Worldwide Differential Equations

Robert McOwen

 

 

 

Worldwide Differential Equations

Worldwide Differential Equations with Linear Algebra
Robert McOwen – Northeastern University

ISBN-10: 0-9842071-2-0
ISBN-13: 978-0-9842071-2-1
265 Pages
©2012 Worldwide Center of Mathematics, LLC

Digital PDF | $14.95 go >
Print BW | $39.95 go >

 

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.

 

Contents

 

Chapter 1. First-Order Differential Equations
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

Chapter 2. Second-order Differential Equations

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

Chapter 3. Laplace Transform
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

Chapter 4. Systems of Linear Equations and Matrices
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

Chapter 5. Vector Spaces
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

Chapter 6. Linear Transformations and Eigenvalues
6.1 Introduction to Transformations & Eigenvalues
6.2 Diagonalization and Similarity
6.3 Symmetric and Orthogonal Matrices
6.4 Additional Exercises

Chapter 7. Systems of First-Order Equations
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

Appendices
A. Complex Numbers
B. Review of Partial Fractions
C. Table of Integrals
D. Table of Laplace Transforms
E. Answers to Some Exercises

 

Features

 

Adam, We need some content for here

 

Supplements

 

Select Solution Videos.
Videos will be added here as they are produced

Section 1.3 #4 go >
Section 1.4 #3 go >
     
Section 2.1 #4 go >
Section 2.1 #5 go >
Section 2.2 #9 go >
Section 2.3 #2c go >
Section 2.3 #3b go >
Section 2.4 #1 go >
Section 2.4 #7a go >
Section 2.5 #1b go >
Section 2.5 #2b go >
Section 2.6 #3b go >
Section 2.6 #6a go >
     
Section 3.1 #4c go >
Section 3.1 #4d go >
Section 3.1 #7a go >
Section 3.2 #3a go >
Section 3.3 #1b go >
Section 3.3 #2b go >
Section 3.3 #3a go >
Section 3.3 #6a go >
Section 3.4 #5a go >
     
Section 4.2 #3a go >
Section 4.3 #2d go >
Section 4.3 #3d go >
Section 4.4 #4f go >
Section 4.5 #1b go >
Section 4.6 #1d go >
     
Section 5.3 #5a go >
Section 5.3 #6a go >
Section 5.4 #1c go >
Section 5.4 #1d go >
Section 5.5 #1b go >
Section 5.5 #3a go >
     
Section 6.1 #1a go>
     
Section 7.2 #1a go>
Section 7.3 #1b go>
     
     

 

Author

 

Robert McOwen: Worldwide Differential Equations
Robert McOwen received his Ph.D. in Mathematics from UC Berkeley in 1978. After a one-year AMS-NSF postdoctoral fellowship that he took at the Courant Institute at NYU, he joined the Math Department at Northeastern University in Boston. Since then, he has taught many courses in analysis and differential equations at both the undergraduate and graduate levels. In 1996 he published a graduate-level textbook in partial differential equations; the second edition was published in 2003 and is still in use by many mathematics departments around the world. In 1997 he wrote a series of computer labs to accompany an undergraduate course in ordinary differential equations, which were packaged by the Publisher with the textbook and used for many years by all sections of the course at Northeastern. He continues to teach graduate and undergraduate courses in analysis and differential equations, and conducts research into the theory of partial differential equations.