Introduction to Linear Algebra and Differential Equations [NOOK Book]

Overview



Excellent introductory text for students with one 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.
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Introduction to Linear Algebra and Differential Equations

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Overview



Excellent introductory text for students with one 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.
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Product Details

  • ISBN-13: 9780486158310
  • Publisher: Dover Publications
  • Publication date: 9/7/2012
  • Series: Dover Books on Mathematics
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 416
  • Sales rank: 501,050
  • File size: 19 MB
  • Note: This product may take a few minutes to download.

Table of Contents

Preface
1. Complex Numbers
1.1 Introduction
1.2 The Algebra of Complex Numbers
1.3 The Geometry of Complex Numbers
1.4 Two-dimensional Vectors
1.5 Functions of a Complex Variable
1.6 Exponential Function
1.7 Power Series
2. Linear Algebraic Equations
2.1 Introduction
2.2 Matrices
2.3 Elimination Method
2.4 Determinants
2.5 Inverse of a Matrix
2.6 Existence and Uniqueness Theorems
3. Vector Spaces
3.1 Introduction
3.2 Three-dimensional Vectors
3.3 Axioms of a Vector Space
3.4 Dependence and Independence of Vectors
3.5 Basis and Dimension
3.6 Scalar Product
3.7 Orthonormal Bases
3.8 Infinite-dimensional Vector Spaces
4. Linear Transformations
4.1 Introduction
4.2 Definitions and Examples
4.3 Matrix Representations
4.4 Changes of Bases
4.5 Characteristic Values and Characteristic Vectors
4.6 Symmetric and Hermitian Matrices
4.7 Jordan Forms
5. First Order Differential Equations
5.1 Introduction
5.2 An Example
5.3 Basic Definitions
5.4 First Order Linear Equations
5.5 First Order Nonlinear Equations
5.6 Applications of First Order Equations
5.7 Numerical Methods
5.8 Existence and Uniqueness
6. Linear Differential Equations
6.1 Introduction
6.2 General Theorems
6.3 Variation of Parameters
6.4 Equations with Constant Coefficients
6.5 Method of Undetermined Coefficients
6.6 Applications
6.7 Green's Functions
7. Laplace Transforms
7.1 Introduction
7.2 Existence of the Transform
7.3 Transforms of Certain Functions
7.4 Inversion of the Transform
7.5 Solution of Differential Equations
7.6 Applications
7.7 Uniqueness of the Transform
8. Power-Series Methods
8.1 Introduction
8.2 Solution near Ordinary Points
8.3 Solution near Regular Singular Points
8.4 Bessel Functions
8.5 Boundary-value Problems
8.6 Convergence Theorems
9. Systems of Differential Equations
9.1 Introduction
9.2 First Order Systems
9.3 Linear First Order Systems
9.4 Linear First Order Systems with Constant Coefficients
9.5 Higher Order Linear Systems
9.6 Existence and Uniqueness Theorem
Answers and Hints for Selected Exercises; Index
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Sort by: Showing all of 2 Customer Reviews
  • Anonymous

    Posted February 20, 2013

    Useless

    This book is useless. It does not function. The nook app skips pages, the fonts are ridiculous and arbitrary, there are hundreds, maybe thousands of serious mistakes in the text. I am furious that I was forced to buy this book for a class and the ebook form of it was USELESS. You basically just stole my money.
    I can't believe I am forced to give it one star. I wish the rating system had negative 3 or 4 stars so I could give this book the rating it deserves.

    Was this review helpful? Yes  No   Report this review
  • Anonymous

    Posted November 8, 2000

    And the reason is . . .?

    Makes a very good reference book, but as a high school student completing calculus, it was a bit challenging to grasp the concepts. Dettman shows great understanding of the math, but is in need of developing his editorial skills.

    Was this review helpful? Yes  No   Report this review
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