Advanced Engineering Mathematics, 10e Student Solutions Manual and Study Guide, Volume 2: Chapters 13 - 25

Erwin O. Kreyszig was a German Canadian applied mathematician and the Professor of Mathematics at Carleton University in Ottawa, Ontario, Canada. He was a pioneer in the field of applied mathematics: non-wave replicating linear systems.

• PART D: COMPLEX ANALYSIS…257Chapter 13. Numbers and Functions. Complex Differentiation…25713.1 Complex Numbers and Their Geometric Representation…25813.2 Polar Form of Complex Numbers. Powers and Roots…26113.3 Derivative. Analytic Function…26713.4 Cauchy–Riemann Equations. Laplace’s Equation…26913.5 Exponential Function…27413.6 Trigonometric and Hyperbolic Functions. Euler’s Formula…27713.7 Logarithm. General Power. Principal Value…279Chapter 14: Complex Integration…28314.1 Line Integral in the Complex Plane…28314.2 Cauchy’s Integral Theorem…28814.3 Cauchy’s Integral Formula…29114.4 Derivatives of Analytic Functions…295Chapter 15: Power Series, Taylor Series…29815.1 Sequences, Series, Convergence Tests…29815.2 Power Series…30315.3 Functions Given by Power Series…30615.4 Taylor and Maclaurin Series…30915.5 Uniform Convergence. Optional…312Chapter 16: Laurent Series. Residue Integration…31616.1 Laurent Series…31616.2 Singularities and Zeros. Infinity…32016.3 Residue Integration Method…32216.4 Residue Integration of Real Integrals…326Chapter 17: Conformal Mapping…33217.1 Geometry of Analytic Functions: Conformal Mapping…33317.2 Linear Fractional Transformations. (Möbius Transformations)…33917.3 Special Linear Fractional Transformations…34317.4 Conformal Mapping by Other Functions…34717.5 Riemann Surfaces. Optional…352Chapter 18: Complex Analysis and Potential Theory…35318.1 Electrostatic Fields…35418.2 Use of Conformal Mapping. Modeling…35818.3 Heat Problems…35918.4 Fluid Flow…36118.5 Poisson’s Integral Formula for Potentials…36418.6 General Properties of Harmonic Functions. Uniqueness Theorem for the Dirchlet Problem…367PART E: NUMERIC ANALYSIS…373Chapter 19: Numerics in General…37319.1 Introduction…37419.2 Solution of Equations by Iteration…37919.3 Interpolation…38419.4 Spline Interpolation…38919.5 Numeric Integration and Differentiation…393Chapter 20: Numeric Linear Algebra…40020.1 Linear Systems: Gauss Elimination…40020.2 Linear Systems: LU-Factorization, Matrix Inversion…40420.3 Linear Systems: Solution by Iteration…41020.4 Linear Systems: Ill-Conditioning, Norms…41520.5 Least Squares Method…41920.6 Matrix Eigenvalue Problems: Introduction…42420.7 Inclusion of Matrix Eigenvalues…42420.8 Power Method for Eigenvalues…42920.9 Tridiagonalization and QR-Factorization…434Chapter 21: Numerics for ODEs and PDEs…44221.1 Methods for First-Order ODEs…44221.2 Multistep Methods…44521.3 Methods for Systems and Higher Order ODEs…44621.4 Methods for Elliptic PDEs…45221.5 Neumann and Mixed Problems. Irregular Boundary…45421.6 Methods for Parabolic PDEs…45921.7 Method for Hyperbolic PDEs…462PART F: OPTIMIZATION, GRAPHS…465Chapter 22: Unconstrained Optimization. Linear Programming…46522.1 Basic Concepts. Unconstrained Optimization: Method of Steepest Descent…46522.2 Linear Programming…47122.3 Simplex Method…47422.4 Simplex Method. Difficulties…479Chapter 23: Graphs. Combinatorial Optimization…48223.1 Graphs and Digraphs…48223.2 Shortest Path Problems. Complexity…48423.3 Bellman’s Principle. Dijkstra’s Algorithm…48723.4 Shortest Spanning Trees: Greedy Algorithm…49023.5 Shortest Spanning Trees: Prim’s Algorithm…49323.6 Flows in Networks23.7 Maximum Flow: Ford–Fulkerson Algorithm…49723.8 Bipartite Graphs. Assignment Problems…499PART G: PROBABILITY, STATISTICS…502Chapter 24: Data Analysis, Probability Theory…50224.1 Data Representation. Average. Spread…50224.2 Experiments, Outcomes, Events…50724.3 Probability…50924.4 Permutations and Combinations…51224.5 Random Variables. Probability Distributions…51624.6 Mean and Variance of a Distribution…52024.7 Binomial, Poisson, and Hypergeometric Distributions…52324.8 Normal Distribution…52624.9 Distribution of Several Random Variables…530Chapter 25: Mathematical Statistics…53325.1 Introduction. Random Sampling…53325.2 Point Estimation of Parameters…53325.3 Confidence Intervals…53625.4 Testing of Hypotheses. Decisions…54025.5 Quality Control…54325.6 Acceptance Sampling…54425.7 Goodness of Fit. Chi-Square Test…54725.8 Nonparametric Tests…54925.9 Regression. Fitting Straight Lines. Correlation…551