Scientific Computing with MATLAB  book cover
2nd Edition

Scientific Computing with MATLAB

ISBN 9781498757775
Published March 1, 2016 by Chapman and Hall/CRC
604 Pages 259 B/W Illustrations

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Book Description

Scientific Computing with MATLAB®, Second Edition improves students’ ability to tackle mathematical problems. It helps students understand the mathematical background and find reliable and accurate solutions to mathematical problems with the use of MATLAB, avoiding the tedious and complex technical details of mathematics. This edition retains the structure of its predecessor while expanding and updating the content of each chapter.

The book bridges the gap between problems and solutions through well-grouped topics and clear MATLAB example scripts and reproducible MATLAB-generated plots. Students can effortlessly experiment with the scripts for a deep, hands-on exploration. Each chapter also includes a set of problems to strengthen understanding of the material.

Table of Contents

Computer Mathematics Languages — An Overview
Computer Solutions to Mathematics Problems
Summary of Computer Mathematics Languages
Outline of the Book

Fundamentals of MATLAB Programming and Scientific Visualization
Essentials in MATLAB Programming
Fundamental Mathematical Calculations
Flow Control Structures of MATLAB Language
Writing and Debugging MATLAB Functions
Two-Dimensional Graphics
Three-Dimensional Graphics
Four-Dimensional Visualization

Calculus Problems
Analytical Solutions to Limit Problems
Analytical Solutions to Derivative Problems
Analytical Solutions to Integral Problems
Series Expansions and Finite-Term Series Approximations
Infinite Series and Products
Path Integrals and Line Integrals
Surface Integrals
Numerical Differentiation
Numerical Integration Problems

Linear Algebra Problems
Inputting Special Matrices
Fundamental Matrix Operations
Fundamental Matrix Transformations
Solving Matrix Equations
Nonlinear Functions and Matrix Function Evaluations

Integral Transforms and Complex-Valued Functions
Laplace Transforms and Their Inverses
Fourier Transforms and Their Inverses
Other Integral Transforms
z Transforms and Their Inverses
Essentials of Complex-Valued Functions
Solving Complex-Valued Function Problems
Solutions of Difference Equations

Nonlinear Equations and Numerical Optimization Problems
Nonlinear Algebraic Equations
Nonlinear Equations with Multiple Solutions
Unconstrained Optimization Problems
Constrained Optimization Problems
Mixed Integer Programming Problems
Linear Matrix Inequalities
Solutions of Multi-Objective Programming Problems
Dynamic Programming and Shortest Path Planning

Differential Equation Problems
Analytical Solution Methods for Some Ordinary Differential Equations
Numerical Solutions to Ordinary Differential Equations
Transforms to Standard Differential Equations
Solutions to Special Ordinary Differential Equations
Solutions to Delay Differential Equations
Solving Boundary Value Problems
Introduction to Partial Differential Equations
Solving ODEs with Block Diagrams in Simulink

Data Interpolation and Functional Approximation Problems
Interpolation and Data Fitting
Spline Interpolation and Numerical Calculus
Fitting Mathematical Models from Data
Rational Function Approximations
Special Functions and Their Plots
Signal Analysis and Digital Signal Processing

Probability and Mathematical Statistics Problems
Probability Distributions and Pseudorandom Numbers
Solving Probability Problems
Fundamental Statistical Analysis
Statistical Estimations
Statistical Hypothesis Tests
Analysis of Variance
Principal Component Analysis

Topics on Nontraditional Mathematical Branches
Fuzzy Logic and Fuzzy Inference
Rough Set Theory and Its Applications
Neural Network and Applications in Data Fitting Problems
Evolutionary Computing and Global Optimization Problem Solutions
Wavelet Transform and Its Applications in Data Processing
Fractional-Order Calculus

MATLAB Functions Index

Exercises and Bibliography appear at the end of each chapter.

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Dingyü Xue is a professor of control engineering in the College of Information Science and Engineering at Northeastern University in China. Dr. Xue is the author or coauthor of many books on MATLAB®-based control, simulation, and mathematical problem solutions, including Computer Aided Control Systems Design with MATLAB, Solving Advanced Applied Mathematical Problems Using MATLAB, and System Simulation Techniques with MATLAB and Simulink. His current research interests include CAD of control systems, system simulation, and fractional order control. He earned his D.Phil. from Sussex University.

YangQuan Chen is the director and founder of the Mechatronics, Embedded Systems and Automation (MESA) Lab in the School of Engineering at the University of California, Merced. He is the topic editor-in-chief of field robotics for the International Journal of Advanced Robotic Systems, a founding editorial board member of Unmanned Systems, and an editorial board member of several other leading journals. Dr. Chen is also the author or coauthor of many books, including Distributed-Order Dynamic Systems: Stability, Simulation, Applications and Perspectives, Fractional Order Motion Controls, Remote Sensing and Actuation Using Unmanned Vehicles, System Simulation Techniques with MATLAB and Simulink, and Modeling, Analysis and Design of Control Systems in MATLAB and Simulink. His research interests include unmanned aerial systems and UAV-based personal remote sensing, cyber-physical systems, the modeling and control of renewable energy systems, mechatronics, and applied fractional calculus. He earned his Ph.D. from Nanyang Technological University.


Praise for the First Edition:
"… this volume has many interesting cases to illustrate the power of MATLAB."
Bulletin of the Belgian Mathematical Society, Volume 20, 2013

"The reader’s ability to tackle mathematical problems can be significantly enhanced after reading this book. … This book can be used as a reference text for almost all college students, both undergraduates and graduates, in almost all disciplines that require certain levels of applied mathematics. This book will be a good desktop reference for many who have graduated from college and are still involved in solving mathematical problems in their jobs. A lot of MATLAB function designed by the authors and some third-party free toolboxes are also presented in the book."
Zentralblatt MATH, 1156

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