Worldwide Differential Equations with Linear Algebra

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Robert McOwen– Northeastern University

ISBN-10: 0-9842071-2-0
ISBN-13: 978-0-9842071-2-1
265 Pages
©2019 Worldwide Center of Mathematics, LLC

Digital | $19.95
Print | $39.95 + shipping

 

Features

 

contents

 

Supplements

Introduction

Dr. McOwen’s Differential Equations with Linear Algebra is a concisely written textbook filled with the information necessary to understand the basics of both differential equations and linear algebra. The first part of the book teaches students first and second order differential equations and Laplace transformations; the second part of the book discusses the basics of linear algebra and how one can examine matrices; the third and final part of the book deals with problems that require knowledge in both linear algebra and differential equations.

The book features exercises that test a student’s understanding of the basic concepts, with answers to all included at the back of the book. Additionally, there are supplemental exercises for classes that are more advanced, with answers to odd numbered exercises in the appendix. Electronic resources are included to supplement the book, and the format of the book is such that the instructor can choose which topics to cover and which to omit.


Features

This textbook is designed for a one-semester undergraduate course in ordinary differential equations and linear algebra. Here are some of its features:

i) First and second-order differential equations are covered in Chapters 1 & 2, the Laplace transform in Chapter 3, linear algebra (matrices, vector spaces, and eigenvalues) in Chapters 4-6, and systems of differential equations in Chapter 7. Other texts on this subject tend to alternate more between differential equations and linear algebra.

ii) This text adopts a fairly concise writing style and careful selection of topics to keep the book shorter than many others on this subject. Moreover, the material is arranged in such a way as to conveniently allow the instructor to select which topics to cover and which to leave out.

iii) Exercises at the end of each section develop basic skills, and exercises at the end of each chapter provide more challenging problems. Answers to all basic skill problems are provided in the appendix, as are the answers to the odd-numbered challenging problems.


  • Written by an award-winning mathematics professor with over 30 years of teaching experience
  • Down-to-Earth exposition, presented as it would be spoken in class
  • Completely rigorous definitions, statements of theorems, and proofs
  • Hyperlinked table of contents, index, and cross-references
  • Video-solutions to select exercises
  • PDF format, compatible with all computers, tablets, and mobile devices
  • Low cost in electronic or print form

Contents

  • 1.1 Differential Equations and Mathematical Models
  • 1.2 Geometric Analysis and Existence/Uniqueness
  • 1.3 Separable Equations & Applications
  • 1.4 Linear Equations & Applications
  • 1.5 Additional Methods
  • 1.6 Additional Exercises
  • 2.1 Introduction to Higher-Order Equations
  • 2.2 General Solutions for Second-Order Equations
  • 2.3 Homogeneous Equations with Constant Coefficients
  • 2.4 Free Mechanical Vibrations
  • 2.5 Nonhomogeneous Equations with Constant Coefficients
  • 2.6 Forced Mechanical Vibrations
  • 2.7 Electrical Circuits
  • 2.8 Additional Exercises
  • 3.1 Laplace Transform and Its Inverse
  • 3.2 Transforms of Derivatives and Initial Value Problems
  • 3.3 Shifting Theorems
  • 3.4 Discontinuous Inputs
  • 3.5 Convolutions
  • 3.6 Additional Exercises
  • 4.1 Introduction to Systems and Matrices
  • 4.2 Gaussian Elimination
  • 4.3 Reduced Row-Echelon Form and Rank
  • 4.4 Inverse of a Square Matrix
  • 4.5 The Determinant of a Square Matrix
  • 4.6 Cofactor Expansions
  • 4.7 Additional Exercises
  • 5.1 Vectors in Rn
  • 5.2 General Vector Spaces
  • 5.3 Subspaces and Spanning Sets
  • 5.4 Linear Independence
  • 5.5 Bases and Dimension
  • 5.6 Row and Column Spaces
  • 5.7 Inner Products and Orthogonality
  • 5.8 Additional Exercises
  • 6.1 Introduction to Transformations & Eigenvalues
  • 6.2 Diagonalization and Similarity
  • 6.3 Symmetric and Orthogonal Matrices
  • 6.4 Additional Exercises
  • 7.1 Introduction to First-Order Systems
  • 7.2 Theory of First-Order Linear Systems
  • 7.3 Eigenvalue Method for Homogeneous Systems
  • 7.4 Applications to Multiple Tank Mixing
  • 7.5 Applications to Mechanical Vibrations
  • 7.6 Additional Exercises
  • A. Complex Numbers
  • B. Review of Partial Fractions
  • C. Table of Integrals
  • D. Table of Laplace Transforms
  • E. Answers to Some Exercises

 

 

Supplements

  • Worldwide Differential Equations w/ Linear Algebra Solution Manual (faculty) go > — Faculty may request the available free digital resources online.
  • Worldwide Differential Equations w/ Linear Algebra Video Playlist (free) go > — Worldwide Differential Equations w/ Linear Algebra features associated video selections made available free on the Center of Math YouTube Channel. Video links are directly embedded in the digital textbook.
  • WebAssign go > — Worldwide Differential Equations w/ Linear Algebra is available with WebAssign. WebAssign is a powerful digital solution designed by educators to enrich the teaching and learning experience. WebAssign provides extensive content, instant assessment, and superior support.