DE Lessons

Monday	Tuesday	Wednesday	Thursday	Friday
1/20	1/21	1/22 Braun 1.2	1/23	1/24 Braun 1.4
Linear Algebra Lesson 1: Vectors and Matrices
1/27 Braun 2.1	1/28	1/29 Braun 2.2	1/30 Quiz 1	1/31 Braun 2.2.1
Linear Algebra Lesson 2: Solving Linear Systems
2/3 Braun 2.2.2	2/4	2/5 Braun 2.3	2/6 Quiz 2	2/7 Braun 2.5
Linear Algebra Lesson 3: Matrix Inverses
2/10 Braun 2.5	2/11	2/12 Braun 2.5	2/13 Review	2/14 Exam 1
Linear Algebra Lesson 4: Determinants
2/17 Oscillators	2/18	2/19 Braun 3.1	2/20 Quiz 3	2/21 LinAlg 5
2/24 LinAlg 6	2/25	2/26 LinAlg 6	2/27 Quiz 4	2/28 LinAlg 7
3/2 LinAlg 7	3/3	3/4 LinAlg 8	3/5 Quiz 5	3/6 LinAlg 8
3/9 Braun 3.8	3/10	3/11 Braun 3.8	3/12 Quiz 6	3/13 Braun 3.9
3/16 Spring Break	3/17	3/18	3/19	3/20
3/23 Braun 3.9	3/24	3/25 Review	3/26 Review	3/27 Exam 2
3/30 Braun 3.10	3/31	4/1 Braun 3.10	4/2 Quiz 7	4/3 Braun 3.10
4/6 Braun 3.11	4/7	4/8 Braun 3.11	4/9 Quiz 8	4/10 Braun 4.7
4/13 Braun 4.10	4/14	4/15 Braun 4.10	4/16 Review	4/17 Exam 3
4/20 Braun 5.1-5.3	4/21	4/22 Braun 5.1-5.3	4/23 Quiz 9	4/24 Braun 5.4
4/27 Braun 5.4	4/28	4/29 Braun 5.5	4/30 Quiz 10	5/1 Braun 5.5
5/4 Braun 5.6	5/5	5/6 Braun 5.6	5/7 Quiz 10	5/8 Review

Vectors and Matrices

Resource:	LinAlg1.html
Homework:	LinAlg1HW.html

First Order Linear

Resource:	Braun, Section 1.2
Homework:	Braun, Section 1.2: Exercises 1, 3, 4, 6, 11, 15, 16, 20-23 Do not do the limits in 20-23
	faculty.sfasu.edu/judsontw/ode/html-20180819/firstlook05.html Exercises 1-20
Challenge:	Braun, Section 1.2: Exercises 17, 18, 19
Applications:	Braun, Section 1.3; Art Forgeries Judson, 1.1.1; Exponential Growth Judson, 1.3.1 - 1.3.4; RC Circuits and Slope Fields Judson, 1.5.1 - 1.5.2; Mine Tailings Judson, 1.5.3; Mixing Models Judson, 1.5.4; Finance Models

Separable

Resource:	Braun, Section 1.4
Homework:	Braun, Section 1.4: Exercises 1-10
	faculty.sfasu.edu/judsontw/ode/html-20180819/firstlook02.html Exercises 1-9, 10-21
Challenge:	Braun, Section 1.4: Exercises 11, 13-18
Applications:	Braun, Section 1.8(c); Orthogonal Trajectories Braun 1.8 Example 2 Braun 1.8 #12 Braun 1.8 #14 Judson, 1.1.2; Logistic Growth Logistic Growth Curve Judson, 1.2.2; Newton's Law of Cooling

Solving Linear Systems

Resource:	LinAlg2.html
Homework:	LinAlg2HW.html
	LSPG.html

Second Order Linear

Resource:	Braun, Section 2.1
Homework:	Braun, Section 2.1: Exercises 1-9
Challenge:	Braun, Section 2.1: Exercises 10-19
Applications:	Judson, 4.1.1; RLC Circuit

Distinct Real Roots

Resource:	Braun, Section 2.2
Homework:	Braun, Section 2.2: Exercises 1-8 (Note Braun's remark for problems 3 and 5)
	faculty.sfasu.edu/judsontw/ode/html-20180819/firstlook01.html Exercises 11-14
Challenge:	Braun, Section 2.2: Exercises 9-12

Matrix Inverses

Resource:	LinAlg3.html
Homework:	LinAlg3HW.html

Complex Roots

Resource:	Braun, Section 2.2.1
Homework:	Braun, Section 2.2.1: Exercises 1-6, 8-10
Challenge:	Braun, Section 2.2.1: Exercises 12-19
Applications:	Judson, 2.3.1; Crane's and Duffing's Equation

