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.

The presentation of this book is on the comprehensible application of techniques for the approximation of the mathematical problems that are frequently observed in physical sciences, engineering technology and mathematical physics. The acceptance of the technique for the solution has been justified from mathematical point of view. The Software required for the approximate solution of the problems applying the appropriate Methods, numerically developed is the set of programs written in C++ (Turbo).

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.