancillaries available for use as a textbook. FEATURES Includes numerous computer illustrations and tutorials using MATLAB®and Maple® Covers the major topics of vector geometry, differentiation, and integration in several variables Instructors’ ancillaries available upon adoption |
| calculus with matlab: MATLAB Symbolic Algebra and Calculus Tools Cesar Lopez, 2014-12-19 MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Symbolic Algebra and Calculus Tools introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at symbolic variables and functions, you will learn how to solve equations in MATLAB, both symbolically and numerically, and how to simplify the results. Extensive coverage of polynomial solutions, inequalities and systems of equations are covered in detail. You will see how MATLAB incorporates vector, matrix and character variables, and functions thereof. MATLAB is a powerful symbolic manipulator which enables you to factorize, expand and simplify complex algebraic expressions over all common fields (including over finite fields and algebraic field extensions of the rational numbers). With MATLAB you can also work with ease in matrix algebra, making use of commands which allow you to find eigenvalues, eigenvectors, determinants, norms and various matrix decompositions, among many other features. Lastly, you will see how you can use MATLAB to explore mathematical analysis, finding limits of sequences and functions, sums of series, integrals, derivatives and solving differential equation. |
| calculus with matlab: A Matlab Companion for Multivariable Calculus Jeffery Cooper, 2001 Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, A MatLab Companion for Multivariable Calculus introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton's method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http://www.harcourt-ap.com/matlab.html. Computer-oriented material that complements the essential topics in multivariable calculus Main ideas presented with examples of computations and graphics displays using MATLAB Numerous examples of short code in the text, which can be modified for use with the exercises MATLAB files are used to implement graphics displays and contain a collection of mfiles which can serve as demos |
| calculus with matlab: Engineering Mathematics with MATLAB Won Y. Yang et. al, 2019-02-01 Chapter 1: Vectors and Matrices 1.1 Vectors 1.1.1 Geometry with Vector 1.1.2 Dot Product 1.1.3 Cross Product 1.1.4 Lines and Planes 1.1.5 Vector Space 1.1.6 Coordinate Systems 1.1.7 Gram-Schmidt Orthonolization 1.2 Matrices 1.2.1 Matrix Algebra 1.2.2 Rank and Row/Column Spaces 1.2.3 Determinant and Trace 1.2.4 Eigenvalues and Eigenvectors 1.2.5 Inverse of a Matrix 1.2.6 Similarity Transformation and Diagonalization 1.2.7 Special Matrices 1.2.8 Positive Definiteness 1.2.9 Matrix Inversion Lemma 1.2.10 LU, Cholesky, QR, and Singular Value Decompositions 1.2.11 Physical Meaning of Eigenvalues/Eigenvectors 1.3 Systems of Linear Equations 1.3.1 Nonsingular Case 1.3.2 Undetermined Case - Minimum-Norm Solution 1.3.3 Overdetermined Case - Least-Squares Error Solution 1.3.4 Gauss(ian) Elimination 1.3.5 RLS (Recursive Least Squares) Algorithm Problems Chapter 2: Vector Calculus 2.1 Derivatives 2.2 Vector Functions 2.3 Velocity and Acceleration 2.4 Divergence and Curl 2.5 Line Integrals and Path Independence 2.5.1 Line Integrals 2.5.2 Path Independence 2.6 Double Integrals 2.7 Green's Theorem 2.8 Surface Integrals 2.9 Stokes' Theorem 2.10 Triple Integrals 2.11 Divergence Theorem Problems Chapter 3: Ordinary Differential Equation 3.1 First-Order Differential Equations 3.1.1 Separable Equations 3.1.2 Exact Differential Equations and Integrating Factors 3.1.3 Linear First-Order Differential Equations 3.1.4 Nonlinear First-Order Differential Equations 3.1.5 Systems of First-Order Differential Equations 3.2 Higher-Order Differential Equations 3.2.1 Undetermined Coefficients 3.2.2 Variation of Parameters 3.2.3 Cauchy-Euler Equations 3.2.4 Systems of Linear Differential Equations 3.3 Special Second-Order Linear ODEs 3.3.1 Bessel's Equation 3.3.2 Legendre's Equation 3.3.3 Chebyshev's Equation 3.3.4 Hermite's Equation 3.3.5 Laguerre's Equation 3.4 Boundary Value Problems Problems Chapter 4: Laplace Transform 4.1 Definition of the Laplace Transform 4.1.1 Laplace Transform of the Unit Step Function 4.1.2 Laplace Transform of the Unit Impulse Function 4.1.3 Laplace Transform of the Ramp Function 4.1.4 Laplace Transform of the Exponential Function 4.1.5 Laplace Transform of the Complex Exponential Function 4.2 Properties of the Laplace Transform 4.2.1 Linearity 4.2.2 Time Differentiation 4.2.3 Time Integration 4.2.4 Time Shifting - Real Translation 4.2.5 Frequency Shifting - Complex Translation 4.2.6 Real Convolution 4.2.7 Partial Differentiation 4.2.8 Complex Differentiation 4.2.9 Initial Value Theorem (IVT) 4.2.10 Final Value Theorem (FVT) 4.3 The Inverse Laplace Transform 4.4 Using of the Laplace Transform 4.5 Transfer Function of a Continuous-Time