Introduction to Linear Algebra and Differential Equations

ISBN-10: 0486651916
ISBN-13: 9780486651910
Edition: Reprint 
Authors: John W. Dettman
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Description: Excellent introductory text for students with 1 year of calculus. Topics include complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms,  More...

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Book details

List price: $16.95
Publisher: Dover Publications, Incorporated
Publication date: 12/1/1986
Binding: Paperback
Pages: 416
Size: 5.75" wide x 8.75" long x 1.00" tall
Weight: 1.188
Language: English

Excellent introductory text for students with 1 year of calculus. Topics include complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions and boundary-value problems. Includes 48 black-and-white illustrations. Exercises with solutions. Index.

Preface
Complex Numbers
Introduction
The Algebra of Complex Numbers
The Geometry of Complex Numbers
Two-dimensional Vectors
Functions of a Complex Variable
Exponential Function
Power Series
Linear Algebraic Equations
Introduction
Matrices
Elimination Method
Determinants
Inverse of a Matrix
Existence and Uniqueness Theorems
Vector Spaces
Introduction
Three-dimensional Vectors
Axioms of a Vector Space
Dependence and Independence of Vectors
Basis and Dimension
Scalar Product
Orthonormal Bases
Infinite-dimensional Vector Spaces
Linear Transformations
Introduction
Definitions and Examples
Matrix Representations
Changes of Bases
Characteristic Values and Characteristic Vectors
Symmetric and Hermitian Matrices
Jordan Forms
First Order Differential Equations
Introduction
An Example
Basic Definitions
First Order Linear Equations
First Order Nonlinear Equations
Applications of First Order Equations
Numerical Methods
Existence and Uniqueness
Linear Differential Equations
Introduction
General Theorems
Variation of Parameters
Equations with Constant Coefficients
Method of Undetermined Coefficients
Applications
Green's Functions
Laplace Transforms
Introduction
Existence of the Transform
Transforms of Certain Functions
Inversion of the Transform
Solution of Differential Equations
Applications
Uniqueness of the Transform
Power-Series Methods
Introduction
Solution near Ordinary Points
Solution near Regular Singular Points
Bessel Functions
Boundary-value Problems
Convergence Theorems
Systems of Differential Equations
Introduction
First Order Systems
Linear First Order Systems
Linear First Order Systems with Constant Coefficients
Higher Order Linear Systems
Existence and Uniqueness Theorem
Answers and Hints for Selected Exercises
Index

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