Scientific Computing with MATLAB

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.

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
Index





Exercises and Bibliography appear at the end of each chapter.