For each week there will be a link to a page with a reading assignment and a homework assignment.
This schedule is tentative. It will get more accurate as the semester progresses. No week's topics should be taken as final until the homework is linked. Solutions to the homework assignments will be posted after the due date for each assignment.
The following abbreviations will be used:
Book
Ordinary Differential Equations (second edition) by Polking, Boggess & Arnold
Manual
Ordinary Differential Equations using MATLAB (third edition) by Arnold & Polking
Week #1:
August 28--September 1
Assignment #1 Solutions #1 |
Introduction to ODEs
Plotting in MATLAB ODEs and their solutions Solutions to separable equations |
Week #2:
September 4--8
Assignment #2 Solutions #2 (Textbook) (changes: each pb=10 points; pb 1/2.3 t=612244 s; pb 4/2.3 is ok if "a" is used instead of "a-g") Solutions #2 (Manual) |
Solutions to separable equations
Models of motion Linear equations |
Week #3:
September 11--15
Assignment #3 Solutions #3 |
Linear Equations
Mixing problems Existence and Uniqueness |
Week #4: September 18--22 |
Uniqueness; Dependence on initial conditions
Autonomous equations and stability |
Week #5:
September 25--29
Assignment #4 Solutions #4 |
Modelling
Numerical methods - Euler's method You can download dfield, pplane, odesolve, eul, rk2, rk4 from http://math.rice.edu/~dfield |
Week #6:
October 2--6
Assignment #5 Solutions #5 |
Runge-Kutta methods; ODE45
Vectors and matrices |
Week #7: October 9--13 |
Solving systems of linear equations
Properties of solution spaces Homogeneous and Inhomogeneous systems; nullspace |
Week #8 :
October 16--20
Assignment #6 Solutions #6 |
Subspaces (base, span, linear dependence and independence)
Determinants |
Week #9:
October 23--October 27
Assignment #7 Solutions #7 |
Introduction to systems
Geometric interpretation of solutions (pplane); Qualitative analysis Linear systems of ODEs; Solutions to systems You can download pplane from http://math.rice.edu/~dfield |
Week #10:
October 30---November 3
Assignment #8 Solutions #8 |
Eigenvalues, eigenvectors, and solutions of systems
Planar systems of ODEs; Phase plane portraits |
Week #11: November 6---November 10 |
The exponential of a matrix
Higher order dimensional systems |
Week #12:
November 13---17
Assignment #9 Solutions #9 |
Higher order linear equations
Examples (planar systems and high linear equations) |
Week #13: November 20--24 |
Inhomogeneous systems and equations (Variation of parameters and Undetermined coefficients) |
Week #14:
November 27--December 1
Assignment #9 continued Solutions #9 continued |
2^{nd} order equations; Vibrating springs (handout)
Forced harmonic oscillators, forcing and resonance (handout) The linearization of nonlinear systems |
Week #15: December 4--8 |
Invariant sets and the use of nullclines
Long term behavior of planar systems |