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

ISBN-13: 9781118266700 / Angielski / Miękka / 2015 / 320 str.

Erwin Kreyszig

Opis

This is the student Solutions Manual to accompany Advanced Engineering Mathematics, Volume 2, Tenth Edition.

This market-leading text is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self contained subject matter parts for maximum flexibility. The new edition continues with the tradition of providing instructors and students with a comprehensive and up-to-date resource for teaching and learning engineering mathematics, that is, applied mathematics for engineers and physicists, mathematicians and computer scientists, as well as members of other disciplines.

Spis treści

PART D: COMPLEX ANALYSIS 257

Chapter 13. Numbers and Functions. Complex Differentiation 257

13.1 Complex Numbers and Their Geometric Representation 258

13.2 Polar Form of Complex Numbers. Powers and Roots 261

13.3 Derivative. Analytic Function 267

13.4 Cauchy Riemann Equations. Laplace s Equation 269

13.5 Exponential Function 274

13.6 Trigonometric and Hyperbolic Functions. Euler s Formula 277

13.7 Logarithm. General Power. Principal Value 279

Chapter 14: Complex Integration 283

14.1 Line Integral in the Complex Plane 283

14.2 Cauchy s Integral Theorem 288

14.3 Cauchy s Integral Formula 291

14.4 Derivatives of Analytic Functions 295

Chapter 15: Power Series, Taylor Series 298

15.1 Sequences, Series, Convergence Tests 298

15.2 Power Series 303

15.3 Functions Given by Power Series 306

15.4 Taylor and Maclaurin Series 309

15.5 Uniform Convergence. Optional 312

Chapter 16: Laurent Series. Residue Integration 316

16.1 Laurent Series 316

16.2 Singularities and Zeros. Infinity 320

16.3 Residue Integration Method 322

16.4 Residue Integration of Real Integrals 326

Chapter 17: Conformal Mapping 332

17.1 Geometry of Analytic Functions: Conformal Mapping 333

17.2 Linear Fractional Transformations. (Möbius Transformations) 339

17.3 Special Linear Fractional Transformations 343

17.4 Conformal Mapping by Other Functions 347

17.5 Riemann Surfaces. Optional 352

Chapter 18: Complex Analysis and Potential Theory 353

18.1 Electrostatic Fields 354

18.2 Use of Conformal Mapping. Modeling 358

18.3 Heat Problems 359

18.4 Fluid Flow 361

18.5 Poisson s Integral Formula for Potentials 364

18.6 General Properties of Harmonic Functions. Uniqueness Theorem for the Dirchlet Problem 367

PART E: NUMERIC ANALYSIS 373

Chapter 19: Numerics in General 373

19.1 Introduction 374

19.2 Solution of Equations by Iteration 379

19.3 Interpolation 384

19.4 Spline Interpolation 389

19.5 Numeric Integration and Differentiation 393

Chapter 20: Numeric Linear Algebra 400

20.1 Linear Systems: Gauss Elimination 400

20.2 Linear Systems: LU–Factorization, Matrix Inversion 404

20.3 Linear Systems: Solution by Iteration 410

20.4 Linear Systems: Ill–Conditioning, Norms 415

20.5 Least Squares Method 419

20.6 Matrix Eigenvalue Problems: Introduction 424

20.7 Inclusion of Matrix Eigenvalues 424

20.8 Power Method for Eigenvalues 429

20.9 Tridiagonalization and QR–Factorization 434

Chapter 21: Numerics for ODEs and PDEs 442

21.1 Methods for First–Order ODEs 442

21.2 Multistep Methods 445

21.3 Methods for Systems and Higher Order ODEs 446

21.4 Methods for Elliptic PDEs 452

21.5 Neumann and Mixed Problems. Irregular Boundary 454

21.6 Methods for Parabolic PDEs 459

21.7 Method for Hyperbolic PDEs 462

PART F: OPTIMIZATION, GRAPHS 465

Chapter 22: Unconstrained Optimization. Linear Programming 465

22.1 Basic Concepts. Unconstrained Optimization: Method of Steepest Descent 465

22.2 Linear Programming 471

22.3 Simplex Method 474

22.4 Simplex Method. Difficulties 479

Chapter 23: Graphs. Combinatorial Optimization 482

23.1 Graphs and Digraphs 482

23.2 Shortest Path Problems. Complexity 484

23.3 Bellman s Principle. Dijkstra s Algorithm 487

23.4 Shortest Spanning Trees: Greedy Algorithm 490

23.5 Shortest Spanning Trees: Prim s Algorithm 493

23.6 Flows in Networks

23.7 Maximum Flow: Ford Fulkerson Algorithm 497

23.8 Bipartite Graphs. Assignment Problems 499

PART G: PROBABILITY, STATISTICS 502

Chapter 24: Data Analysis, Probability Theory 502

24.1 Data Representation. Average. Spread 502

24.2 Experiments, Outcomes, Events 507

24.3 Probability 509

24.4 Permutations and Combinations 512

24.5 Random Variables. Probability Distributions 516

24.6 Mean and Variance of a Distribution 520

24.7 Binomial, Poisson, and Hypergeometric Distributions 523

24.8 Normal Distribution 526

24.9 Distribution of Several Random Variables 530

Chapter 25: Mathematical Statistics 533

25.1 Introduction. Random Sampling 533

25.2 Point Estimation of Parameters 533

25.3 Confidence Intervals 536

25.4 Testing of Hypotheses. Decisions 540

25.5 Quality Control 543

25.6 Acceptance Sampling 544

25.7 Goodness of Fit. Chi–Square Test 547

25.8 Nonparametric Tests 549

25.9 Regression. Fitting Straight Lines. Correlation 551