Advanced engineering mathematics / Dennis G. Zill, Michael R. Cullen.

Format:

Book

Author/Creator:

Zill, Dennis G., 1940-

Contributor:

Cullen, Michael R.

Language:

English

Subjects (All):

Engineering mathematics.

Matemáticas para ingenieros.

Local Subjects:

Matemáticas para ingenieros.

Physical Description:

xxxiii, 929, 14, 49, 23 pages : illustrations (some color) ; 29 cm

Edition:

Third edition.

Place of Publication:

Sudbury, Mass. : Jones and Bartlett Publishers, [2006]

Contents:

Project for Section 3.7 Road Mirages / Anton M. Jopko, Ph.D. xv

Project for Section 3.10 The Ballistic Pendulum / Warren S. Wright xvii

Project for Section 8.1 Two-Ports in Electrical Circuits / Gareth Williams, Ph.D. xviii

Project for Section 8.2 Traffic Flow / Gareth Williams, Ph.D. xx

Project for Section 8.15 Temperature Dependence of Resistivity / Anton M. Jopko, Ph.D. xxii

Project for Section 9.16 Minimal Surfaces / Jeff Dodd, Ph.D. xxiii

Project for Section 14.3 The Hydrogen Atom / Matheus Grasselli, Ph.D. xxv

Project for Section 15.4 The Uncertainty Inequality in Signal Processing / Jeff Dodd, Ph.D. xxviii

Project for Section 15.4 Fraunhofer Diffraction by a Circular Aperture / Anton M. Jopko, Ph.D. xxx

Project for Section 16.2 Instabilities of Numerical Methods / Dmitry Pelinovsky, Ph.D. xxxii

