Introduction to Linear Algebra and Differential Equations

Name: Introduction to Linear Algebra and Differential Equations
Price: 4.36 USD
Availability: InStock
ISBN: 9780486651910

ISBN-10: 0486651916

ISBN-13: 9780486651910

Edition: Reprint

Authors: John W. Dettman

List price: $16.95

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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, Bessel functions and boundary-value problems. Includes 48 black-and-white illustrations. Exercises with solutions. Index.

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: 0.946
Language: English



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