MATH 308 - Suggested Weekly Schedule

Notes:

1. This is a Fall (or Spring) schedule. In Summer, the schedule is
   accelerated by 50% in order to accommodate a 10-week session.
2. Assignments incorporating dsolve, ode45, dfield,and pplane will be made.
   They will be created so as to be gradeable within a 3.5 hour/week timeframe.

• Week 1
  • Section 1.1: Some Bacic Mathematical Models; Direction Fields
  • Section 1.2: Solutions of Some Differential Equations
  • Section 1.3: Classification of Differential Equations
  • JAVA: dfield app illustrated in class (20 minutes)
• Week 2
  • Section 2.1: Linear Equations; Method of Integrating Factors
  • Section 2.2: Separable Equations
  • Section 2.3: Modeling with First Order Equations
• Week 3
  • 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
  • MATLAB: dsolve command illustrated in class (20 minutes)
• Week 4
  • Section 3.1: Homogeneous Equations with Constant Coefficients
  • Section 3.2: Solutions of Linear Homogeneous Equations
  • Section 3.3: Complex Roots of the Characteristic Equation
• Week 5
  • Section 3.4: Repeated Roots; Reduction of Order
  • Section 3.5: Nonhomogeneous Equations; Method of Undetermined Coefficients
  • Section 3.6: Variation of Parameters
• Week 6
  • Section 3.7: Mechanical and Electrical Vibrations
  • Section 3.8: Forced Vibrations
  • Exam 1 (Chapters 1-3)
• Week 7
  • Section 6.1: Definition of the Laplace Transform
  • Section 6.2: Solution of Initial Value Problems [via Laplace Transforms]
  • Section 6.3: Step Functions
• Week 8
  • Section 6.4: Differential Equations with Discontinuous Forcing Functions
  • Section 6.5: Impulse Functions
  • Section 6.6: The Convolution Integral
• Week 9
  • Section 5.1: Review of Power Series
  • Section 5.2: Series Solutions Near an Ordinary Point I
• Week 10
  • Section 5.3: Series Solutions Near an Ordinary Point II
  • Section 7.1: Introduction [to Systems of 1st Order Equations]
  • Section 7.2: Review of Matrices
  • Section 7.3: Linear Algebraic Equations; Eigenvalues, Eigenvectors
• Week 11
  • Section 7.4: Basic Theory of Systems of First Order Linear Equations
  • Section 7.5: Homogeneous Linear Equations with Constant Coefficients
  • Section 7.6: Complex Eigenvalues
  • Section 7.7: Fundamental Matrices
  • Exam 2 (Chapters 3, 5, 6)
• Week 12
  • Section 7.8: Repeated Eigenvalues
  • Section 7.9: Nonhomogeneous Linear Systems
• Week 13
  • Section 9.1: The Phase Plane: Linear Systems
  • Section 9.2: Autonomous Systems and Stability
  • JAVA: pplane app illustrated in class (20 minutes)
  • Thanksgiving break (in Fall semester)
• Week 14
  • Section 9.3: Locally Linear Systems
  • Section 8.1: The Euler or Tangent Line Method
  • Section 8.2: Improvements on the Euler Method
  • MATLAB: ode45 command illustrated in class (20 minutes)
• Week 15
  • Section 8.3: The Runge-Kutta Method
  • Final Exams