Math 254 -- Introduction to Ordinary Differential Equations

Fall 2016

When: MWF 1200--1250
Where: PAS 414
Instructor: Kevin K Lin

Office: Math 606
Phone: 626-6628
E-mail: klin@math.arizona.edu

Course web page (this page):
http://math.arizona.edu/~klin/254

D2L page:
https://d2l.arizona.edu/d2l/home/520850

Office hours: see here

About this course

Course policy, last updated on August 22, 2016.

Course calendar.

Syllabus, last updated on December 09, 2016.

Announcements

(Last revised on December 05, 2016.) 
- Final exam <2016-12-15 Thu> :: 
  - 10:30 -- 12:30 in our usual room
  - The final will be cumulative, up to and including
    Section 5.4 (phase planes).

- HW13 due <2016-12-07 Wed> :: 
  - Section 5.4 #2, 6, 10.  (Problem 6 asks for the
    "critical point set", which is just the set of all fixed
    points.)
  - Strogatz 6.3.1.  (You are welcome to use a computer
    program like pplane to check your answer.)

- HW12 due <2016-11-30 Wed> ::
  - Section 9.5 #35(a,b,c)
  - Section 9.6 #1, 6, 13(a)
  - Section 9.7 #2, 4
  - Section 7.9 #4

- HW11 due <2016-11-18 Fri> (note revised due date) ::
  - Section 9.4 #21, 22, 23, 25, 37*
  - Section 9.5 #2, 11, 12, 19
  - *: EXTRA CREDIT.  This problem is a bit harder than the
    others.  Make sure you can do all the other problems
    before doing this one.
  - I won't be adding more problems.

- HW10 due <2016-11-02 Wed> ::
  - Section 7.6 #20, 22, 24, 26, 36, 50.
  - Section 7.7 #8, 10, 12, 14, 20*, 26.
    (* We did not discuss integral equations in class, but
    they can be solved in a straightforward way using the
    Laplace transforms.  See example in Section 7.7.)
  - Section 7.8 #2, 3, 4, 5, 9, 11, 14, 18, 28.

- HW9 due <2016-10-26 Wed> :: 
  - Section 7.4 #1, 3, 5, 6, 10, 22, 24, 26.
  - Section 7.5 #3, 4, 8, 9, 18, 21, 36.
  - Section 7.6 #4, 5, 7, 11, 14.

- HW8 due <2016-10-19 Wed> ::
  - Section 7.2 #1, 2, 4, 7, 9, 10, 31.
  - Section 7.3 #1, 2, 3, 4, 8, 12, 16, 25.
    - (For #12 and 16, you can either use a trig identity OR
      express sine and cosine in terms of complex
      exponentials.)

- HW7 due <2016-10-07 Fri> ::
  - Section 4.5 #2, 9, 10, 11, 12, 31, 32.
  - Section 4.6 #4, 10, 18.

- HW6 due <2016-10-05 Wed> ::
  - Section 4.4 #1, 3, 5, 7, 10, 18, 20, 22, 28, 30, 32.

- A short glossary of terms so far

- Note on existence + uniqueness

- Get dfield and pplane from http://math.rice.edu/~dfield/dfpp.html

- older announcements

Syllabus

(Last revised on December 09, 2016.)
  • Week 1 <2016-08-22 Mon>
  • 1.1 Introduction
  • 1.2 Initial value problems (IVPs)
  • 1.3 Direction fields
  • Week 2 <2016-08-29 Mon>
  • 1.4 Euler's method
  • 2.1, 2.2 First-order separable ODEs
  • 2.3 Linear 1st-order ODEs via integrating factors
  • Week 3 <2016-09-05 Mon> (Labor Day)
  • 2.4 Exact equations
  • 2.5 Integrating factors
  • 4.1 Linear 2nd-order ODEs: mass-spring systems
  • 4.2 Linear 2nd-order homogeneous ODEs
  • Week 4 <2016-09-12 Mon>
  • Review
  • EXAM 1 on <2016-09-14 Wed>
  • 4.2 Linear 2nd-order homogeneous ODEs
  • Week 5 <2016-09-19 Mon>
  • complex numbers
  • complex numbers
  • complex exponentials + 4.3 Auxiliary equations with complex roots
  • Week 6 <2016-09-26 Mon>
  • 4.3 continued; 4.4 Inhomogeneous problems and undetermined coefficients
  • 4.4 continued
  • 4.5 Superposition
  • Week 7 <2016-10-03 Mon>
  • 4.6 Variation of parameters
  • 4.6 Variation of parameters
  • 4.9, 4.10 mechanical vibrations
  • Review
  • Week 8 <2016-10-10 Mon>
  • EXAM 2 on <2016-10-10 Mon>
  • 7.1, 7.2 Laplace transform
  • 7.2, 7.3 Laplce transform and its properties
  • 5.4 nonlinear systems or 5.5 biomath applications
  • (we may come back to nonlinear systems later, if there
  • 5.6 mass-spring systems
  • 5.7 electrical
  • Week 9 <2016-10-17 Mon>
  • 7.4 Inverse Laplace transform
  • 7.5 Solving IVPs
  • 7.5 continued
  • Week 10 <2016-10-24 Mon>
  • 7.6 Laplace transforms of discontinuous and periodic
  • 7.6 continued
  • 7.7 Convolutions
  • Week 11 <2016-10-31 Mon>
  • 7.8 Impulses and delta functions
  • Review
  • EXAM 3 on <2016-11-04 Fri>
  • Week 12 <2016-11-07 Mon> (Veterans Day)
  • 9.5 Homogeneous linear systems with constant coefficients
  • More on homogeneous linear systems; matrix notation;
  • Veterans Day
  • 9.1 Matrix methods: introduction
  • 9.2 Linear algebraic equations
  • 9.2 continued
  • 8.1 series solutions: Taylor approximation
  • 8.2 Power series
  • 8.3 Power series solutions
  • Week 13 <2016-11-14 Mon>
  • More on homogeneous linear systems and their phase portraits
  • Homogeneous linear systems: quick review
  • 9.6 Complex eigenvalues
  • 9.3 Matrices and vectors
  • 9.3 continued; 9.4 linear systems in normal form
  • 9.4 continued
  • Week 14 <2016-11-21 Mon> (Thanksgiving)
  • Repeated eigenvalues. 9.7 Nonhomogeneous linear systems
  • 9.7 continued
  • Thanksgiving
  • Week 15 <2016-11-28 Mon>
  • 9.7 continued; 7.9 Laplace transforms and systems
  • 5.4 Phase plane
  • Phase plane continued
  • 4.8 Qualitative considerations for variable coefficient equations
  • 8.1 Taylor series solutions
  • 8.2 Power series and analytic functions
  • 8.3 Power series solutions
  • Week 16 <2016-12-05 Mon> (short week)
  • Linearization, local stability, and phase portrait for the
  • Review
  • 8.4 Equations with analytic coefficients
  • FINAL EXAM <2016-12-15 Thu> at 1030
This page was last updated on September 16, 2018.