System Problems 300 Chapter 5: The Z-transform 5.1 Definition of the Z-transform 5.2 Properties of the Z-transform 5.2.1 Linearity 5.2.2 Time Shifting - Real Translation 5.2.3 Frequency Shifting - Complex Translation 5.2.4 Time Reversal 5.2.5 Real Convolution 5.2.6 Complex Convolution 5.2.7 Complex Differentiation 5.2.8 Partial Differentiation 5.2.9 Initial Value Theorem 5.2.10 Final Value Theorem 5.3 The Inverse Z-transform 5.4 Using The Z-transform 5.5 Transfer Function of a Discrete-Time System 5.6 Differential Equation and Difference Equation Problems Chapter 6: Fourier Series and Fourier Transform 6.1 Continuous-Time Fourier Series (CTFS) 6.1.1 Definition and Convergence Conditions 6.1.2 Examples of CTFS 6.2 Continuous-Time Fourier Transform (CTFT) 6.2.1 Definition and Convergence Conditions 6.2.2 (Generalized) CTFT of Periodic Signals 6.2.3 Examples of CTFT 6.2.4 Properties of CTFT 6.3 Discrete-Time Fourier Transform (DTFT) 6.3.1 Definition and Convergence Conditions 6.3.2 Examples of DTFT 6.3.3 DTFT of Periodic Sequences 6.3.4 Properties of DTFT 6.4 Discrete Fourier Transform (DFT) 6.5 Fast Fourier Transform (FFT) 6.5.1 Decimation-in-Time (DIT) FFT 6.5.2 Decimation-in-Frequency (DIF) FFT 6.5.3 Computation of IDFT Using FFT Algorithm 6.5.4 Interpretation of DFT Results 6.6 Fourier-Bessel/Legendre/Chebyshev/Cosine/Sine Series 6.6.1 Fourier-Bessel Series 6.6.2 Fourier-Legendre Series 6.6.3 Fourier-Chebyshev Series 6.6.4 Fourier-Cosine/Sine Series Problems Chapter 7: Partial Differential Equation 7.1 Elliptic PDE 7.2 Parabolic PDE 7.2.1 The Explicit Forward Euler Method 7.2.2 The Implicit Forward Euler Method 7.2.3 The Crank-Nicholson Method 7.2.4 Using the MATLAB Function 'pdepe()' 7.2.5 Two-Dimensional Parabolic PDEs 7.3 Hyperbolic PDES 7.3.1 The Explict Central Difference Method 7.3.2 Tw-Dimensional Hyperbolic PDEs 7.4 PDES in Other Coordinate Systems 7.4.1 PDEs in Polar/Cylindrical Coordinates 7.4.2 PDEs in Spherical Coordinates 7.5 Laplace/Fourier Transforms for Solving PDES 7.5.1 Using the Laplace Transform for PDEs 7.5.2 Using the Fourier Transform for PDEs Problems Chapter 8: Complex Analysis 509 8.1 Functions of a Complex Variable 8.1.1 Complex Numbers and their Powers/Roots 8.1.2 Functions of a Complex Variable 8.1.3 Cauchy-Riemann Equations 8.1.4 Exponential and Logarithmic Functions 8.1.5 Trigonometric and Hyperbolic Functions 8.1.6 Inverse Trigonometric/Hyperbolic Functions 8.2 Conformal Mapping 8.2.1 Conformal Mappings 8.2.2 Linear Fractional Transformations 8.3 Integration of Complex Functions 8.3.1 Line Integrals and Contour Integrals 8.3.2 Cauchy-Goursat Theorem 8.3.3 Cauchy's Integral Formula 8.4 Series and Residues 8.4.1 Sequences and Series 8.4.2 Taylor Series 8.4.3 Laurent Series 8.4.4 Residues and Residue Theorem 8.4.5 Real Integrals Using Residue Theorem Problems Chapter 9: Optimization 9.1 Unconstrained Optimization 9.1.1 Golden Search Method 9.1.2 Quadratic Approximation Method 9.1.3 Nelder-Mead Method 9.1.4 Steepest Descent Method 9.1.5 Newton Method 9.2 Constrained Optimization 9.2.1 Lagrange Multiplier Method 9.2.2 Penalty Function Method 9.3 MATLAB Built-in Functions for Optimization 9.3.1 Unconstrained Optimization 9.3.2 Constrained Optimization 9.3.3 Linear Programming (LP) 9.3.4 Mixed Integer Linear Programing (MILP) Problems Chapter 10: Probability 10.1 Probability 10.1.1 Definition of Probability 10.1.2 Permutations and Combinations 10.1.3 Joint Probability, Conditional Probability, and Bayes' Rule 10.2 Random Variables 10.2.1 Random Variables and Probability Distribution/Density Function 10.2.2 Joint Probability Density Function 10.2.3 Conditional Probability Density Function 10.2.4 Independence 10.2.5 Function of a Random Variable 10.2.6 Expectation, Variance, and Correlation 10.2.7 Conditional Expectation 10.2.8 Central Limit Theorem - Normal Convergence Theorem 10.3 ML Estimator and MAP Estimator 653 Problems |
| calculus with matlab: Calculus Problem Solutions with MATLAB® Dingyü Xue, 2020-03-23 This book focuses on solving practical problems in calculus with MATLAB. Descriptions and sketching of functions and sequences are introduced first, followed by the analytical solutions of limit, differentiation, integral and function approximation problems of univariate and multivariate functions. Advanced topics such as numerical differentiations and integrals, integral transforms as well as fractional calculus are also covered in the book. |
| calculus with matlab: Calculus and Differential Equations with MATLAB Pramote Dechaumphai, 2016-06-30 Calculus and Differential Equations with MATLAB presents a clear, easy-to-understand on how to use MATLAB to solve calculus and differential equation problems. The book contains eleven chapters with essential materials that are taught in calculus and differential equation courses. These include: - Limits, differentiation and integration. - Taylor, maclaurin and other infinite series. - Ordinary differential equations. - Laplace and Fourier transforms. - Partial differential equations. - Numerical and finite element methods. - Special functions (error, gamma, beta, Bessel, Airy, Legendre, etc.). Exact solutions are derived before showing MATLAB commands to provide the same solutions. Numerical methods are used to obtain approximate solutions when exact solutions are not available. The book contains a large number of examples and homework problems to demonstrate the capability of symbolic mathematics in MATLAB for solving calculus and differential equation problems. |
