DE Lessons

Monday	Tuesday	Wednesday	Thursday	Friday
6/3	6/4	6/5	6/6	6/7 Braun 1.2 Braun 1.4
Linear Algebra Lesson 1: Vectors and Matrices
6/10 Braun 1.9 Braun 1.10	6/11	6/12 Braun 2.1	6/13 Quiz 1	6/14 Braun 2.2
Linear Algebra Lesson 2: Solving Linear Systems
6/17 Braun 2.2.1 Braun 2.2.2	6/18	6/19 Braun 2.3	6/20 Quiz 2	6/21 Braun 2.4
Linear Algebra Lesson 3: Matrix Inverses
6/24 Braun 2.5	6/25	6/26 Review	6/27 Quiz 3	6/28 Exam 1
Linear Algebra Lesson 4: Determinants
7/1 Braun 2.8	7/2	7/3 Braun 3.1	7/4 Holiday	7/5 LinAlg 5
7/8 LinAlg 6	7/9	7/10 LinAlg 7	7/11 Quiz 4	7/12 LinAlg 7
7/15 LinAlg 8	7/16	7/17 LinAlg 8	7/18 Quiz 5	7/19 Exam 2
7/22 Braun 3.8	7/23	7/24 Braun 3.8	7/25 Quiz 6	7/26 Braun 3.9
7/29 Braun 3.9	7/30	7/31 Braun 3.10	8/1 Quiz 7	8/2 Braun 3.10
8/5 Braun 3.11	8/6	8/7 Braun 3.11	8/8 Quiz 8	8/9 Exam 3
8/12 Braun 5.1-5.3	8/13	8/14 Braun 5.4 Braun 5.5	8/15 Quiz 9	8/16 Braun 5.6

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
	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 Judson, 1.2.2; Newton's Law of Cooling

Exact

Resource:	Braun, Section 1.9
Homework:	Braun, Section 1.9: Exercises 3-11 (check each equation for exactness; solve only those which are exact), 12, 13, 14
Challenge:	Braun, Section 1.9: Exercises 15, 16

Solving Linear Systems

Resource:	LinAlg2.html
Homework:	LinAlg2HW.html

Picard Iteration

Resource:	Braun, Section 1.10
Homework:	Braun, Section 1.10: Exercises 1-3, 5-6 (find $y_1$ and $y_2$), 10-11 (find $y_1$)
	faculty.sfasu.edu/judsontw/ode/html-20180819/firstlook06.html Exercises 1(c) (find $y_1$ and $y_2$), 1(e) (find $x_1$, $x_2$, and $x_3$), 5
Applications:	Judson, 1.6.2; Existence of Solutions

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

Variation of Parameters

Resource:	Braun, Section 2.4
Homework:	Braun, Section 2.4: Exercises 1-6, 9 Hint for 9: $y_1 = t^2$ and $y_2 = 1/t$
Challenge:	Braun, Section 2.4: Exercises 10, 12

Judicious Guessing

Resource:	Braun, Section 2.5
	JudiciousGuessing.jpg
	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

Series Solutions

Resource:	Braun, Section 2.8
	Series Example pdf
Homework:	Braun, Section 2.8: Exercises 1-11, 12 (a)
Challenge:	Braun, Section 2.8: Exercises 12 (b), 13-17

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
Homework:	Braun, Section 3.10: Exercises 1-8 Note: 2, 5, 6, and 7 can be done with Jordan cycles and by finding the matrix exponential. 1 and 3 can only be done with Jordan cycles. 4 and 8 only with the matrix exponential.
Challenge:	Braun, Section 3.10: Exercises 9-20

Matrix Exponential

Resource:	Braun, Section 3.11
	EigenReview.pdf
	EigenFlowChart.jpg
Homework:	Braun, Section 3.11: Exercises 1-11

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
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.