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Advanced Engineering Mathematics / Edition 10

Advanced Engineering Mathematics / Edition 10

by Erwin Kreyszig


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Advanced Engineering Mathematics / Edition 10

The content and character of mathematics needed in applications are changing rapidly. Introduces students of engineering, physics, mathematics and computer science to those areas that are vital to address practical problems. The Seventh Edition offers a self-contained treatment of ordinary differential equations, linear algebra, vector calculus, fourier analysis and partial differential equations, complex analysis, numerical methods, optimization and graphs, probability and statistics. New in this edition are: many sections rewritten to increase readability; problems have been revised and more closely related to examples; instructors manual quadrupled in content; improved balance between applications, algorithmic ideas and theory; reorganized differential equations and linear algebra sections; added and improved examples throughout.

Product Details

ISBN-13: 9780470458365
Publisher: Wiley
Publication date: 12/08/2010
Pages: 1280
Sales rank: 402,988
Product dimensions: 8.40(w) x 10.10(h) x 1.90(d)

Table of Contents

Introduction, General Commands1
Part A.Ordinary Differential Equations (ODE's)6
Chapter 1First-Order ODE's7
Ex. 1.1General Solutions7
Ex. 1.2Direction Fields8
Ex. 1.3Mixing Problems10
Ex. 1.4Integrating Factors11
Ex. 1.5Bernoulli's Equation12
Ex. 1.6RL-Circuit13
Problems for Chapter 114
Chapter 2Linear ODE's of Second and Higher Order17
Ex. 2.1General Solution. Initial Value Problem17
Ex. 2.2Mass-Spring System. Complex Roots. Damped Oscillations19
Ex. 2.3The Three Cases of Damping19
Ex. 2.4The Three Cases for an Euler-Cauchy Equation21
Ex. 2.5Wronskian22
Ex. 2.6Nonhomogeneous Linear ODE's23
Ex. 2.7Solution by Undetermined Coefficients24
Ex. 2.8Solution by Variation of Parameters25
Ex. 2.9Forced Vibrations. Resonance. Beats26
Ex. 2.10RLC-Circuit27
Problems for Chapter 228
Chapter 3Systems of Differential Equations. Phase Plane, Qualitative Methods31
Ex. 3.1Solving a System of ODE's by DSolve. Initial Value Problem31
Ex. 3.2Use of Matrices in Solving Systems of ODE's33
Ex. 3.3Critical Points. Node34
Ex. 3.4Proper Node, Saddle Point, Center, Spiral Point36
Ex. 3.5Pendulum Equation37
Ex. 3.6Nonhomogeneous System38
Ex. 3.7Method of Undetermined Coefficients39
Problems for Chapter 340
Chapter 4Series Solutions of Differential Equations42
Ex. 4.1Power Series Solutions. Plots from Them. Numerical Values43
Ex. 4.2Legendre Polynomials44
Ex. 4.3Legendre's Differential Equation45
Ex. 4.4Orthogonality. Fourier-Legendre Series47
Ex. 4.5Frobenius Method48
Ex. 4.6Bessel's Equation. Bessel Functions50
Problems for Chapter 452
Chapter 5Laplace Transform Method for Solving ODE's55
Ex. 5.1Transforms and Inverse Transforms55
Ex. 5.2Differential Equations56
Ex. 5.3Forced Vibrations. Resonance58
Ex. 5.4Unit Step Function (Heaviside Function), Dirac's Delta59
Ex. 5.5Solution of Systems by Laplace Transform61
Ex. 5.6Formulas on General Properties of the Laplace Transform62
Problems for Chapter 564