| calculus with matlab: Physical Oceanography Reza Malek-Madani, 2012-04-20 Accessible to advanced undergraduate students, Physical Oceanography: A Mathematical Introduction with MATLAB demonstrates how to use the basic tenets of multivariate calculus to derive the governing equations of fluid dynamics in a rotating frame. It also explains how to use linear algebra and partial differential equations (PDEs) to solve basic i |
| calculus with matlab: Advanced Engineering Mathematics with MATLAB Dean G. Duffy, 2021-12-30 In the four previous editions the author presented a text firmly grounded in the mathematics that engineers and scientists must understand and know how to use. Tapping into decades of teaching at the US Navy Academy and the US Military Academy and serving for twenty-five years at (NASA) Goddard Space Flight, he combines a teaching and practical experience that is rare among authors of advanced engineering mathematics books. This edition offers a smaller, easier to read, and useful version of this classic textbook. While competing textbooks continue to grow, the book presents a slimmer, more concise option. Instructors and students alike are rejecting the encyclopedic tome with its higher and higher price aimed at undergraduates. To assist in the choice of topics included in this new edition, the author reviewed the syllabi of various engineering mathematics courses that are taught at a wide variety of schools. Due to time constraints an instructor can select perhaps three to four topics from the book, the most likely being ordinary differential equations, Laplace transforms, Fourier series and separation of variables to solve the wave, heat, or Laplace's equation. Laplace transforms are occasionally replaced by linear algebra or vector calculus. Sturm-Liouville problem and special functions (Legendre and Bessel functions) are included for completeness. Topics such as z-transforms and complex variables are now offered in a companion book, Advanced Engineering Mathematics: A Second Course by the same author. MATLAB is still employed to reinforce the concepts that are taught. Of course, this Edition continues to offer a wealth of examples and applications from the scientific and engineering literature, a highlight of previous editions. Worked solutions are given in the back of the book. |
| calculus with matlab: Programming Mathematics Using MATLAB Lisa A. Oberbroeckling, 2020-05-27 Providing an alternative to engineering-focused resources in the area, Programming Mathematics Using MATLAB® introduces the basics of programming and of using MATLAB® by highlighting many mathematical examples. Emphasizing mathematical concepts through the visualization of programming throughout the book, this useful resource utilizes examples that may be familiar to math students (such as numerical integration) and others that may be new (such as fractals). Additionally, the text uniquely offers a variety of MATLAB® projects, all of which have been class-tested thoroughly, and which enable students to put MATLAB® programming into practice while expanding their comprehension of concepts such as Taylor polynomials and the Gram-Schmidt process. Programming Mathematics Using MATLAB® is appropriate for readers familiar with sophomore-level mathematics (vectors, matrices, multivariable calculus), and is useful for math courses focused on MATLAB® specifically and those focused on mathematical concepts which seek to utilize MATLAB® in the classroom. |
| calculus with matlab: Mathematical Methods for Physics J. R. Claycomb, 2018-03-20 This book may be used by students and professionals in physics and engineering that have completed first-year calculus and physics. An introductory chapter reviews algebra, trigonometry, units and complex numbers that are frequently used in physics. Examples using MATLAB and Maple for symbolic and numerical calculations in physics with a variety of plotting features are included in all 16 chapters. The book applies many of mathematical concepts covered in Chapters 1-9 to fundamental physics topics in mechanics, electromagnetics; quantum mechanics and relativity in Chapters 10-16. Companion files are included with MATLAB and Maple worksheets and files, and all of the figures from the text. Features: • Each chapter includes the mathematical development of the concept with numerous examples • MATLAB & Maple examples are integrated in each chapter throughout the book • Applies the mathematical concepts to fundamental physics principles such as relativity, mechanics, electromagnetics, etc. • Introduces basic MATLAB and Maple commands and programming structures • Includes companion files with MATLAB and Maple files and worksheets, and all of the figures from the text |
