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Advanced Engineering Mathematics

Advanced Engineering Mathematics - 2nd edition

ISBN13: 978-0763713577

Cover of Advanced Engineering Mathematics 2ND 00 (ISBN 978-0763713577)
ISBN13: 978-0763713577
ISBN10: 0763713570
Edition: 2ND 00
Copyright: 2000
Publisher: Jones & Bartlett Publishers
Published: 2000
International: No

Advanced Engineering Mathematics - 2ND 00 edition

ISBN13: 978-0763713577

Dennis G. Zill and Michael R. Cullen

ISBN13: 978-0763713577
ISBN10: 0763713570
Edition: 2ND 00
Copyright: 2000
Publisher: Jones & Bartlett Publishers
Published: 2000
International: No

Advanced Engineering Mathematics is a compendium of many mathematical topics, all of which are loosely related by the expedient of either being needed or useful in courses and subsequent careers in science and engineering. Consequently, this book represents the most accurate list of what constitutes "engineering mathematics." For flexibility in topic selection, the text is divided into five major sections that illustrate the backbone of science/engineering related mathematics. The first eight chapters of this book constitute a complete short course in ordinary differential equations.

Key Features

  • Real-world applications, current examples, and a many illustrations help students visualize important concepts and apply the material to everyday life.
  • A complete Solutions Manual is available for the instructor, and a Student Solutions Manual that provides the answers to every third problem.
  • Text includes boxed definitions and boxed theorems for easy reference.
  • Zill devotes an entire section to Fast Fourier Transforms (FFT), and provides problems using the FFT. Mathematical Models for differential equations are also given special attention.
  • Zill has provided Remark sections throughout the text that alert students to certain discussions that require special attention.
  • New to this Edition! The five major sections of the text open with an essay by an acknowledged expert in the field of engineering, this helps to provide students with real-life context to the course material.

Author Bio

Zill, Dennis G. : Loyola Marymount University

Ph.D. in applied mathematics from Iowa State University. Currently professor of mathematics and former chair of the math dept at Loyola Marymount University in Los Angeles.

Cullen, Michael R. :

Michael R. Cullen late of Loyola Marymount University

Table of Contents

Part I: Ordinary Differential Equations

Chapter 1. Introduction to Differential Equations

1.1. Definitions and Terminology
1.2. Initial-Value Problems
1.3. Differential Equations as Mathematical Models

Chapter 1. Review Exercises

Chapter 2. First-Order Differential Equations

2.1. Solution Curves Without the Solution
2.2. Separable Variables
2.3. Linear Equations
2.4. Exact Equations
2.5. Solutions by Substitutions
2.6. A Numerical Solutions
2.7. Linear Models
2.8. Nonlinear
2.9. Systems: Linear and Nonlinear Models

Chapter 2. Review Exercises

Chapter 3. Higher-Order Differential Equations

3.1. Preliminary Theory: Linear and Nonlinear Models
3.2. Reduction of Order
3.3. Homogenous Linear Equations with Constant Coefficients
3.4. Undetermined
3.5. Variations of Parameters
3.6. Cauchy-Euler Equation
3.7. Nonlinear Equations
3.8. Linear Models: Initial-Value Problems
3.9. Linear Models: Boundary-Value Problems
3.10. Nonlinear Models
3.11. Solving Systems of Linear Models

Chapter 3. Review Exercises

Chapter 4. The Laplace Transform

4.1. Definition of the Laplace Transform
4.2. The Inverse Transform and Transforms of Derivations
4.3. Translation Theorems
4.4. Additional Operational Properties
4.5. Dirac Delta Function
4.6. Solving Systems of Linear Equations

Chapter 4. Review Exercises

Chapter 5. Series Solutions of Linear Equations

5.1. Solutions about Ordinary Points
5.2. Solutions about Singular Points
5.3. Two Special Equations

Chapter 5. Review Exercises

Chapter 6. Numerical Solutions of Ordinary Differential Equations

6.1. Euler Methods and Error Analysis
6.2. Runge-Kutta Methods
6.3. Methods
6.4. Higher-Order Equations and Systems
6.5. Second-Order Boundary-Value Problems

Chapter 6 Review Exercises

Part II: Vectors, Matrices, and Vector Calculus

Chapter 7. Vectors

7.1. Vectors in 2-Space
7.2. Vectors in 3-Space
7.3. The Dot Product
7.4. The Cross Product
7.5. Lines and Planes in 3-Space
7.6. Vector Spaces

Chapter 7. Review Exercises

Chapter 8. Matrices

8.1. Matrix Algebra
8.2. Systems of Linear Algebraic Equations
8.3. Rank of a Matrix
8.4. Determinants
8.5. Properties of Determinants
8.6. Inverse of a Matrix
8.7. Cramer's Rule
8.8. The Eigenvalue Problem
8.9. Power of Matrices
8.10. Orthogonal Matrices
8.11. Approximation of Eigenvalues
8.12. Diagonalization
8.13. Cryptography
8.14. An Error-Correcting Code
8.15. Method of Least Squares
8.16. Discrete Compartmental Models