Part B.Linear Algebra, Vector Calculus66
Chapter 6Matrices, Vectors, Determinants. Linear Systems of Equations66
Ex. 6.1Matrix Addition, Scalar Multiplication, Matrix Multiplication. Vectors66
Ex. 6.2Special Matrices69
Ex. 6.3Changing and Composing Matrices, Accessing Entries. Submatrices70
Ex. 6.4Solution of a Linear System73
Ex. 6.5Linear Systems: A Further Case74
Ex. 6.6Gauss Elimination; Back Substitution75
Problems for Chapter 677
Chapter 7Matrix Eigenvalue Problems79
Ex. 7.1Eigenvalues, Eigenvectors, Accessing Spectrum79
Ex. 7.2Real Matrices with Complex Eigenvalues81
Ex. 7.3Orthogonal Matrices and Transformations81
Ex. 7.4Complex Matrices83
Ex. 7.5Similarity of Matrices. Diagonalization84
Problems for Chapter 786
Chapter 8Vectors in R[superscript 2] and R[superscript 3]. Dot and Cross Products. Grad, Div, Curl88
Ex. 8.1Vectors, Addition, Scalar Multiplication89
Ex. 8.2Inner Product. Cross Product89
Ex. 8.3Differentiation of Vectors. Curves and their Properties91
Ex. 8.4Gradient. Directional Derivative. Potential92
Ex. 8.5Divergence, Laplacian, Curl94
Problems for Chapter 895
Chapter 9Vector Integral Calculus. Integral Theorems98
Ex. 9.1Line Integrals98
Ex. 9.2Independence of Path99
Ex. 9.3Double Integrals. Moments of Inertia100
Ex. 9.4Green's Theorem in the Plane101
Ex. 9.5Surface Integrals. Flux103
Ex. 9.6Divergence Theorem of Gauss104
Ex. 9.7Stokes's Theorem106
Problems for Chapter 9107
Part C.Fourier Analysis and Partial Differential Equations110
Chapter 10Fourier Series, Integrals, and Transforms110
Ex. 10.1Functions of Period 2[pi]. Even Functions. Gibbs Phenomenon111
Ex. 10.2Functions of Arbitrary Period. Odd Functions112
Ex. 10.3Half-Range Expansions114
Ex. 10.4Rectifier117
Ex. 10.5Trigonometric Approximation. Minimum Square Error117
Ex. 10.6Fourier Integral, Fourier Transform118
Problems for Chapter 10119
Chapter 11Partial Differential Equations (PDE's)122
Ex. 11.1Wave Equation. Separation of Variables. Animation122
Ex. 11.2One-Dimensional Heat Equation124
Ex. 11.3Heat Equation, Laplace Equation125
Ex. 11.4Rectangular Membrane. Double Fourier Series127
Ex. 11.5Laplacian. Circular Membrane. Bessel Equation128
Problems for Chapter 11131
Part D.Complex Analysis133
Chapter 12Complex Numbers and Functions. Conformal Mapping133
Ex. 12.1Complex Numbers. Polar Form. Plotting133
Ex. 12.2Equations. Roots. Sets in the Complex Plane136
Ex. 12.3Cauchy-Riemann Equations. Harmonic Functions138
Ex. 12.4Conformal Mapping140
Ex. 12.5Exponential, Trigonometric, and Hyperbolic Functions143
Ex. 12.6Complex Logarithm145
Problems for Chapter 12147
Chapter 13Complex Integration149
Ex. 13.1Indefinite Integration of Analytic Functions149
Ex. 13.2Integration: Use of Path. Path Dependence149
Ex. 13.3Contour Integration by Cauchy's Integral Theorem and Formula151
Problems for Chapter 13153
Chapter 14Power Series, Taylor Series154
Ex. 14.1Sequences and their Plots154
Ex. 14.2Convergence Tests for Complex Series155
Ex. 14.3Power Series. Radius of Convergence156
Ex. 14.4Taylor Series156
Ex. 14.5Uniform Convergence158
Problems for Chapter 14160
Chapter 15Laurent Series. Residue Integration162
Ex. 15.1Laurent Series162
Ex. 15.2Singularities and Zeros163
Ex. 15.3Residue Integration164