| calculus with matlab: Fractional-Order Control Systems Dingyü Xue, 2017-07-10 This book explains the essentials of fractional calculus and demonstrates its application in control system modeling, analysis and design. It presents original research to find high-precision solutions to fractional-order differentiations and differential equations. Numerical algorithms and their implementations are proposed to analyze multivariable fractional-order control systems. Through high-quality MATLAB programs, it provides engineers and applied mathematicians with theoretical and numerical tools to design control systems. Contents Introduction to fractional calculus and fractional-order control Mathematical prerequisites Definitions and computation algorithms of fractional-order derivatives and Integrals Solutions of linear fractional-order differential equations Approximation of fractional-order operators Modelling and analysis of multivariable fractional-order transfer function Matrices State space modelling and analysis of linear fractional-order Systems Numerical solutions of nonlinear fractional-order differential Equations Design of fractional-order PID controllers Frequency domain controller design for multivariable fractional-order Systems Inverse Laplace transforms involving fractional and irrational Operations FOTF Toolbox functions and models Benchmark problems for the assessment of fractional-order differential equation algorithms |
| calculus with matlab: MATLAB® by Example Munther Gdeisat, Francis Lilley, 2012-12-31 MATLAB By Example guides the reader through each step of writing MATLAB programs. The book assumes no previous programming experience on the part of the reader, and uses multiple examples in clear language to introduce concepts and practical tools. Straightforward and detailed instructions allow beginners to learn and develop their MATLAB skills quickly. The book consists of ten chapters, discussing in detail the integrated development environment (IDE), scalars, vectors, arrays, adopting structured programming style using functions and recursive functions, control flow, debugging, profiling, and structures. A chapter also describes Symbolic Math Toolbox, teaching readers how to solve algebraic equations, differentiation, integration, differential equations, and Laplace and Fourier transforms. Containing hundreds of examples illustrated using screen shots, hundreds of exercises, and three projects, this book can be used to complement coursework or as a self-study book, and can be used as a textbook in universities, colleges and high schools. - No programming experience necessary to learn MATLAB - Examples with screenshots and plentiful exercises throughout help make MATLAB easy to understand - Projects enable readers to write long MATLAB programs, and take the first step toward being a professional MATLAB programmer |
| calculus with matlab: Numerical Computing with MATLAB Cleve B. Moler, 2010-08-12 A revised textbook for introductory courses in numerical methods, MATLAB and technical computing, which emphasises the use of mathematical software. |
| calculus with matlab: Differential Equations and Linear Algebra Gilbert Strang, 2015-02-12 Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor. |
| calculus with matlab: Multivariable Calculus with MATLAB® Ronald L. Lipsman, Jonathan M. Rosenberg, 2017-12-06 This comprehensive treatment of multivariable calculus focuses on the numerous tools that MATLAB® brings to the subject, as it presents introductions to geometry, mathematical physics, and kinematics. Covering simple calculations with MATLAB®, relevant plots, integration, and optimization, the numerous problem sets encourage practice with newly learned skills that cultivate the reader’s understanding of the material. Significant examples illustrate each topic, and fundamental physical applications such as Kepler’s Law, electromagnetism, fluid flow, and energy estimation are brought to prominent position. Perfect for use as a supplement to any standard multivariable calculus text, a “mathematical methods in physics or engineering” class, for independent study, or even as the class text in an “honors” multivariable calculus course, this textbook will appeal to mathematics, engineering, and physical science students. MATLAB® is tightly integrated into every portion of this book, and its graphical capabilities are used to present vibrant pictures of curves and surfaces. Readers benefit from the deep connections made between mathematics and science while learning more about the intrinsic geometry of curves and surfaces. With serious yet elementary explanation of various numerical algorithms, this textbook enlivens the teaching of multivariable calculus and mathematical methods courses for scientists and engineers. |
