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. 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. 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. l 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. 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.