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Texas A&M University
Mathematics

MATH 308 - Suggested Weekly Schedule

Note: This is a fall or spring schedule. In summer, this schedule is accelerated by 50% in order to accommodate a 10-week session.

MATH 308. Differential Equations.(3-0) Credit 3.0. Ordinary differential equations, solutions in series, solutions using Laplace transforms, systems of differential equations. Prerequisites: MATH 251 or equivalent; knowledge of computer algebra system.

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.

    Please send comments, questions, or suggestions to Alisa Baron at "alisa@math.tamu.edu".
    Updated October 1, 2009 rlc