Chapter 8. Review Exercises

Chapter 9. Vector Calculus

9.1. Vector Functions
9.2. Motion on a Curve
9.3. Curvature and Components of Acceleration
9.4. Functions of Several Variables
9.5. The Directional Derivative
9.6. Planes and Normal Lines
9.7. Divergence and Curl
9.8. Line Integrals
9.9. Line Integrals Independent of the Path
9.10. Review of Double Integrals
9.11. Double Integrals in Polar Coordinates
9.12. Green's Theorem
9.13. Surface Integrals
9.14. Strokes' Theorem
9.15. Review of Triple Integrals
9.16. Divergence Theorem
9.17. Change of Variables in Multiple Integrals

Chapter 9. Review Exercises

Part III: Systems of Differential Equations

Chapter 10. System of Linear Differential Equations

10.1. Preliminary
10.2. Homogeneous Linear Systems
10.3. Solution by Diagonalization
10.4. Nonhomogenous Linear Systems
10.5. Matrix Exponential

Chapter 10. Review Exercise

Chapter 11. Systems of Nonlinear Differential Equations

11.1. Autonomous Systems, Critical Points, and Periodic Solutions
11.2. Stability of Linear Systems
11.3. Linearization and Local Stability
11.4. Modeling Using Autonomous Systems
11.5. Periodic Solutions, Limit Cycles, and Global Stability

Chapter 11. Review Exercise

Part IV: Fourier Series and Partial Differential Equations

Chapter 12. Orthogonal Functions and Fourier Series

12.1. Orthogonal Functions
12.2. Fourier Series
12.3. Fourier Cosine and Sine Series
12.4. Complex Fourier Series and Frequency Spectrum
12.5. Sturm-Liouville Problem
12.6. Bessel and Legendre Series

Chapter 12. Review Exercises

Chapter 13. Boundary-Value Problems in Rectangular Coordinates

13.1. Separable Partial Differential Equations
13.2. Classical Equations and Boundary-Value Problems
13.3. Heat Equation
13.4. Wave Equation
13.5. Laplace's Equation
13.6. Nonhomogeneous Equations and Boundary Conditions
13.7. Orthogonal Series Expansions
13.8. Fourier Series in Two Variable

Chapter 13. Review Exercises

Chapter 14. Boundary-Value Problems in Other Coordinate Systems

14.1. Problems Involving Laplace's Equation in Polar Coordinates
14.2. Problems in Polar and Cylindrical Coordinates: Bessel Functions
14.3. Problems in Spherical Coordinates: Legendre Polynomials

Chapter 14. Review Exercises

Chapter 15. Integral Transform Model

15.1. Error Function
15.2. Applications of the Laplace Transform
15.3. Fourier Integral
15.4. Fourier Transforms
15.5. Fast Fourier Transform

Chapter 15. Review Exercises

Chapter 16. Numerical Solutions to Partial Differential Equations

16.1. Elliptic Equations
16.2. Parabolic Equations
16.3. Hyperbolic Equations

Chapter 16. Review Exercises

Part V: Complex Analysis

Chapter 17. Functions of a Complex Variable

17.1. Complex Numbers
17.2. Form of Complex Numbers; Power and Roots
17.3. Sets of Points in the Complex Plane
17.4. Functions of a Complex Variable; Analyticity
17.5. Cauchy-Reimann Equations
17.6. Exponential and Logarithmic Functions
17.7. Trigonometric and Hyperbolic Functions
17.8. Inverse Trigonometric and Hyperbolic Functions

Chapter 17. Review Exercise

Chapter 18. Integration in the Complex Plane

18.1. Contour Integrals
18.2. Cauchy-Goursat Theorem
18.3. Independence of Path
18.4. Cauchy's Integral Formula

Chapter 18. Review Exercises

Chapter 19. Series and Residues

19.1. Sequences and Series
19.2. Taylor Series
19.3. Laurent Series
19.4. Zeros and Poles
19.5. Residues and Residue Theorem
19.6. Evaluation of Real Integrals

Chapter 19. Review Exercises

Chapter 20. Conformal Mappings and Applications

20.1. Complex Functions as Mappings
20.2. Conformal Mapping and the Dirichlet Problem
20.3. Linear Fractional Transformations
20.4. Schwarz-Christoffel Transformations
20.5. Poisson Integral Formulas
20.6. Applications

Chapter 20. Review Exercise

Appendix I Some Derivative and Integral Formulas
Appendix II Gamma Function; Exercises
Appendix III Table of Laplace Transforms
Appendix IV Conformal Mappings
Appendix V Some BASIC Programs for Numerical Methods
Appendix VI Selected Answers for Odd-Numbered Problems

Selected Answers for Odd-Numbered Problems

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