Differential Equations and Linear Algebra (427J)
Course information:
Unique: 54005
Lecture: 11:00-12:30pm, T Th, CPE 2.214
Textbook: Martin Braun, Differential Equations and Their Applications: An Introduction to Applied Mathematics, 4th edition ; ISBN-13: 978-0387978949
Instructor: Arie Israel (arie AT math DOT utexas DOT edu)
Office hours: 9:00am-12:00pm, W, RLM 12.126
Discussion session: 8:00-9:00am, M W, RLP 0.126
TA: Yan Zhou (yzhou AT math DOT utexas DOT edu)
TA office hours: 10:00-12:00pm, M, RLM 13.152
First day handout:
Schedule:
- Lecture 1 (08/30): Braun 1.1, 1.2
- Lecture 2 (09/04): Braun 1.4
- Lecture 3 (09/06): Braun 1.9
- Lecture 4 (09/11): Braun 1.10, Braun 2.1
- Lecture 5 (09/13): Braun 2.2
- Lecture 6 (09/18): Braun 2.3, 2.4
- Lecture 7 (09/20): Braun 2.5
- Midterm Exam 1 (09/24): Braun chapter 1 + sections 2.1-2.5
- Lecture 8 (09/25): Braun 2.6
- Lecture 9 (09/27): Braun 2.6
- Lecture 10 (10/02): Braun 2.8
- Lecture 11 (10/04): Braun 2.8
- Lecture 12 (10/09): 3.1, Linear Algebra 1
- Lecture 13 (10/11): Linear Algebra 2
- Lecture 14 (10/16): Linear Algebra 3
- Lecture 15 (10/18): Linear Algebra 4
- Lecture 16 (10/23): Linear Algebra 5
- Lecture 17 (10/25): Linear Algebra 6
- Lecture 18 (10/30): Linear Algebra 7
- Midterm Exam 2 (10/31): Braun sections 2.6, 2.8, 3.1, 3.2, 3.3, 3.7; supplementary linear algebra notes.
- Lecture 19 (11/01): Linear Algebra 8
- Lecture 20 (11/06): Linear Algebra 9, Braun 3.8
- Lecture 21 (11/08): Braun 3.8, 3.9
- Lecture 22 (11/13): Braun 3.9
- Lecture 23 (11/15): Braun 3.10, 3.11
- Midterm Exam 3 (11/19): Braun sections 3.4, 3.5, 3.6, 3.8, 3.9, 3.10, 3.11; supplementary linear algebra notes.
- Lecture 24 (11/20): Braun 5.1, 5.2
- Lecture 25 (11/27): Braun 5.3, 5.4
- Lecture 26 (11/29): Braun 5.4, 5.5
- Lecture 27 (12/04): Braun 5.6
- Final Review (12/06)
- Final Exam (12/15): 7-10 PM; Location: CPE 2.214
Lecture 1: First Order Linear (section 1.2)
Homework:
- Braun, Section 1.2: (page 9) 1, 3, 4, 6, 11, 13, 15, 16 (solutions)
- faculty.sfasu.edu/judsontw/ode/html/firstlook05.html
Exercises 1-20
Challenge:
- Braun, Section 1.2: 17, 18, 19
Notes:
Mathlets:
Lecture 2: Separable Equations (section 1.4), Exact Equations (section 1.9)
Homework:
- Braun, Section 1.4: (page 24) 1, 2, 3, 4, 6, 8, 9 (solutions)
- faculty.sfasu.edu/judsontw/ode/html/firstlook02.html
Exercises 2-9, 14-20
Challenge:
- Braun, Section 1.4: 11, 13-18
Notes:
Lecture 4: Existence & Uniqueness Theorem (section 1.10), Second Order Linear Equations (section 2.1)
Homework:
- Braun, Section 2.1: (page 136) 1 - 7 (solutions)
Challenge:
- Braun, Section 2.1: 12, 15
Notes:
Just for fun:
Lecture 5: Second Order Constant Coefficient Linear Equations (section 2.2)
Homework:
- Braun, Section 2.2: (page 140) 1, 2, 4, 5, 6, 8, 9, 10, 12; (page 149) 1, 4, 5, 6 (solutions)
Challenge:
- Braun, Section 2.2: (page 149) 11, 12, 13, 17, 18
Modeling:
Notes:
Lecture 6: Second Order Constant Coefficient Linear Equations cont'd (section 2.2), Inhomogeneous Equations (section 2.3), Variation of Parameters (section 2.4)
Homework:
- Braun, Section 2.2: (page 144) 1, 2, 5, 6, 8, 9, 13 (solutions)
- http://faculty.sfasu.edu/judsontw/ode/html/secondorder01.html#exercises-secondorder01
Exercises 1-20
Challenge:
- Braun, Section 2.2: (page 140) 9; (page 144) 14, 15, 17, 18
Notes:
Lecture 8: Judicious Guessing (section 2.5), Mechanical Vibrations (section 2.6)
Homework:
- Braun, Section 2.5: (page 164) 11
- Braun, Section 2.6: (page 172) 1, 2, 3, 4, 5
Challenge Problems:
- Braun, Section 2.6: 7, 8
Notes:
Lecture 17: Linear Transformations and Null Space
Note: This is the last lecture which will be covered on Midterm Exam #2 (October 31).
Homework:
- Braun, Section 3.7: (page 332) 4-9, 13, 17, 19, 20, 21
- Hint: For problem 13: Apply the usual Gaussian Elimination Procedure to the augmented matrix of the system. At the end of the procedure, the final column may contain the variable lambda in several positions. Then it is straightforward to determine the equation lambda must satisfy in order that the system is consistent.
Notes:
Lecture 18: Systems of ODEs
Homework:
- Braun, Section 3.4: (page 296) 1, 2, 5, 6, 7, 10 (solutions)
Notes:
Lecture 19: Determinants and Invertibility
Homework:
- Braun, Section 3.5: (page 308) 5, 6, 8 (solutions)
- additional problems
Notes:
Lecture 20: Invertibility and Matrix Algebra
Homework:
- Braun, Section 3.6: (page 320) 9, 10, 11, 12 (solutions)
Notes:
Lecture 21: Systems of ODEs I: Real Eigenvalues
Homework:
- Braun, Section 3.8: (page 340) 1, 2, 3, 4, 6, 7, 8, 10, 11 (solutions)
Notes:
Lecture 22: Systems of ODEs II: Real Eigenvalues cont'd, Complex Eigenvalues
Homework:
- Braun, Section 3.9: (page 344) 1, 2, 5, 8 (solutions)
Notes:
Lecture 23: Systems of ODEs III: Repeated Eigenvalues
Homework:
- Braun, Section 3.10: (page 352) 1,2,3,4,5,6,7
Notes:
Lecture 24: Two-point boundary value problems
Homework:
- Braun, Section 5.1: (page 480) 1,2,3,4 (solutions)
Notes:
Lecture 25: The Heat Equation, Separation of Variables, and Fourier Sine Series
Homework:
- Braun, Section 5.3: (page 486) 1-2.
- Braun, Section 5.5: (page 498) 6,7,9
- Braun, Section 5.6: (page 502) 1
- Solution Set #1: link
- Solution Set #2: link (these cover different problems from the first solution set).
Notes:
Lecture 27: Return to the Heat Equation
Notes:
Homework:
- Braun, Section 5.5: (page 498) 1,2,3,4
- Braun, Section 5.6: (page 502) 2,4,5,6 (solutions)