Course Materials
Required calculator
You can use any calculator you wish when you do your homework, but your instructor's best advice is to put your graphing calculator away until you get into your Junior-level courses. Once you know the mathematics it's easy to learn to do it on the calculator or computer. If you rely on the calculator when learning mathematics, you are almost certain to miss some of the essential aspects of the subject.
The only calculator permitted on tests will be the Casio fx-260. This is the same calculator that is legal for the SAT. This calculator is inexpensive, and is available through the VHCC bookstore as well as online.
The textbook is
Elementary Differential Equations
Video lectures are now posted online through YouTube.
If you don't have a fast Internet connection it is recommended that you purchase USB flash memory devices containing the video content formerly on the DVD's. These devices will be made available, at your request, by the VHCC bookstore. The cost will be that of the device itself plus a $5 service charge. You may call the bookstore to ask for the price of the device, which is a 32 GB USB flash memory stick.
To request this option email the instructor with your mailing address.
To contact the VHCC bookstore call 276-739-2400 and ask for the bookstore.
Playing the videos
Nearly any Windows computer will be equipped to play the videos. Computers running other operating systems might not be so equipped.
If your computer is not equipped to play these videos, there are a number of free players that will do so. It is up to you to decide which one best meets your needs.
When I ask for recommendations, the one player that is almost universally recommended is the VLC Player. If you search for VLC player you will easily be able to find and evaluate it. The current website is http://www.videolan.org/vlc/ ; however the site could well change without my being aware of it, so if the link doesn't work do the search.
- The Second Edition has consolidated Chapters 2 and 3 into Chapter 2, and Chapters 4 and 5 into Chapter 3.
- Second Edition sections 3.11 - 3.13 correspond to Chapter 5 of the first edition and are not covered.
- First Edition Chapter 6 is now Second Edition Chapter 4.
- First Edition Chapter 7 is Second Edition Chapter 5
- First Edition Chapter 8 is Second Edition Chapter 6.
- Second Edition coverage will therefore be Chapters 1 - 4, excepting Sections 3.11 - 3.13; plus approximately half of Chapter 5 and some topics from Chapter 6.
Elementary Differential Equations
ISBN-10: 0201709260
ISBN-13: 9780201709261Publisher: Pearson
Copyright: 2003
Format: Cloth; 760 pp
Published: 12/06/20021. Introduction to Differential Equations.
Examples of Differential Equations.Direction Fields.
2. First Order Linear Differential Equations.
Existence and Uniqueness.First Order Linear Homogeneous Differential Equations.First Order Linear Nonhomogeneous Differential Equations.Introduction to Mathematical Models.Mixing Problems and Cooling Problems.
3. First Order Nonlinear Differential Equations.
Existence and Uniqueness.Separable First Order Equations.Exact Differential Equations.Bernoulli Equations.The Logistic Population Model.One-Dimensional Motion with Air Resistance.One-Dimensional Dynamics with Distance as the Independent Variable.Euler's Method.
4. Second Order Linear Differential Equations.
Existence and Uniqueness.The General Solution of Homogeneous Equations.Fundamental Sets and Linear Independence.Constant Coefficient Homogeneous Equations.Real Repeated Roots; Reduction of Order.Complex Roots.Unforced Mechanical Vibrations.The General Solution of the Linear Nonhomogeneous Equation.The Method of Undetermined Coefficients.The Method of Variation of Parameters.Forced Mechanical Vibrations, Electrical Networks, and Resonance.
6. First Order Linear Systems.
The Calculus of Matrix Functions.Existence and Uniqueness.Homogeneous Linear Systems.Fundamental Sets and Linear Independence.Constant Coefficient Homogeneous Systems.Complex Eigenvalues.
Repeated Eigenvalues.Nonhomogeneous Linear Systems.Euler's Method for Systems of Differential Equations.Diagonalization.Propagator Matrices, Functions of a Matrix and the Exponential Matrix.
7. Laplace Transforms.
The Laplace Transform.Laplace Transform Pairs.Review of Partial Fractions.Solving Scalar Problems. Laplace Transforms of Periodic Functions.Solving Systems of Differential Equations.Convolution.The Delta Function and Impulse Response.
8. Nonlinear Systems.
Existence and Uniqueness.Equilibrium Solutions and Direction Fields.Conservative Systems.Stability.Linearization and the Local Picture.The Two-dimensional Linear System y1=Ay.Predator-Prey Population Models.
Elementary Differential Equations Bound with IDE CD Package, 2/E
ISBN-10: 0321398491
ISBN-13: 9780321398499Publisher: Pearson
Copyright: 2006
Format: Cloth Bound w/CD-ROM
Published: 09/28/2005
Status: Instock
Table of Contents
1: INTRODUCTION TO DIFFERENTIAL EQUATIONS
1.1 Examples of Differential Equations
1.2 Direction Fields
2: FIRST ORDER DIFFERENTIAL EQUATIONS
2.1 Introduction
2.2 First Order Linear Differential Equations
2.3 Introduction to Mathematical Models
2.4 Population Dynamics and Radioactive Decay
2.5 First Order Nonlinear Differential Equations
2.6 Separable First Order Equations
2.7 Exact Differential Equations
2.8 The Logistic Population Model
2.9 Applications to Mechanics
2.10 Euler’s Method
2.11 Review Exercises
3: SECOND AND HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS
3.1 Introduction
3.2 The General Solution of Homogeneous Equations
3.3 Constant Coefficient Homogeneous Equations
3.4 Real Repeated Roots; Reduction of Order
3.5 Complex Roots
3.6 Unforced Mechanical Vibrations
3.7 The General Solution of a Linear Nonhomogeneous Equation
3.8 The Method of Undetermined Coefficients
3.9 The Method of Variation of Parameters
3.10 Forced Mechanical Vibrations, Electrical Networks, and Resonance
3.11 Higher Order Linear Homogeneous Differential Equations
3.12 Higher Order Homogeneous Constant Coefficient Differential Equations
3.13 Higher Order Linear Nonhomogeneous Differential Equations
3.14 Review Exercises
4: FIRST ORDER LINEAR SYSTEMS
4.1 Introduction
4.2 Existence and Uniqueness
4.3 Homogeneous Linear Systems
4.4 Constant Coefficient Homogeneous Systems and the Eigenvalue Problem
4.5 Real Eigenvalues and the Phase Plane
4.6 Complex Eigenvalues
4.7 Repeated Eigenvalues
4.8 Nonhomogeneous Linear Systems
4.9 Numerical Methods for Systems of Differential Equations
4.10 The Exponential Matrix and Diagonalization
4.11 Review Exercises
5: LAPLACE TRANSFORMS
5.1 Introduction
5.2 Laplace Transform Pairs
5.3 The Method of Partial Fractions
5.4 Laplace Transforms of Periodic Functions and System Transfer Functions
5.5 Solving Systems of Differential Equations
5.6 Convolution
5.7 The Delta Function and Impulse Response
6: NONLINEAR SYSTEMS
6.1 Introduction
6.2 Equilibrium Solutions and Direction Fields
6.3 Conservative Systems
6.4 Stability
6.5 Linearization and the Local Picture
6.6 Two-Dimensional Linear Systems
6.7 Predator-Prey Population Models