Differential equations : a modeling approach / Glenn Ledder.
Publication details: Boston : McGraw-Hill Higher Education, c2005.Description: xvii, 665 p. : ill. ; 24 cmISBN:- 9780072422290
- 0072422297 (acidfree paper)
- 515.35 22 LED
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| 515.35 LED 3 Differential equations : a modeling approach / | 515.35 LED 4 Differential equations : a modeling approach / | 515.35 LED 5 Differential equations : a modeling approach / | 515.35 LED 6 Differential equations : a modeling approach / | 515.35 LED 7 Differential equations : a modeling approach / | 515.35004 EDW. 1 Differential equations : C. Henry Edwards, David E. Penney ; with assistance of David Calvis. | 515.45 RAH. 1 Integral equations and their applications / |
CONTENT
CHAPTER 1 INTRODUCTION
1.1 Natural Decay and Natural Growth
1.2 Differential Equations and Solutions
1.3 Mathematical Models and Mathematical Modeling
CHAPTER 2 BASIC CONCEPTS AND TECHNIQUES
2.1 A Collection of Mathematical Models
2.2 Separable First-Order Equations
2.3 Slope Fields
2.4 Existence of Unique Solutions
2.5 Euler's Method, etc.
CHAPTER 3 HOMOGENEOUS LINEAR EQUATIONS
3.1 Linear Oscillators
3.2 Systems of Linear Algebraic Equations
3.3 Theory of Homogeneous Linear Equations
3.4 Homogeneous Equations with Constant Coefficients
3.5 Real Solutions from Complex Characteristic Values, etc.
CHAPTER 4 NON-HOMOGENEOUS LINEAR EQUATIONS
4.1 More on Linear Oscillator Model
4.2 General Solutions for Non-homogeneous Equations
4.3 The Method of Undetermined Coefficients, etc.
CHAPTER 5 AUTONOMOUS EQUATIONS AND SYSTEMS
5.1 Population Models
5.2 The Phase Line
5.3 The Phase Plane, ETC.
CHAPTER 6 ANALYTICAL METHODS FOR SYSTEMS
6.1 Compartment Models
6.2 Eigenvalues and Eigenspaces
6.3 Linear Trajectories, etc.
CHAPTER 7 THE LAPLACE TRANSFORM
7.1 Piece wise-Continuous Functions
7.2 Definitions and Properties of the Laplace Transform
7.3 Solution of Initial-Value Problems with the Laplace Transform, etc.
CHAPTER 8 VIBRATING STRING: A FOCUSED INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
8.1 Transverse Vibration of a String
8.2 The General Solution of the Wave Equation
8.3 Vibration Model of a Finite String, etc.
CHAPTER A SOME ADDITIONAL TOPICS
A.1 Using Integrating Factors to Solve First -Order Linear Equations
A.2 Proof of the Existence and Uniqueness Theorem for first-order Equations
A.3 Error in Numerical Methods, etc.
Includes Index: p. 661-665
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