| calculus with matlab: Calculus Kevin M. O'Connor, O'Connor, 2005 Correlated directly to Calculus: The Language of Change, an engaging new text by David Cohen and James Henle, this outstanding lab manual provides numerous labs, projects, and exercises to teach students how to use MATLAB. Written in a friendly and accessible style, this is the ideal resource for students to practice what they've learned in the text. |
| calculus with matlab: Differential Equations with MATLAB Mark McKibben, Micah D. Webster, 2014-09-08 A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs). The text presents a unifying picture inherent to the study and analysis of more than 20 distinct models spanning disciplines such as physics, engineering, and finance. The first part of the book presents systems of linear ODEs. The text develops mathematical models from ten disparate fields, including pharmacokinetics, chemistry, classical mechanics, neural networks, physiology, and electrical circuits. Focusing on linear PDEs, the second part covers PDEs that arise in the mathematical modeling of phenomena in ten other areas, including heat conduction, wave propagation, fluid flow through fissured rocks, pattern formation, and financial mathematics. The authors engage students by posing questions of all types throughout, including verifying details, proving conjectures of actual results, analyzing broad strokes that occur within the development of the theory, and applying the theory to specific models. The authors’ accessible style encourages students to actively work through the material and answer these questions. In addition, the extensive use of MATLAB® GUIs allows students to discover patterns and make conjectures. |
| calculus with matlab: Applied Computational Modelling with MATLAB (Custom Edition) W & WILLIAM YUCHANG (G.), 2018-06-25 This custom edition is published for Central Queensland University. |
| calculus with matlab: Computational Partial Differential Equations Using MATLAB Jichun Li, Yi-Tung Chen, 2008-10-20 This textbook introduces several major numerical methods for solving various partial differential equations (PDEs) in science and engineering, including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques that include the classic finite difference method and the finite element method as well as state-of-the-art numerical |
| calculus with matlab: An Introduction to the Numerical Simulation of Stochastic Differential Equations Desmond J. Higham, Peter E. Kloeden, 2020-12 |
| calculus with matlab: Calculus with Matlab Frank G. Hagin, Jack K. Cohen, 1996 May be used in conjunction with any calculus text. Contains projects and syntax instruction. |
| calculus with matlab: A MatLab® Companion to Complex Variables A. David Wunsch, 2018-09-03 This book is intended for someone learning functions of a complex variable and who enjoys using MATLAB. It will enhance the exprience of learning complex variable theory and will strengthen the knowledge of someone already trained in ths branch of advanced calculus. ABET, the accrediting board for engineering programs, makes it clear that engineering graduates must be skilled in the art of programming in a language such as MATLAB®. Supplying students with a bridge between the functions of complex variable theory and MATLAB, this supplemental text enables instructors to easily add a MATLAB component to their complex variables courses. A MATLAB® Companion to Complex Variables provides readers with a clear understanding of the utility of MATLAB in complex variable calculus. An ideal adjunct to standard texts on the functions of complex variables, the book allows professors to quickly find and assign MATLAB programming problems that will strengthen students’ knowledge of the language and concepts of complex variable theory. The book shows students how MATLAB can be a powerful learning aid in such staples of complex variable theory as conformal mapping, infinite series, contour integration, and Laplace and Fourier transforms. In addition to MATLAB programming problems, the text includes many examples in each chapter along with MATLAB code. Fractals, the most recent interesting topic involving complex variables, demands to be treated with a language such as MATLAB. This book concludes with a Coda, which is devoted entirely to this visually intriguing subject. MATLAB is not without constraints, limitations, irritations, and quirks, and there are subtleties involved in performing the calculus of complex variable theory with this language. Without knowledge of these subtleties, engineers or scientists attempting to use MATLAB for solutions of practical problems in complex variable theory suffer the risk of making major mistakes. This book serves as an early warning system about these pitfalls. |
