C++ Solutions for Mathematical Problems

Description

Cover Preface Contents Chapter 1 Preliminary Mathematical Viewpoints 1.1 Environment Numerically Developed 1.2 Error Spread 1.2.1 Error Reduction Chapter 2 Computing Surface Areas 2.1 Evaluation of the Definite Integral 2.2 Areas of Curves 2.3 Surfaces in 2-Dimensional Space 2.4 Related Software for the Solution Chapter 3 Systems of Simultaneous Equations 3.1 Preliminary Concepts 3.2 Matrix Relationship 3.2.1 Matrix Product 3.2.2 Nonsingular Matrix: Inverse Matrix 3.2.3 Matrix Transposition 3.3 Systems of Linear Equations 3.3.1 Gauss Elimination 3.3.2 Cramer’s Rule 3.3.3 Matrix Inversion 3.3.4 LU-Decomposition 3.4 Related Software for the Solution Chapter 4 First Order Initial-Value Problems 4.1 Preliminary Concepts 4.2 Methods for Solution 4.3 Exact Equations 4.4 Linear Equations 4.5 Bernoulli’s Equation 4.6 Riccati Equation 4.7 System of Simultaneous Differential Equations 4.8 Related Software for the Solution Chapter 5 Second Order Initial-Value Problems 5.1 Preliminary Concepts 5.2 Linear Homogeneous Type 5.3 Linear Nonhomogeneous Type 5.3.1 Method of Undetermined Coefficients 5.3.2 Euler’s Equation 5.3.3 Method of Variation of Parameters 5.4 Nonlinear Equations 5.5 Related Software for the Solution Chapter 6 Computing Operational Series 6.1 Analytic Numerical Series 6.1.1 Infinite Series. Convergence and Divergence 6.1.2 Comparison Test. Condition for Convergence 6.1.3 D’Alembert Test (Test-Ratio Test) 6.2 Power Series Solution 6.2.1 Introduction 6.2.2 Series Expansion 6.2.3 First Order Equations 6.2.4 Second Order Equations 6.3 Fourier Series Solution 6.3.1 Fourier Coefficients 6.3.2 Dirichlet’s Principles 6.3.3 Even and Odd Functions 6.3.4 Any Arbitrary Interval [–1, 1] 6.4 Related Software for the Solution Chapter 7 Boundary-Value Problems for Ordinary Differential Equations 7.1 Introduction 7.2 Linear Boundary Value Problems 7.3 Nonlinear Equations 7.4 Related Software for the Solution Chapter 8 Partial Differential Equations 8.1 Introduction 8.2 Wave Equation 8.3 Heat Equation 8.4 Laplace Equation 8.5 Poisson Equation 8.6 Related Software for the Solution Chapter 9 Laplace Transforms 9.1 Introduction 9.2 Laplace Transforms of Functions 9.3 Evaluation of Derivatives and Integrals 9.4 Inverse Laplace Transforms 9.5 Convolutions 9.6 Application to Differential Equations Chapter 10 Problems to be Worked Out Chapter 11 A Short Review on C++ 11.1 Basic Structure of a C++ Program 11.2 The Keywords from C++ 11.3 Identifiers in C++ 11.4 The Features of C++ 11.5 Loop Statements 11.6 The For Loop 11.7 Pointers Appendix I Mathematical Relations Appendix II Using the Program Disc (CPPSOLMP) References