Differential Equations with Boundary-Value Problems, 8th Edition

✍ Scribed by Dennis G. Zill, Warren S. Wright

• Publisher: Cengage Learning
• Year: 2012
• Tongue: English
• Leaves: 673
• Edition: 8
• Category: Library

✦ Synopsis

NOTE: This book DOES NOT come with Access Code

DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 8th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible book speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Written in a straightforward, readable, and helpful style, the book provides a thorough treatment of boundary-value problems and partial differential equations.

✦ Table of Contents

Cover
Review of Differentiation
Brief Table of Integrals
Title Page
Copyright
Contents
Preface
Projects
Ch 1: Introduction to Differential Equations
1.1 Definitions and Terminology
Exercises 1.1
1.2 Initial-Value Problems
Exercises 1.2
1.3 Differential Equations as Mathematical Models
Exercises 1.3
Chapter 1 in Review
Ch 2: First-Order Differential Equations
2.1 Solution Curves without a Solution
Exercises 2.1
2.2 Separable Equations
Exercises 2.2
2.3 Linear Equations
Exercises 2.3
2.4 Exact Equations
Exercises 2.4
2.5 Solutions by Substitutions
Exercises 2.5
2.6 A Numerical Method
Exercises 2.6
Chapter 2 in Review
Ch 3: Modeling with First-Order Differential Equations
3.1 Linear Models
Exercises 3.1
3.2 Nonlinear Models
Exercises 3.2
3.3 Modeling with Systems of First-Order DEs
Exercises 3.3
Chapter 3 in Review
Ch 4: Higher-Order Differential Equations
4.1 Preliminary Theory-Linear Equations
Exercises 4.1
4.2 Reduction of Order
Exercises 4.2
4.3 Homogeneous Linear Equations with Constant Coefficients
Exercises 4.3
4.4 Undetermined Coefficients-Superposition Approach
Exercises 4.4
4.5 Undetermined Coefficients-Annihilator Approach
Exercises 4.5
4.6 Variation of Parameters
Exercises 4.6
4.7 Cauchy-Euler Equation
Exercises 4.7
4.8 Green's Functions
Exercises 4.8
4.9 Solving Systems of Linear DEs by Elimination
Exercises 4.9
4.10 Nonlinear Differential Equations
Exercises 4.10
Chapter 4 in Review
Ch 5: Modeling with Higher-Order Differential Equations
5.1 Linear Models: Initial-Value Problems
Exercises 5.1
5.2 Linear Models: Boundary-Value Problems
Exercises 5.2
5.3 Nonlinear Models
Exercises 5.3
Chapter 5 in Review
Ch 6: Series Solutions of Linear Equations
6.1 Review of Power Series
Exercises 6.1
6.2 Solutions about Ordinary Points
Exercises 6.2
6.3 Solutions about Singular Points
Exercises 6.3
6.4 Special Functions
Exercises 6.4
Chapter 6 in Review
Ch 7: The Laplace Transform
7.1 Definition of the Laplace Transform
Exercises 7.1
7.2 Inverse Transforms and Transforms of Derivatives
Exercises 7.2
7.3 Operational Properties I
Exercises 7.3
7.4 Operational Properties II
Exercises 7.4
7.5 The Dirac Delta Function
Exercises 7.5
7.6 Systems of Linear Differential Equations
Exercises 7.6
Chapter 7 in Review
Ch 8: Systems of Linear First-Order Differential Equations
8.1 Preliminary Theory-Linear Systems
Exercises 8.1
8.2 Homogeneous Linear Systems
Exercises 8.2
8.3 Nonhomogeneous Linear Systems
Exercises 8.3
8.4 Matrix Exponential
Exercises 8.4
Chapter 8 in Review
Ch 9: Numerical Solutions of Ordinary Differential Equations
9.1 Euler Methods and Error Analysis
Exercises 9.1
9.2 Runge-Kutta Methods
Exercises 9.2
9.3 Multistep Methods
Exercises 9.3
9.4 Higher-Order Equations and Systems
Exercises 9.4
9.5 Second-Order Boundary-Value Problems
Exercises 9.5
Chapter 9 in Review
Ch 10: Plane Autonomous Systems
10.1 Autonomous Systems
Exercises 10.1
10.2 Stability of Linear Systems
Exercises 10.2
10.3 Linearization and Local Stability
Exercises 10.3
10.4 Autonomous Systems as Mathematical Models
Exercises 10.4
Chapter 10 in Review
Ch 11: Fourier Series
11.1 Orthogonal Functions
Exercises 11.1
11.2 Fourier Series
Exercises 11.2
11.3 Fourier Cosine and Sine Series
Exercises 11.3
11.4 Sturm-Liouville Problem
Exercises 11.4
11.5 Bessel and Legendre Series
Exercises 11.5
Chapter 11 in Review
Ch 12: Boundary-Value Problems in Rectangular Coordinates
12.1 Separable Partial Differential Equations
Exercises 12.1
12.2 Classical PDEs and Boundary-Value Problems
Exercises 12.2
12.3 Heat Equation
Exercises 12.3
12.4 Wave Equation
Exercises 12.4
12.5 Laplace's Equation
Exercises 12.5
12.6 Nonhomogeneous Boundary-Value Problems
Exercises 12.6
12.7 Orthogonal Series Expansions
Exercises 12.7
12.8 Higher-Dimensional Problems
Exercises 12.8
Chapter 12 in Review
Ch 13: Boundary-Value Problems in Other Coordinate Systems
13.1 Polar Coordinates
Exercises 13.1
13.2 Polar and Cylindrical Coordinates
Exercises 13.2
13.3 Spherical Coordinates
Exercises 13.3
Chapter 13 in Review
Ch 14: Integral Transforms
14.1 Error Function
Exercises 14.1
14.2 Laplace Transform
Exercises 14.2
14.3 Fourier Integral
Exercises 14.3
14.4 Fourier Transforms
Exercises 14.4
Chapter 14 in Review
Ch 15: Numerical Solutions of Partial Differential Equations
15.1 Laplace's Equation
Exercises 15.1
15.2 Heat Equation
Exercises 15.2
15.3 Wave Equation
Exercises 15.3
Chapter 15 in Review
Appendixes
Appendix I: Gamma Function
Appendix II: Matrices
Appendix III: Laplace Transforms
Answers for Selected Odd-Numbered Problems
Index