| calculus with matlab: Linear Programming with MATLAB Michael C. Ferris, Olvi L. Mangasarian, Stephen J. Wright, 2007-01-01 A self-contained introduction to linear programming using MATLAB® software to elucidate the development of algorithms and theory. Exercises are included in each chapter, and additional information is provided in two appendices and an accompanying Web site. Only a basic knowledge of linear algebra and calculus is required. |
| calculus with matlab: A Guide to MATLAB Brian R. Hunt, Ronald L. Lipsman, Jonathan M. Rosenberg, 2001-08-06 This book is a short, focused introduction to MATLAB and should be useful to both beginning and experienced users. |
| calculus with matlab: Introduction to GNU Octave Jason Lachniet, 2018-11-21 A brief introduction to scientific computing with GNU Octave. Designed as a textbook supplement for freshman and sophomore level linear algebra and calculus students. |
| calculus with matlab: Practical MATLAB Irfan Turk, 2019-10-29 Apply MATLAB programming to the mathematical modeling of real-life problems from a wide range of topics. This pragmatic book shows you how to solve your programming problems, starting with a brief primer on MATLAB and the fundamentals of the MATLAB programming language. Then, you’ll build fully working examples and computational models found in the financial, engineering, and scientific sectors. As part of this section, you’ll cover signal and image processing, as well as GUIs. After reading and using Practical MATLAB and its accompanying source code, you’ll have the practical know-how and code to apply to your own MATLAB programming projects. What You Will Learn Discover the fundamentals of MATLAB and how to get started with it for problem solving Apply MATLAB to a variety of problems and case studies Carry out economic and financial modeling with MATLAB, including option pricing and compound interest Use MATLAB for simulation problems such as coin flips, dice rolling, random walks, and traffic flows Solve computational biology problems with MATLAB Implement signal processing with MATLAB, including currents, Fast Fourier Transforms (FFTs), and harmonic analysis Process images with filters and edge detection Build applications with GUIs Who This Book Is For People with some prior experience with programming and MATLAB. |
| calculus with matlab: Learning MATLAB Tobin A. Driscoll, 2009-07-23 A handbook for MATLAB which gives a focused approach to the software for students and professional researchers. |
| calculus with matlab: The Mathematics of Derivatives Securities with Applications in MATLAB Mario Cerrato, 2012-02-24 Quantitative Finance is expanding rapidly. One of the aspects of the recent financial crisis is that, given the complexity of financial products, the demand for people with high numeracy skills is likely to grow and this means more recognition will be given to Quantitative Finance in existing and new course structures worldwide. Evidence has suggested that many holders of complex financial securities before the financial crisis did not have in-house experts or rely on a third-party in order to assess the risk exposure of their investments. Therefore, this experience shows the need for better understanding of risk associate with complex financial securities in the future. The Mathematics of Derivative Securities with Applications in MATLAB provides readers with an introduction to probability theory, stochastic calculus and stochastic processes, followed by discussion on the application of that knowledge to solve complex financial problems such as pricing and hedging exotic options, pricing American derivatives, pricing and hedging under stochastic volatility and an introduction to interest rates modelling. The book begins with an overview of MATLAB and the various components that will be used alongside it throughout the textbook. Following this, the first part of the book is an in depth introduction to Probability theory, Stochastic Processes and Ito Calculus and Ito Integral. This is essential to fully understand some of the mathematical concepts used in the following part of the book. The second part focuses on financial engineering and guides the reader through the fundamental theorem of asset pricing using the Black and Scholes Economy and Formula, Options Pricing through European and American style options, summaries of Exotic Options, Stochastic Volatility Models and Interest rate Modelling. Topics covered in this part are explained using MATLAB codes showing how the theoretical models are used practically. Authored from an academic’s perspective, the book discusses complex analytical issues and intricate financial instruments in a way that it is accessible to postgraduate students with or without a previous background in probability theory and finance. It is written to be the ideal primary reference book or a perfect companion to other related works. The book uses clear and detailed mathematical explanation accompanied by examples involving real case scenarios throughout and provides MATLAB codes for a variety of topics. |
