Math 316: Differential Equations (Fall 2011)

Instructor

Name: Volker Elling
Office: East Hall 2856
Upcoming office hours: Thursday December 15 4-6 pm; Tuesday December 20 4-6 pm
Uniqname: velling (for contact by email etc)

Class

No class on: Mon Oct 17 (study break), Fri Nov 25 (Thanksgiving recess).

Section 1

Time: MWF 1 - 2 pm
Room: 1512 CCL

Section 2

Time: MWF 2 - 3 pm
Room: EH 2866

Content

The class is based on "Elementary Differential Equations and Boundary Value Problems", Boyce/DiPrima, Wiley, 9th edition (2009). [If you prefer to use an older edition: the material in older editions is mostly the same, but the problem sets are different and renumbered; obtaining the right problems is up to you.] The class will cover most of Chapters 1-3, parts of 4, most of 5-7 and parts of 9.

Lecture	Book sections	Material
1	Ch. 1	Introduction, examples, modelling
2	8.1, Ch. 1	Euler method, examples, modelling
3	Ch. 1, 2.2	Modelling, visualization; separable ODE
4	2.2	Separable ODE, integration techniques
5	2.2	Separable ODE, integration techniques
6	2.1	Linear scalar 1st order ODE
7	2.8	Existence and uniqueness
8	2.8	Existence and uniqueness
9	4.1	Higher order linear scalar constant-coefficient ODE
10	4.1	Complex numbers refresher
11	4.1, 4.2	Complex numbers; higher order linear scalar constant-coefficient ODE
12	4.1, 3.2	Existence for linear higher-order ODE; inhomogeneous-homogeneous; Wronskian
13	3.2, 3.6	Variation of parameters
14	3.6, 3.7	Variation of parameters, oscillators
15	Review
16	3.4	Reduction of order
17	5.1, 5.2	Power series solutions, convergence
18	5.3	Power series, regular singular points, characteristic exponent
19	5.4, 5.5	Regular singular points, Bessel equation
20	6.1, 6.2	Laplace transform
21	6.1-6.3	Laplace transform, solving ODE
22	6.3,6.4	Laplace transform, impulse function solving ODE
23/24	6.3-6.6	convolution
25	not in book	Some control theory, convolution in image processing, applications
26	7.1, 7.4	First-order linear systems
27	Review	Ch. 3-6
28/29	7.1-7.4	Fundamental matrix, Wronskian, algebraic adjoint
30	7.1-7.6	Propagator, dy/dt=Ay with constant A, diagonalization
31	Ch. 7	exp(tA) for diagonalizable A
32	Ch. 7	exp(tA) for real A; Jordan normal form
33	7.8, 7.9	Jordan normal form; dy/dt=Ay+b(t)
34	9.1, 9.2	Trajectories for real 2x2 A; linearization
35	9.1-9.3	Stability and asymptotic stability, anharmonic oscillator
36	9.6	Hamiltonian systems, stability
37	Review	Ch. 7, 9.1-9.3

Lecture notes

Will be posted on CTools.

Grading and policies

The final grades are based approximately on 5% homeworks, 25% first and second midterm, 45% final. All grades will be posted on CTools as soon as available.

Exams

Changed: For the exams, paper help (books, notes, reference cards, ...) is allowed, but no electronic devices (calculators, smartphones, laptops, ...).

Midterm 1

Room: in-class
Date: Wednesday October 12, 2011, at class times

Midterm 2

Room: in-class
Date: Monday November 14, 2011, at class times

Final

Section 1 (MWF 1-2 pm)

Room: CCL 1512
Date: Wednesday, December 21, 1:30-3:30 pm

Section 2 (MWF 2-3 pm)

Room: Dennison 413
Date: Friday, December 16, 1:30-3:30 pm

Homeworks

Will be assigned on CTools, along with solutions when available. About ten homeworks will be assigned. The grader may choose to correct only a subset of the problems on each homework. Late homeworks cannot be accepted. Although some discussions are ok, each student should solve the homework independently.