Part 1 Ordinary Differential Equations 3

Chapter 1 Introduction to Differential Equations 4

1.2 Initial-Value Problems 14

1.3 Differential Equations as Mathematical Models 21

Chapter 2 First-Order Differential Equations 35

2.1 Solution Curves Without a Solution 36

2.1.1 Direction Fields 36

2.1.2 Autonomous First-Order DEs 38

2.2 Separable Variables 45

2.3 Linear Equations 52

2.4 Exact Equations 60

2.5 Solutions by Substitutions 67

2.6 A Numerical Method 71

2.7 Linear Models 75

2.8 Nonlinear Models 85

2.9 Modeling with Systems of First-Order DEs 94

Chapter 3 Higher-Order Differential Equations 104

3.1 Preliminary Theory: Linear Equations 105

3.1.1 Initial-Value and Boundary-Value Problems 105

3.1.2 Homogeneous Equations 107

3.1.3 Nonhomogeneous Equations 112

3.2 Reduction of Order 116

3.3 Homogeneous Linear Equations with Constant Coefficients 119

3.4 Undetermined Coefficients 126

3.5 Variation of Parameters 135

3.6 Cauchy-Euler Equation 140

3.7 Nonlinear Equations 145

3.8 Linear Models: Initial-Value Problems 150

3.8.1 Spring/Mass Systems: Free Undamped Motion 150

3.8.2 Spring/Mass Systems: Free Damped Motion 153

3.8.3 Spring/Mass Systems: Driven Motion 156

3.8.4 Series Circuit Analogue 159

3.9 Linear Models: Boundary-Value Problems 166

3.10 Nonlinear Models 174

3.11 Solving Systems of Linear Equations 183

Chapter 4 The Laplace Transform 193

4.1 Definition of the Laplace Transform 194

4.2 The Inverse Transform and Transforms of Derivatives 199

4.2.1 Inverse Transforms 199

4.2.2 Transforms of Derivatives 201

4.3 Translation Theorems 207

4.3.1 Translation on the s-axis 207

4.3.2 Translation on the t-axis 210

4.4 Additional Operational Properties 218

4.4.1 Derivatives of Transforms 218

4.4.2 Transforms of Integrals 220

4.4.3 Transform of a Periodic Function 223

4.5 The Dirac Delta Function 228

4.6 Systems of Linear Differential Equations 231

Chapter 5 Series Solutions of Linear Differential Equations 239

5.1 Solutions about Ordinary Points 240

5.1.1 Review of Power Series 240

5.1.2 Power Series Solutions 242

5.2 Solutions about Singular Points 251

5.3 Special Functions 260

5.3.1 Bessel Functions 260

5.3.2 Legendre Functions 267

Chapter 6 Numerical Solutions of Ordinary Differential Equations 275

6.1 Euler Methods and Error Analysis 276

6.2 Runge-Kutta Methods 280

6.3 Multistep Methods 286

6.4 Higher-Order Equations and Systems 288

6.5 Second-Order Boundary-Value Problems 293

Part 2 Vectors, Matrices, and Vector Calculus 299

Chapter 7 Vectors 300

7.1 Vectors in 2-Space 301

7.2 Vectors in 3-Space 307

7.3 Dot Product 312

7.4 Cross Product 319

7.5 Lines and Planes in 3-Space 324

7.6 Vector Spaces 331

7.7 Gram-Schmidt Orthogonalization Process 340

Chapter 8 Matrices 347

8.1 Matrix Algebra 348

8.2 Systems of Linear Algebraic Equations 357

8.3 Rank of a Matrix 368

8.4 Determinants 373

8.5 Properties of Determinants 378

8.6 Inverse of a Matrix 385

8.6.1 Finding the Inverse 385

8.6.2 Using the Inverse to Solve Systems 391

8.7 Cramer's Rule 395

8.8 The Eigenvalue Problem 398

8.9 Powers of Matrices 404

8.10 Orthogonal Matrices 408

8.11 Approximation of Eigenvalues 415

8.12 Diagonalization 422

8.13 Cryptography 431

8.14 An Error-Correcting Code 434

8.15 Method of Least Squares 440

8.16 Discrete Compartmental Models 443

Chapter 9 Vector Calculus 451

9.1 Vector Functions 452

9.2 Motion on a Curve 458

9.3 Curvature and Components of Acceleration 463

9.4 Partial Derivatives 467

9.5 Directional Derivatives 474

9.6 Tangent Planes and Normal Lines 480

9.7 Divergence and Curl 483

9.8 Line Integrals 489

9.9 Independence of Path 498

9.10 Double Integrals 505

9.11 Double Integrals in Polar Coordinates 514

9.12 Green's Theorem 519

9.13 Surface Integrals 524

9.14 Stokes' Theorem 533

9.15 Triple Integrals 539

9.16 Divergence Theorem 550

9.17 Change of Variables in Multiple Integrals 556

Part 3 Systems of Differential Equations 567

Chapter 10 Systems of Linear Differential Equations 568

10.1 Preliminary Theory 569

10.2 Homogeneous Linear Systems 576

10.2.1 Distinct Real Eigenvalues 577

10.2.2 Repeated Eigenvalues 580

10.2.3 Complex Eigenvalues 584

10.3 Solution by Diagonalization 589

10.4 Nonhomogeneous Linear Systems 592

10.4.1 Undetermined Coefficients 592

10.4.2 Variation of Parameters 595

10.4.3 Diagonalization 597

10.5 Matrix Exponential 600

Chapter 11 Systems of Nonlinear Differential Equations 606

11.1 Autonomous Systems 607

11.2 Stability of Linear Systems 613

11.3 Linearization and Local Stability 622

11.4 Autonomous Systems as Mathematical Models 631

11.5 Periodic Solutions, Limit Cycles, and Global Stability 639

Part 4 Fourier Series and Partial Differential Equations 651

Chapter 12 Orthogonal Functions and Fourier Series 652

12.1 Orthogonal Functions 653

12.2 Fourier Series 658

12.3 Fourier Cosine and Sine Series 663

12.4 Complex Fourier Series 670

12.5 Sturm-Liouville Problem 674

12.6 Bessel and Legendre Series 681

12.6.1 Fourier-Bessel Series 682

12.6.2 Fourier-Legendre Series 685

Chapter 13 Boundary-Value Problems in Rectangular Coordinates 689

13.1 Separable Partial Differential Equations 690

13.2 Classical Equations and Boundary-Value Problems 694

13.3 Heat Equation 699

13.4 Wave Equation 702

13.5 Laplace's Equation 707

13.6 Nonhomogeneous BVPs 712

13.7 Orthogonal Series Expansions 719

13.8 Fourier Series in Two Variables 723

Chapter 14 Boundary-Value Problems in Other Coordinate Systems 728

14.1 Problems in Polar Coordinates 729

14.2 Problems in Cylindrical Coordinates 734

14.3 Problems in Spherical Coordinates 740

Chapter 15 Integral Transform Method 745

15.1 Error Function 746

15.2 Applications of the Laplace Transform 747

15.3 Fourier Integral 755

15.4 Fourier Transforms 760

15.5 Fast Fourier Transform 766

Chapter 16 Numerical Solutions of Partial Differential Equations 777

16.1 Laplace's Equation 778

16.2 The Heat Equation 783

16.3 The Wave Equation 789

Part 5 Complex Analysis 795

Chapter 17 Functions of a Complex Variable 796

17.1 Complex Numbers 797

17.2 Powers and Roots 801

17.3 Sets in the Complex Plane 805

17.4 Functions of a Complex Variable 808

17.5 Cauchy-Riemann Equations 814

17.6 Exponential and Logarithmic Functions 819

17.7 Trigonometric and Hyperbolic Functions 825

17.8 Inverse Trigonometric and Hyperbolic Functions 829

Chapter 18 Integration in the Complex Plane 833

18.1 Contour Integrals 834

18.2 Cauchy-Goursat Theorem 839

18.3 Independence of Path 844

18.4 Cauchy's Integral Formulas 850

Chapter 19 Series and Residues 857

19.1 Sequences and Series 858

19.2 Taylor Series 863

19.3 Laurent Series 869

19.4 Zeros and Poles 877

19.5 Residues and Residue Theorem 880

19.6 Evaluation of Real Integrals 886

Chapter 20 Conformal Mappings 894

20.1 Complex Functions as Mappings 895

20.2 Conformal Mappings 899

20.3 Linear Fractional Transformations 906

20.4 Schwarz-Christoffel Transformations 912

20.5 Poisson Integral Formulas 917

20.6 Applications 921

I Some Derivative and Integral Formulas APP-2

II Gamma Function APP-4

III Table of Laplace Transforms APP-6

IV Conformal Mappings APP-9.

Notes:

Includes bibliographical references and index.

Other Format:

Online version: Zill, Dennis G., 1940- Advanced engineering mathematics.

ISBN:

9780763745912

076374591X

9780763739140

0763739146

OCLC:

62290475