Ex. 15.4Real Integrals of Rational Functions of cos and sin166
Ex. 15.5Improper Real Integrals of Rational Functions167
Problems for Chapter 15169
Chapter 16Complex Analysis in Potential Theory171
Ex. 16.1Complex Potential. Related Plots171
Ex. 16.2Use of Conformal Mapping172
Ex. 16.3Fluid Flow173
Ex. 16.4Series Representation of Potential175
Ex. 16.5Mean Value Theorem for Analytic Functions176
Problems for Chapter 16177
Part E.Numerical Methods179
Chapter 17Numerical Methods in General179
Ex. 17.1Loss of Significant Digits. Quadratic Equation179
Ex. 17.2Fixed-Point Iteration180
Ex. 17.3Solving Equations by Newton's Method182
Ex. 17.4Solving Equations by the Secant Method183
Ex. 17.5Solving Equations by the Bisection Method. Module183
Ex. 17.6Polynomial Interpolation185
Ex. 17.7Spline Interpolation186
Ex. 17.8Numerical Integration188
Problems for Chapter 17189
Chapter 18Numerical Linear Algebra191
Ex. 18.1Gauss Elimination. Pivoting191
Ex. 18.2Doolittle LU-Factorization193
Ex. 18.3Cholesky Factorization195
Ex. 18.4Gauss-Jordan Elimination. Matrix Inversion196
Ex. 18.5Gauss-Seidel Iteration for Linear Systems198
Ex. 18.6Vector and Matrix Norms. Condition Numbers199
Ex. 18.7Fitting Data by Least Squares202
Ex. 18.8Approximation of Eigenvalues: Collatz Method203
Ex. 18.9Approximation of Eigenvalues: Power Method204
Ex. 18.10Approximation of Eigenvalues: QR-Factorization205
Problems for Chapter 18210
Chapter 19Numerical Methods for Differential Equations213
Ex. 19.1Euler Method213
Ex. 19.2Improved Euler Method214
Ex. 19.3Classical Runge-Kutta Method (RK). Module215
Ex. 19.4Adams-Moulton Multistep Method217
Ex. 19.5Classical Runge-Kutta Method for Systems (RKS)219
Ex. 19.6Classical Runge-Kutta-Nystroem Method (RKN)220
Ex. 19.7Laplace Equation. Boundary Value Problem221
Ex. 19.8Heat Equation. Crank-Nicolson Method225
Problems for Chapter 19228
Part F.Optimization, Graphs230
Chapter 20Unconstrained Optimization. Linear Programming230
Ex. 20.1Method of Steepest Descent230
Ex. 20.2Simplex Method of Constrained Optimization232
Problems for Chapter 20234
Chapter 21No examples, no problems
Part G.Probability and Statistics235
Chapter 22Data Analysis. Probability Theory235
Ex. 22.1Data Analysis: Mean, Variance, Standard Deviation235
Ex. 22.2Data Analysis: Histograms236
Ex. 22.3Discrete Probability Distributions237
Ex. 22.4Normal Distribution241
Problems for Chapter 22243
Chapter 23Mathematical Statistics245
Ex. 23.1Random Numbers245
Ex. 23.2Confidence Interval for the Mean of the Normal Distribution With Known Variance246
Ex. 23.3Confidence Interval for the Mean of the Normal Distribution With Unknown Variance. t-Distribution247
Ex. 23.4Confidence Interval for the Variance of the Normal Distribution. x[superscript 2]-Distribution248
Ex. 23.5Test for the Mean of the Normal Distribution249
Ex. 23.6Test for the Mean: Power Function249
Ex. 23.7Test for the Variance of the Normal Distribution251
Ex. 23.8Comparison of Means252
Ex. 23.9Comparison of Variances. F-Distribution253
Ex. 23.10Chi-Square Test for Goodness of Fit253
Ex. 23.11Regression254
Problems for Chapter 23256
Appendix 1ReferencesA1
Appendix 2Answers to Odd-Numbered ProblemsA2

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