Repeated Roots

Resource:	Braun, Section 2.2.2
Homework:	Braun, Section 2.2.2: Exercises 1-7
	faculty.sfasu.edu/judsontw/ode/html-20180819/secondorder01.html Exercises 1-20
Challenge:	Braun, Section 2.2.2: Exercises 8-20

Second Order Nonhomogeneous

Resource:	Braun, Section 2.3
Homework:	Braun, Section 2.3: Exercises 1-3
Challenge:	Braun, Section 2.3: Exercises 4 and 5

Determinants

Resource:	LinAlg4.html
Homework:	LinAlg4HW.html

Judicious Guessing

Resource:	Braun, Section 2.5
	JudGuess.pdf
	Judson: Undetermined Coefficients
	Judson: Strategy
Homework:	Braun, Section 2.5: Exercises 1-14
	faculty.sfasu.edu/judsontw/ode/html-20180819/secondorder02.html Exercises 1-24
Challenge:	Braun, Section 2.5: Exercises 15, 16, 18

Harmonic Oscillators

Resource:	Oscillators.html
	Judson: Spring-Mass Model
	Judson: Spring-Mass Equation
	Judson: Oscillators with Sage
Applications:	Judson, 4.1.1; RLC Circuits Judson, 4.4.1; Resonance and Architecture Judson, 4.4.2; Beats Judson, 4.4.5; The Tacoma Narrows Bridge

Linear Systems

Resource:	Braun, Section 3.1
	Pesticide Example pdf
Homework:	Braun, Section 3.1: Exercises 4-9
Applications:	Judson, 3.2.1; Mixing Problem

Vector Spaces

Resource:	LinAlg5.html
Homework:	Memorize Blue Boxes

Subspaces

Resource:	LinAlg6.html
Homework:	LinAlg6HW.html

Span

Resource:	LinAlg7.html
Homework:	LinAlg7HW.html

Basis

Resource:	LinAlg8.html
	LinAlgReview.html
Homework:	LinAlg8HW.html

Real Eigenvalues

Resource:	Braun, Section 3.8
	Solution to number 3
Homework:	Braun, Section 3.8: Exercises 1-12 Hint for 6: p(λ)=λ⁴-64 λ³
Challenge:	Braun, Section 3.8: Exercises 14-21

Complex Eigenvalues

Resource:	Braun, Section 3.9
	Solution to number 4
	Complex Alternative Questions
Homework:	Braun, Section 3.9: Exercises 1-8 Note: For 7, just find the general solution. Do not solve the IVP. The solution in the textbook is wrong.
Challenge:	Braun, Section 3.9: Exercise 9

Generalized Eigenvectors

Resource:	Braun, Section 3.10
	Solution to example 2
	Solution to number 5
	Generalized Eigenvectors and Arrow Diagrams
	Generalized Eigenvectors Examples
Homework:	Braun, Section 3.10: Exercises 1-8 (Include Arrow Diagrams)
Challenge:	Braun, Section 3.10: Exercises 9-20

Matrix Exponential

Resource:	Braun, Section 3.11
	Judson, 3.9; The Matrix Exponential
	EigenReview.pdf
Homework:	Braun, Section 3.11: Exercises 1-7

Phase Plane

Resource:	Braun, Section 4.7
	Phase Plane Portraits
	MIT Phase Plane Mathlet
Homework:	Braun, Section 4.7: Exercises 1-11
	Judson 3.7 Exercises 1-8

Nonlinear Systems

Resource:	Braun, Section 4.10
	nonlinear.pdf
	Lotka Volterra Equations
	Judson, 2.2; The Geometry Of Systems
	Judson, 5.1; Linearization of Nonlinear Systems
Homework:	Braun, Section 4.10: Exercises 3, 4 Describe the phase plane at each equilibrium point.
	Judson, 5.1 Exercises 1-9 Describe the phase plane at each equilibrium point.

PDEs and Heat Equation

Resource:	Braun, Sections 5.1, 5.2, 5.3
	Heat Equation and Fourier Series
Homework:	Braun, Section 5.3: Exercises 1, 2

Fourier Series

Resource:	Braun, Sections 5.4
	https://en.wikipedia.org/wiki/Fourier_series
Homework:	Braun, Section 5.4: Exercises 1-13

Even and Odd Functions

Resource:	Braun, Sections 5.5
Homework:	Braun, Section 5.5: Exercises 1-11

Solving the Heat Equation

Resource:	Braun, Sections 5.6
Homework:	Braun, Section 5.6: Exercise 1
	Compute the solution to the heat equation for any initial heat distribution for which you can compute the Sine series.