Scientific Computing with MATLAB

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.

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 IndexIndex Exercises and Bibliography appear at the end of each chapter.

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.