Differential Equations and Linear Algebra

ISBN-10: 0136054250
ISBN-13: 9780136054252
Edition: 3rd 2010
List price: $204.40 Buy it from $99.98 Rent it from $82.75
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Description: 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  More...

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Book details

List price: $204.40
Edition: 3rd
Copyright year: 2010
Publisher: Prentice Hall PTR
Publication date: 10/10/2008
Binding: Hardcover
Pages: 792
Size: 8.00" wide x 10.25" long x 1.25" tall
Weight: 3.960
Language: English

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.

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
Accelerationndash;Velocity Models
Numerical Approximation: Euler's Method
A Closer Look at the Euler Method
The Rungendash;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: Second-Order Linear Equations
General Solutions of Linear Equations
Homogeneous Equations with Constant Coefficients
Mechanical Vibrations
Nonhomogeneous Equations and Undetermined Coefficients
Forced Oscillations and Resonance
Eigenvalues and Eigenvectors
Introduction to Eigenvalues
Diagonalization of Matrices
Applications Involving Powers of Matrices
Linear Systems of Differential Equations
First-Order Systems and Applications
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
Existence and Uniqueness of Solutions
Theory of Determinants Answers to Selected Problems
Index
Application Modules The modules listed here follow the indicated sections in the text
Most provide computing projects that illustrate the corresponding text sections
Maple, Mathematica, and MATLAB versions of these investigations are included in the Applications Manual that accompanies this textbook
Computer-Generated Slope Fields and Solution Curves
The Logistic Equation
Indoor Temperature Oscillations
Computer Algebra Solutions
Logistic Modeling of Population Data
Rocket Propulsion
Implementing Euler's Method
Improved Euler Implementation
Runge-Kutta Implementation
Automated Row Operations
Automated Row Reduction
Automated Solution of Linear Systems
Plotting Seco

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