Weekly Schedule

MATH 308. Differential Equations.(3-0) Credit 3.0. Introduction to Ordinary Differential Equations covering abstract ideas of vector space and linear transformation as well as models and applications of these concepts, such as systems of linear equations, matrices and determinants. Prerequisite: MATH 152.

Textbook: Differential Equations, An Introduction to Modern Methods and Applications by William E. Boyce & James R.Brannan

Suggested Schedule

• Chapter 1: 2 days
  • Section 1.1. Some Basic Mathematical Models; Direction Fields
  • Section 1.2. Solutions of Some Differential Equations
• Chapter 2: 5 days
  • Section 2.1. Linear Equations; Method of Integrating Factors - one day
  • Section 2.2. Seperable Equations - one day
  • Section 2.3. Modeling with First Order Equations - one day
  • Section 2.4. Differences Between Linear and Nonlinear Equations
  • Section 2.5. Autonomous Equations and Population Dynamics
  • Section 2.6. Exact Equations and Integrating Factors
  • Do 2.4, 2.5 and 2.6 in two days, doing only one representative example from 2.5
• Chapter 3: 5 days
  • Section 3.1. Systems of Two Linear Algebraic Equations - one day
  • Section 3.2. Systems of Two First Order Linear Differential Equations - one day
  • Section 3.3. Homogeneous Linear Systems with Constant Coefficients - one day
  • Section 3.4. Complex Eigenvalues - one day
  • Section 3.6. A Brief Introduction to Nonlinear Systems - one day
• Chapter 7: 4 days
  • Section 7.1. Autonomous Systems and Stability - one day
  • Section 7.2. Almost Linear Systems - one day
  • Section 7.3. Competing Species - one day
  • Section 7.4. Predator-Prey Equations - one day
  • Section 7.5. Periodic Solutions and Limit Cycles - Optional
  • Section 7.6. Chaos and Strange Attractors: The Lorenz Equations - Optional
• Chapter 4: 5 days
  • Section 4.1. Definitions and Examples
  • Section 4.2. Theory of Second Order Linear Homogeneous Equations (Cover 4.1 and 4.2 in one day)
  • Section 4.3. Linear Homogeneous Equations with Constant Coefficients - one day
  • Section 4.4. Characteristic Equations with Complex Roots - one day
  • Section 4.5. Mechanical and Electrical Vibrations - optional
  • Section 4.6. Nonhomogeneous Equations: Method of Undetermined Coefficients - one day
  • Section 4.7. Forced Vibrations, Frequency Response, and Resonance - optional
  • Section 4.8. Variation of Parameters - one day
• Chapter 5: 8 days
  • Section 5.1. Definition of the Laplace Transform - one day
  • Section 5.2. Properties of the Laplace Transform - one day
  • Section 5.3. The Inverse Laplace Transform - one day
  • Section 5.4. Solving Differential Equations with Laplace Transforms - one day
  • Section 5.5. Discontinuous Functions with Laplace Transforms - one day
  • Section 5.6. Differential Equations with Discontinuous Forcing Functions - one day
  • Section 5.7. Impulse Functions - one day
  • Section 5.8. Convolution Integrals and Their Applications - one day
  • Section 5.9. Linear Systems and Feedback Control - optional
• Chapter A (Appendix A): 4 days
  • Section A.1. Matrices
  • Section A.2. Systems of Linear Algebraic Equations, Linear Independence, and Rank
  • Section A.3. Determinants and Inverses
  • Section A.4. the Eigenvalue Problem
• Chapter 6: 6 days
  • Section 6.1. Definitiions and Examples
  • Section 6.2. Basic Theory of First order Linear Systems
  • Section 6.3. Homogeneous Linear systems with Constant Coefficients
  • Section 6.4. Complex Eigenvalues
  • Section 6.5. Fundamental Matrices and the Exponential of a Matrix
  • Section 6.6. Nonhomogeneous Linear Systems

Add in three days for exams and this will give a total of 42 days.

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Please send comments, questions, or suggestions to Alisa Baron at "alisa@math.tamu.edu".
Last updated FRI, 21/Aug/2009