دانلود کتاب Advanced Engineering Mathematics with MATLAB (Advances in Applied Mathematics)

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Cover Half Title Title Page Copyright Page Dedication Table of Contents Acknowledgments Author Introduction List of Definitions Chapter 1: First-Order Ordinary Differential Equations 1.1 Classification of Differential Equations 1.2 Separation of Variables 1.3 Homogeneous Equations 1.4 Exact Equations 1.5 Linear Equations 1.6 Graphical Solutions 1.7 Numerical Methods Chapter 2: Higher-Order Ordinary Differential Equations 2.1 Homogeneous Linear Equations with Constant Coefficients 2.2 Simple Harmonic Motion 2.3 Damped Harmonic Motion 2.4 Method of Undetermined Coefficients 2.5 Forced Harmonic Motion 2.6 Variation of Parameters 2.7 Euler-Cauchy Equation 2.8 Phase Diagrams 2.9 Numerical Methods Chapter 3: Linear Algebra 3.1 Fundamentals 3.2 Determinants 3.3 Cramer’s Rule 3.4 Row Echelon Form and Gaussian Elimination 3.5 Eigenvalues and Eigenvectors 3.6 Systems of Linear Differential Equations 3.7 Matrix Exponential Chapter 4: Vector Calculus 4.1 Review 4.2 Divergence and Curl 4.3 Line Integrals 4.4 The Potential Function 4.5 Surface Integrals 4.6 Green’s Lemma 4.7 Stokes’ Theorem 4.8 Divergence Theorem Chapter 5: Fourier Series 5.1 Fourier Series 5.2 Properties of Fourier Series 5.3 Half-Range Expansions 5.4 Fourier Series with Phase Angles 5.5 Complex Fourier Series 5.6 The Use of Fourier Series in the Solution of Ordinary Differential Equations 5.7 Finite Fourier Series Chapter 6: The Fourier Transform 6.1 Fourier Transforms 6.2 Fourier Transforms Containing the Delta Function 6.3 Properties of Fourier Transforms 6.4 Inversion of Fourier Transforms 6.5 Convolution 6.6 The Solution of Ordinary Differential Equations by Fourier Transforms 6.7 The Solution of Laplace’s Equation on the Upper Half-Plane 6.8 The Solution of the Heat Equation Chapter 7: The Laplace Transform 7.1 Definition and Elementary Properties 7.2 The Heaviside Step and Dirac Delta Functions 7.3 Some Useful Theorems 7.4 The Laplace Transform of a Periodic Function 7.5 Inversion by Partial Fractions: Heaviside’s Expansion Theorem 7.6 Convolution 7.7 Solution of Linear Differential Equations with Constant Coefficients Chapter 8: The Wave Equation 8.1 The Vibrating String 8.2 Initial Conditions: Cauchy Problem 8.3 Separation of Variables 8.4 D’Alembert’s Formula 8.5 Numerical Solution of the Wave Equation Chapter 9: The Heat Equation 9.1 Derivation of the Heat Equation 9.2 Initial and Boundary Conditions 9.3 Separation of Variables 9.4 The Superposition Integral 9.5 Numerical Solution of the Heat Equation Chapter 10: Laplace’s Equation 10.1 Derivation of Laplace’s Equation 10.2 Boundary Conditions 10.3 Separation of Variables 10.4 Poisson’s Equation on a Rectangle 10.5 Numerical Solution of Laplace’s Equation Chapter 11: The Sturm-Liouville Problem 11.1 Eigenvalues and Eigenfunctions 11.2 Orthogonality of Eigenfunctions 11.3 Expansion in Series of Eigenfunctions 11.4 Finite Element Method Chapter 12: Special Functions 12.1 Legendre Polynomials 12.2 Bessel Functions 12.A Appendix A: Derivation of the Laplacian in Polar Coordinates 12.B Appendix B: Derivation of the Laplacian in Spherical Polar Coordinates Answers to the Odd-Numbered Problems Index