| calculus with matlab: MATLAB Programming for Numerical Analysis Cesar Lopez, 2014-09-22 MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. Programming MATLAB for Numerical Analysis introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. You will first become familiar with the MATLAB environment, and then you will begin to harness the power of MATLAB. You will learn the MATLAB language, starting with an introduction to variables, and how to manipulate numbers, vectors, matrices, arrays and character strings. You will learn about MATLAB’s high-precision capabilities, and how you can use MATLAB to solve problems, making use of arithmetic, relational and logical operators in combination with the common functions and operations of real and complex analysis and linear algebra. You will learn to implement various numerical methods for optimization, interpolation and solving non-linear equations. You will discover how MATLAB can solve problems in differential and integral calculus, both numerically and symbolically, including techniques for solving ordinary and partial differential equations, and how to graph the solutions in brilliant high resolution. You will then expand your knowledge of the MATLAB language by learning how to use commands which enable you to investigate the convergence of sequences and series, and explore continuity and other analytical features of functions in one and several variables. |
| calculus with matlab: Special Functions in Physics with MATLAB Wolfgang Schweizer, 2021-02-18 This handbook focuses on special functions in physics in the real and complex domain. It covers more than 170 different functions with additional numerical hints for efficient computation, which are useful to anyone who needs to program with other programming languages as well. The book comes with MATLAB-based programs for each of these functions and a detailed html-based documentation. Some of the explained functions are: Gamma and Beta functions; Legendre functions, which are linked to quantum mechanics and electrodynamics; Bessel functions; hypergeometric functions, which play an important role in mathematical physics; orthogonal polynomials, which are largely used in computational physics; and Riemann zeta functions, which play an important role, e.g., in quantum chaos or string theory. The book’s primary audience are scientists, professionals working in research areas of industries, and advanced students in physics, applied mathematics, and engineering. |
| calculus with matlab: Solving Optimization Problems with MATLAB® Dingyü Xue, 2020-04-06 This book focuses on solving optimization problems with MATLAB. Descriptions and solutions of nonlinear equations of any form are studied first. Focuses are made on the solutions of various types of optimization problems, including unconstrained and constrained optimizations, mixed integer, multiobjective and dynamic programming problems. Comparative studies and conclusions on intelligent global solvers are also provided. |
| calculus with matlab: A Matlab Companion for Multivariable Calculus Jeffery Cooper, 2001-01-24 Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, A MatLab Companion for Multivariable Calculus introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton's method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http://www.harcourt-ap.com/matlab.html. - Computer-oriented material that complements the essential topics in multivariable calculus - Main ideas presented with examples of computations and graphics displays using MATLAB - Numerous examples of short code in the text, which can be modified for use with the exercises - MATLAB files are used to implement graphics displays and contain a collection of mfiles which can serve as demos |
| calculus with matlab: MATLAB Demystified David McMahon, 2007-04-30 Need to Learn MATLAB? Problem SOLVED! Get started using MATLAB right away with help from this hands-on guide. MATLAB Demystified offers an effective and enlightening method for learning how to get the most out this powerful computational mathematics tool. Using an easy-to-follow format, this book explains the basics of MATLAB up front. You'll find out how to plot functions, solve algebraic equations, and compute integrals. You'll also learn how to solve differential equations, generate numerical solutions of ODEs, and work with special functions. Packed with hundreds of sample equations and explained solutions, and featuring end-of-chapter quizzes and a final exam, this book will teach you MATLAB essentials in no time at all. This self-teaching guide offers: The quickest way to get up and running on MATLAB Hundreds of worked examples with solutions Coverage of MATLAB 7 A quiz at the end of each chapter to reinforce learning and pinpoint weaknesses A final exam at the end of the book A time-saving approach to performing better on homework or on the job Simple enough for a beginner, but challenging enough for an advanced user, MATLAB Demystified is your shortcut to computational precision. |
