Differential Equations and Linear Algebra

by Farlow, Jerry; Hall, James E.; McDill, Jean Marie; West, Beverly

• ISBN13: 9780131860612
• ISBN10: 0131860615
• Edition: 2nd
• Format: Hardcover
• Copyright: 2006-12-26
• Publisher: Pearson

Summary

For sophomore-level courses in Differential Equations and Linear Algebra. Extensively rewritten throughout, the Second Edition of this flexible text features a seamless integration of linear algebra into the discipline of differential equations. Abundant computer graphics, IDE interactive illustration software, and well-thought-out problem sets make it an excellent choice for either the combination DE/LA course or pure differential equations courses. The authorsrs" consistent, reader-friendly presentation encourages students to think both quantitatively and qualitatively when approaching differential equations - and reinforces concepts using similar methods to solve various systems (algebraic, differential, and iterative).

Table of Contents

First-Order Differential Equations
Dynamical Systems: Modeling	p. 1
Solutions and Direction Fields: Qualitative Analysis	p. 11
Separation of Variables: Quantitative Analysis	p. 25
Approximation Methods: Numerical Analysis	p. 33
Picards Theorem: Theoretical Analysis	p. 46
Linearity and Nonlinearity
Linear Equations: The Nature of Their Solutions	p. 55
Solving the First-Order Linear Differential Equation	p. 63
Growth and Decay Phenomena	p. 73
Linear Models: Mixing and Cooling	p. 80
Nonlinear Models: Logistic Equation	p. 87
Systems of Differential Equations: A First Look	p. 100
Linear Algebra
Matrices: Sums and Products	p. 115
Systems of Linear Equations	p. 130
The Inverse of a Matrix	p. 146
Determinants and Cramers Rule	p. 156
Vector Spaces and Subspaces	p. 167
Basis and Dimension	p. 177
Higher-Order Linear Differential Equations
The Harmonic Oscillator	p. 195
Real Characteristic Roots	p. 210
Complex Characteristic Roots	p. 229
Undetermined Coefficients	p. 244
Variation of Parameters	p. 255
Forced Oscillations	p. 261
Conservation and Conversion	p. 274
Linear Transformations
Linear Transformations	p. 285
Properties of Linear Transformations	p. 300
Eigenvalues and Eigenvectors	p. 311
Coordinates and Diagonalization	p. 327
Linear Systems of Differential Equations
Theory of Linear DE Systems	p. 343
Linear Systems with Real Eigenvalues	p. 357
Linear Systems with Nonreal Eigenvalues	p. 372
Stability and Linear Classification	p. 384
Decoupling a Linear DE System	p. 394
Matrix Exponential	p. 400
Nonhomogeneous Linear Systems	p. 410
Nonlinear Systems of Differential Equations
Nonlinear Systems	p. 421
Linearization	p. 431
Numerical Solutions	p. 441
Chaos, Strange Attractors, and Period Doubling	p. 449
Chaos in Forced Nonlinear Systems	p. 456
Laplace Transforms
The Laplace Transform and Its Inverse	p. 467
Solving DEs and IVPs with Laplace Transforms	p. 475
The Step Function and the Delta Function	p. 485
The Convolution Integral and the Transfer Function	p. 499
Laplace Transform Solution of Linear Systems	p. 509
Discrete Dynamical Systems
Iterative Equations	p. 517
Linear Iterative Systems	p. 530
Nonlinear Iterative Equations: Chaos Again	p. 542
Control Theory
Feedback Controls	p. 557
Introduction to Optimal Control	p. 567
Pontryagin Maximum Principle	p. 579
Table of Contents provided by Publisher. All Rights Reserved.