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Product Details:

Language: English
ISBN-10: 0134689542
ISBN-13: 978-0134689548
ISBN-13: 9780134689548

Author: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly West

Table of Content:

1 First-Order Differential Equations
1.1 Dynamical Systems: Modeling
1.2 Solutions and Direction Fields: Qualitative Analysis
1.3 Separation of Variables: Quantitative Analysis
1.4 Approximation Methods: Numerical Analysis
1.5 Picard’s Theorem: Theoretical Analysis

2 Linearity and Nonlinearity
2.1 Linear Equations: The Nature of Their Solutions
2.2 Solving the First-Order Linear Differential Equation
2.3 Growth and Decay Phenomena
2.4 Linear Models: Mixing and Cooling
2.5 Nonlinear Models: Logistic Equation
2.6 Systems of Differential Equations: A First Look

3 Linear Algebra
3.1 Matrices: Sums and Products
3.2 Systems of Linear Equations
3.3 The Inverse of a Matrix
3.4 Determinants and Cramer’s Rule
3.5 Vector Spaces and Subspaces
3.6 Basis and Dimension

4 Higher-Order Linear Differential Equations

4.1 The Harmonic Oscillator
4.2 Real Characteristic Roots
4.3 Complex Characteristic Roots
4.4 Undetermined Coefficients
4.5 Variation of Parameters
4.6 Forced Oscillations
4.7 Conservation and Conversion

5 Linear Transformations
5.1 Linear Transformations
5.2 Properties of Linear Transformations
5.3 Eigenvalues and Eigenvectors
5.4 Coordinates and Diagonalization

6 Linear Systems of Differential Equations
6.1 Theory of Linear DE Systems
6.2 Linear Systems with Real Eigenvalues
6.3 Linear Systems with Nonreal Eigenvalues
6.4 Stability and Linear Classification
6.5 Decoupling a Linear DE System
6.6 Matrix Exponential
6.7 Nonhomogeneous Linear Systems

7 Nonlinear Systems of Differential Equations

7.1 Nonlinear Systems
7.2 Linearization
7.3 Numerical Solutions
7.4 Chaos, Strange Attractors, and Period Doubling
7.5 Chaos in Forced Nonlinear Systems

8 Laplace Transforms
8.1 The Laplace Transform and Its Inverse
8.2 Solving DEs and IVPs with Laplace Transforms
8.3 The Step Function and the Delta Function
8.4 The Convolution Integral and the Transfer Function
8.5 Laplace Transform Solution of Linear Systems

9 Discrete Dynamical Systems
9.1 Iterative Equations
9.2 Linear Iterative Systems
9.3 Nonlinear Iterative Equations: Chaos Again

10 Control Theory
10.1 Feedback Controls
10.2 Introduction to Optimal Control
10.3 Pontryagin Maximum Principle

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