| calculus with matlab: MATLAB for Beginners: A Gentle Approach Peter Kattan, 2008-07-01 This book is written for beginners and students who wish to learn MATLAB. One of the objectives of writing this book is to introduce MATLAB to students in high schools.The material presented is very easy and simple to understand - written in a gentle manner. The topics covered in the book include arithmetic operations, variables, mathematical functions, complex numbers, vectors, matrices, programming, graphs, solving equations, and an introduction to calculus. In addition, the MATLAB Symbolic Math Toolbox is emphasized in this book. There are also over 230 exercises at the ends of chapters for students to practice. Detailed solutions to all the exercises are provided in the second half of the book. The author has been using MATLAB for the past fifteen years and is the author of the best selling book MATLAB Guide to Finite Elements. For the paperback edition, visit Amazon.com. |
| calculus with matlab: An Introduction to Matlab and Mathcad Troy Siemers, 2014 This textbook provides an introduction to programming and problem solving using both Matlab and Mathcad. We provide a balanced selection of introductory exercises and real-world problems (i.e. no “contrived” problems). We include many examples and screenshots to guide the reader. We assume no prior knowledge of Matlab or Mathcad.--Publisher's description. |
| calculus with matlab: Programming for Computations - MATLAB/Octave Svein Linge, Hans Petter Langtangen, 2016-07-28 This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification. |
Calculus Volume 3 - OpenStax
Study calculus online free by downloading Volume 3 of OpenStax's college Calculus textbook and using our accompanying online resources.
Calculus Volume 1 - OpenStax
Study calculus online free by downloading volume 1 of OpenStax's college Calculus textbook and using our accompanying online resources.
Ch. 1 Introduction - Calculus Volume 1 | OpenStax
In this chapter, we review all the functions necessary to study calculus. We define polynomial, rational, trigonometric, exponential, and logarithmic functions.
1.1 Review of Functions - Calculus Volume 1 | OpenStax
This free textbook is an OpenStax resource written to increase student access to high-quality, peer-reviewed learning materials.
Ch. 5 Introduction - Calculus Volume 1 | OpenStax
In this chapter, we first introduce the theory behind integration and use integrals to calculate areas. From there, we develop the Fundamental Theorem of Calculus, which relates …
Preface - Calculus Volume 1 | OpenStax
OpenStax is a nonprofit based at Rice University, and it’s our mission to improve student access to education. Our first openly licensed college textboo...
OpenStax
OpenStax
5.2 The Definite Integral - Calculus Volume 1 | OpenStax
The definite integral generalizes the concept of the area under a curve. We lift the requirements that ... be continuous and nonnegative, and define the...
Index - Calculus Volume 1 | OpenStax
This free textbook is an OpenStax resource written to increase student access to high-quality, peer-reviewed learning materials.
Precalculus 2e - OpenStax
Study precalculus online free by downloading OpenStax's Precalculus 2e textbook and using our accompanying online resources including a precalculus study guide.
Calculus Volume 3 - OpenStax
Study calculus online free by downloading Volume 3 of OpenStax's college Calculus textbook and using our accompanying online resources.
Calculus Volume 1 - OpenStax
Study calculus online free by downloading volume 1 of OpenStax's college Calculus textbook and using our accompanying online resources.
Ch. 1 Introduction - Calculus Volume 1 | OpenStax
In this chapter, we review all the functions necessary to study calculus. We define polynomial, rational, trigonometric, exponential, and logarithmic functions.
1.1 Review of Functions - Calculus Volume 1 | OpenStax
This free textbook is an OpenStax resource written to increase student access to high-quality, peer-reviewed learning materials.
Ch. 5 Introduction - Calculus Volume 1 | OpenStax
In this chapter, we first introduce the theory behind integration and use integrals to calculate areas. From there, we develop the Fundamental Theorem of Calculus, which relates …
Preface - Calculus Volume 1 | OpenStax
OpenStax is a nonprofit based at Rice University, and it’s our mission to improve student access to education. Our first openly licensed college textboo...
OpenStax
OpenStax
5.2 The Definite Integral - Calculus Volume 1 | OpenStax
The definite integral generalizes the concept of the area under a curve. We lift the requirements that ... be continuous and nonnegative, and define the...
Index - Calculus Volume 1 | OpenStax
This free textbook is an OpenStax resource written to increase student access to high-quality, peer-reviewed learning materials.
Precalculus 2e - OpenStax
Study precalculus online free by downloading OpenStax's Precalculus 2e textbook and using our accompanying online resources including a precalculus study guide.
