Differential Equations and Linear Algebra

by Edwards, C. Henry; Penney, David E.

• ISBN13: 9780131481466
• ISBN10: 0131481460
• Edition: 3rd
• Format: Hardcover
• Copyright: 2010-01-01
• Publisher: Prentice Hall

Summary

Known for its real-world applications that grab readers' interest, this proven reference offers a full treatment of linear algebra.Discusses mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. Integrates scientific computing environments like Maple, Mathematica, and MATLAB. Extensively rewrites key sections with a fresh qualitative approach. Adds approximately 300 new computer-generated figures. Adds approximately 300 new or revised problems, many with a qualitative emphasis.A comprehensive reference for anyone who needs to improve their linear algebra skills.

Table of Contents

First Order Differential Equations

Differential Equations and Mathematical Models

Integrals as General and Particular Solutions

Slope Fields and Solution Curves

Separable Equations and Applications

Linear First Order Equations

Substitution Methods and Exact Equations

Mathematical Models and Numerical Methods

Population Models

Equilibrium Solutions and Stability

Acceleration-Velocity Models

Numerical Approximation

A Closer Look at the Euler Method

The Runge-Kutta Method

Linear Systems and Matrices

Introduction to Linear Systems

Matrices and Gaussian Elimination

Reduced Row-Echelon Matrices

Matrix Operations

Inverses of Matrices

Determinants

Linear Equations and Curve Fitting

Vector Spaces

The Vector Space R3

The Vector Space Rn and Subspaces

Linear Combinations and Independence of Vectors

Bases and Dimension for Vector Spaces

Row and Column Spaces

Orthogonal Vectors in Rn

General Vector Spaces

Higher Order Linear Differential Equations

Introduction

General Solutions of Linear Equations

Homogeneous Equations with Constant Coefficients

Mechanical Vibrations

Undetermined Coefficients and Variation of Parameters

Forced Oscillations and Resonance

Eigenvalues and Eigenvectors

Introduction to Eigenvalues

Diagonalization of Matrices

Applications Involving Powers of Matrices

Linear Systems of Differential Equations

Matrices and Linear Systems

The Eigenvalue Method for Linear Systems

Second-Order Systems and Mechanical Applications

Multiple Eigenvalue Solutions

Numerical Methods for Systems

Matrix Exponential Methods

Matrix Exponentials and Linear Systems

Nonhomogeneous Linear Systems

Spectral Decomposition Methods

Nonlinear Systems and Phenomena

Stability and the Phase Plane

Linear and Almost Linear Systems

Ecological Models: Predators and Competitors

Nonlinear Mechanical Systems

Laplace Transform Methods

Laplace Transforms and Inverse Transforms

Transformation of Initial Value Problems

Translation and Partial Fractions

Derivatives, Integrals, and Products of Transforms

Periodic and Piecewise Continuous Input Functions

Power Series Methods

Introduction and Review of Power Series

Power Series Solutions

Frobenius Series Solutions

Bessel Functions

References for Further Study

Existence and Uniqueness of Solutions

Theory of Determinants

Answers to Selected Problems

Index

Table of Contents provided by Publisher. All Rights Reserved.