Scientific Computing with MATLAB

ISBN-13: 9781498757775 / Angielski / Twarda / 2016 / 586 str.

Dingyu Xue; YangQuan Chen

Opis

Enhance Your Students Mathematical Problem-Solving Ability

Scientific Computing with MATLAB(r), 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 Solving Applied Mathematical Problems with MATLAB(r) while expanding and updating the content of each chapter.

Based on the authors extensive teaching, research, and industrial experiences, the text adheres to the following course sequence:

• An overview of the computer languages suitable for mathematics
• Fundamentals of MATLAB programming
• Calculus problems
• Linear algebra problems
• Integral transforms and complex variable functions
• Nonlinear equations and optimization problems
• Differential equations problems
• Data interpolation and functional approximation problems
• Probability and statistics problems
• Nontraditional methods, such as fuzzy logic, rough sets, neural networks, evolution algorithms, wavelets, and fractional calculus

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."

Spis treści

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.