1. The official course schedule should be consulted for anouncement of due dates for labs and homework.
  2. Section references are to the course text:
    Differential Equations: Computing and Modeling, Fourth Edition by C. Henry Edwards and David E. Penney, 2008, Pearson Education.

 

Weekly Schedule
Week 1
Day Lecture Matlab Files Topic
Wed (9/3)
  1. fig1.m
  2. fig2.m
Sections 1.1, 1.2, 1.3 : Mathematical modeling with differential equations, solutions given by integrals, and slope fields
Fri (9/5)
  1. fig1.m
Sections 1.4, 1.5 : Separable and linear first-order differential equations
Week 2
Day Lecture Matlab Files Topic
Mon (9/8)
  1. fig1.m
  2. fig2.m
  3. fig3.m
  4. fig4.m
  5. fig5.m
Section 2.1 : Differential equations for population modeling
Wed (9/10) Section 2.2 : Equilibria and their stability
Fri (9/12) Section 2.3 : Differential equations for kinematics of velocity and acceleration
Week 3
Day Lecture Matlab Files Topic
Mon (9/15) REVIEW
Wed (9/17)
  1. euler1.m
  2. euler2.m
Sections 2.4, 2.5, 2.6 : Numerical methods for approximating solutions of initial-value problems for differential equations
Fri (9/19)
  1. rk.m
REVIEW
Week 4
Day Lecture Matlab Files Topic
Mon (9/22) Section 3.1 : Second-order linear differential equations
Wed (9/24) Complex Numbers
Fri (9/26) Sections 3.2, 3.3 : Second-order linear homogeneous equations with constant coefficients
Week 5
Day Lecture Matlab Files Topic
Mon (9/29) Section 3.3 continued
Wed (10/1)
  1. Mass-spring in action
Section 3.4 : Differential equations governing mechanical vibrations
Fri (10/3) Review
Week 6
Day Lecture Matlab Files Topic
Mon (10/6) Exam 1 : 6-8pm REVIEW
Wed (10/8) Section 3.5 : Nonhomogeneous terms, the method of undetermined coefficients, and the method of variation of parameters
Fri (10/9) Section 3.5 continued
Week 7
Day Lecture Matlab Files Topic
Mon (10/13) Section 3.6 : Forced oscillations and resonance
Wed (10/15) Sections 4.1, 4.2 : First-order systems of differential equations and the method of elimination
Fri (10/16) Section 4.3 : Numerical methods for systems of first-order equations
Week 8
Day Lecture Matlab Files Topic
Mon (10/20) NO CLASS
Wed (10/22) Sections 5.1 : Linear algebra, eigenvalues and eigenvectors
Fri (10/24) Section 5.1 continued
Week 9
Day Lecture Matlab Files Topic
Mon (10/27) Sections 5.1 continued
Wed (10/29) Sections 5.2 : Homogeneous constant-coefficient linear systems and eigenvalues
Fri (10/31) Section 5.2 continued
Week 10
Day Lecture Matlab Files Topic
Mon (11/3) Sections 5.3 : Mechanical vibrations governed by second-order systems of differential equations
Wed (11/5) Sections 6.1 : Phase portraits for autonomous systems, and stability of equilibria
Fri (11/7) Section 6.2 : Linear and almost linear systems; Linearization and the Jacobian matrix
Week 11
Day Lecture Matlab Files Topic
Mon (11/10) EXAM 2 : 6-8pm REVIEW
Wed (11/12) Sections 6.3 : Ecological models of predators and prey
Fri (11/7)
  • rk2.m (Runge-Kutta solver for 2x2 systems)
Section 6.4 : Nonlinear mechanical systems
Week 12
Day Lecture Matlab Files Topic
Mon (11/17)
  1. Lorenz equations (applet)
  2. Lorenz equation (matlab file) (Demonstration of evolving trajectory).
REVIEW
Wed (11/19) Sections 7.1 : Laplace and inverse Laplace transforms
Fri (11/21) Section 7.2 : Application of Laplace transforms to initial-value problems for constant-coefficient linear equations and system
Week 13
Day Lecture Matlab Files Topic
Mon (11/24) Section 7.3 : Laplace transforms involving translation in time and in the transform variable, and use of partial fraction representations
Wed (11/26) NO CLASS
Fri (11/28) NO CLASS
Week 14
Day Lecture Matlab Files Topic
Mon (12/1) Section 7.4 : Products of Laplace transforms and convolution integrals. Differentiation and integration of Laplace transform
Wed (12/3) Sections 7.5 : Laplace transforms of periodic and piecewise continuous functions
Fri (12/5) Section 7.6 : Impulses (delta functions) and impulse response
Week 15
Day Lecture Matlab Files Topic
Mon (12/8) REVIEW