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A Modern Introduction to Differential Equations. Ricardo
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eBay-Artikelnr.:253577582276
Artikelmerkmale
- Artikelzustand
- UPC
- 0046442042390
- ISBN
- 9780618042395
- EAN
- 9780618042395
Über dieses Produkt
Product Identifiers
Publisher
Cengage Learning
ISBN-10
0618042393
ISBN-13
9780618042395
eBay Product ID (ePID)
30307975
Product Key Features
Number of Pages
464 Pages
Language
English
Publication Name
Modern Introduction to Differential Equations
Subject
Differential Equations / General
Publication Year
2002
Type
Textbook
Subject Area
Mathematics
Format
Hardcover
Dimensions
Item Height
0.5 in
Item Weight
36.1 Oz
Item Length
10 in
Item Width
7.9 in
Additional Product Features
Intended Audience
College Audience
LCCN
00-133863
TitleLeading
A
Dewey Edition
22
Illustrated
Yes
Dewey Decimal
515/.35
Table Of Content
Contents 1. Introduction to Differential Equations 1.0 Introduction 1.1 Basic Terminology 1.2 Solutions of Differential Equations 1.3 Technology and Differential Equations 1.4 Summary Project 1-1 2. First-Order Differential Equations 2.0 Introduction 2.1 Separable Equations 2.2 Linear Equations 2.3 Slope Fields 2.4 Phase Lines and Phase Portraits 2.5 Equilibrium Points: Sinks, Sources, and Nodes 2.6 Bifurcations 2.7 Existence and Uniqueness of Solutions 2.8 Summary Project 2-1 Project 2-2 3. The Numerical Approximation of Solutions 3.0 Introduction 3.1 Euler\'s Method 3.2 A Few More Words About Error 3.3 The Improved Euler Method 3.4 More Sophisticated Numerical Methods: Runge-Kutta and Others 3.5 Summary Project 3-1 4. Second- and Higher-Order Equations 4.0 Introduction 4.1 Homogeneous Second-Order Linear Equations with Constant Coefficients 4.2 Nonhomogeneous Second-Order Linear Equations with Constant Coefficients 4.3 Higher-Order Linear Equations with Constant Coefficients 4.4 Higher-Order Equations and Their Equivalent Systems 4.5 Qualitative Analysis of Autonomous Systems 4.6 Existence and Uniqueness 4.7 Numerical Solutions 4.8 Summary Project 4-1 5. Systems of Linear Differential Equations 5.0 Introduction 5.1 Systems and Matrices 5.2 Two-Dimensional Systems of First-Order Linear Equations 5.3 Stability of Linear Systems: Unequal Real Eigenvalues 5.4 Stability of Linear Systems: Equal Real Eigenvalues 5.5 Stability of Linear Systems: Complex Eigenvalues 5.6 Nonhomogeneous Systems 5.7 Generalizations: The n x n Case (n greater or equal to 3) 5.8 Summary Project 5-1 6. The Laplace Transform 6.0 Introduction 6.1 The Laplace Transform of Some Important Functions 6.2 The Inverse Transform and the Convolution 6.3 Transforms of Discontinuous Functions 6.4 Transforms of Impulse Functions--the Dirac Delta Function 6.5 Transforms and Systems of Linear Differential Equations 6.6 Qualitative Analysis via the Laplace Transform 6.7 Summary Project 6-1 7. Systems of Nonlinear Differential Equations 7.0 Introduction 7.1 Equilibria of Nonlinear Systems 7.2 Linear Approximation at Equilibrium Points 7.3 Two Important Examples of Nonlinear Equations and Systems 7.4 Van der Pol\'s Equation and Limit Cycles 7.5 Summary Project 7-1 Appendices A. Some Calculus Concepts and Results B. Vectors and Matrices C. Complex Numbers D. Series Solutions of Differential Equations
Synopsis
Designed for a one-semester course, A Modern Introduction to Differential Equations presents a solid and highly accessible introduction to differential equations, developing the concepts from a dynamic systems perspective and employing technology to treat topics graphically, numerically, and analytically. It thus blends the traditional differential equations text with the best of the more recent reform approaches.
LC Classification Number
QA371.R357 2003
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