Differential Equations and Linear Algebra

ISBN-10: 0131481460

ISBN-13: 9780131481466

Edition: 2nd 2005 (Revised)

List price: $133.33
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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.
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Book details

List price: $133.33
Edition: 2nd
Copyright year: 2005
Publisher: Prentice Hall PTR
Publication date: 3/23/2004
Binding: Hardcover
Pages: 784
Size: 8.25" wide x 10.00" long x 1.25" tall
Weight: 3.542
Language: English

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
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
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
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