Studio session | TA Name and Email | TA Office Hours | ||
D1 | MW 9:05am-9:55am | Skiles 156 | Xiaonan Liu xliu729 AT gatech.edu |
Thursday 4-5pm Clough 280 |
D2 | MW 9:05am-9:55am | Skiles 257 | Kevin Shu kshu8 AT gatech.edu |
Friday 1-2pm Clough 280 |
D3 | MW 10:10am-11:00am | Skiles 156 | Xiaonan Liu xliu729 AT gatech.edu |
Thursday 4-5pm Clough 280 |
Date | Covered topics | Covered textbook sections, slides and additional notes | Homework Set and Recitation Worksheets | |
Week 1 | 01/07 T |
Introduction and terminology (Newton’s Law of Cooling, Direction Fields, Autonomous equations and equilibriums solutions). | Sec 1.1,1.2 | Sec 1.1: #1, 4, 5, 6. Sec 1.2: #1, 5, 14, 17, 19, 25, 26, 28, 29. Studio worksheet 1 (Mon) and solution. |
01/09 R |
Classification of DEs (ODEs and PDEs, order, linearity and standard form); Separable equations; Integrating factors for 1st order linear ODEs. | Sec 1.3, 2.1, 2.2 | Sec 1.3: #1-6,13,16,21,23,32. Sec 2.1: #7, 17, 29, 31, 35, and bonus worksheet. Sec 2.2: #7, 19, 21, 31 and bonus worksheet. Studio worksheet 2 (Wed) and solution. |
|
Week 2 | 01/14 T |
Modeling with First Order Equations (Water tanks and population model). | Sec 2.3 | Sec 2.3: #1, 3, 5, 9, 11, 13, 25. Studio worksheet 3 (Mon) and solution. |
01/16 R |
Differences Between Linear and Nonlinear Equations (Theorems of existence and unicity of the solutions, Intervals of existence of solutions), Autonomous Equations and concavity of the solutions. | Sec 2.4-2.5 | Sec 2.4: #1, 5, 7, 13, 15 and bonus worksheet. Sec 2.5: #1, 2, 5, 7, 9 and bonus worksheet.. Studio worksheet 4 (Wed) and solution |
|
Week 3 | 01/21 T |
Exact Equations, Substitution Methods (Homogeneous and Bernoulli equations). | Sec 2.6,
2.7 Notes: Sec 2.6: On the chain rule. Sec 2.7: Example 1 (Homogeneous equation), Example 2(Bernoulli equation) |
Sec 2.6: #1-8, 18. Sec 2.7: #1-6,23. No studio on Monday (MLK day) |
01/22 W |
Quiz 1 in studio (Covers lectures and studios on 01/07-01/14). More precisely, quiz 1 covers Sec 1.1-2.3. | Quiz 1 sample | Quiz 1: Sections D1,D2 and solution, Section D3 and solution. | |
01/23 R |
System of two 1st order linear equations and second order linear ODEs and Linear Algebra. | Sec 3.1, 3.2. | Sec 3.2: #1-8, 11(a), 15(part (a) only), 25. Studio worksheet 5 (Wed) and solution. |
|
Week 4 | 01/28 T |
Homogeneous linear systems with constant coefficients and introduction of the Wronskian. | Sec 6.1,
3.3.
Notes: Homogeneous linear system with constant coefficients, eigenvectors and diagonalization, On the Wronskian in systems of first order linear DE. |
Sec 6.1: #2, 5, 11; Sec 3.3: #1, 7, 25, 34. Studio worksheet 6 (Mon) and solution. |
01/30 R |
Homogeneous linear systems with constant coefficients and theorems of existence. | Sec 6.2,
3.3. Lecture Notes: 6.2 and 3.3. |
Sec 3.3: #5, 12. Sec 6.2: #8,9. Studio worksheet 7 (Wed) and solution. |
|
Week 5 | 02/04 T |
Homogeneous linear system with constant coefficients, complex eigenvalues and phase portraits. | Sec 3.4.
Note: A catalogue of phase portraits of 2D linear flows. Lecture notes. |
Sec 3.4: #1, 3, 13, 15.
Studio worksheet 8 (Mon) and solution. |
02/05 W |
Quiz 2 in studio (Covers lectures and studios on 01/06-02/05) | Quiz 2: Sections D1,D2 and solution, Section D3 and solution. | ||
02/06 R |
Complex and Repeated Eigenvalues. | Sec 3.5.
Complex phase portraits. |
Sec 3.5: #1, 2, 3, 10, 15, 16. (You may use online calculators to find eigenvalues for 3x3 matrices, but you should find eigenvectors yourself using row reduction.) Studio worksheet 9 (Wed) and solution. |
|
Week 6 | 02/11 T |
General forms of the solutions for homogeneous linear system with constant coefficients, Nondefective Matrices with Complex Eigenvalues. | Sec 6.3,
6.4.
Note on complex eigenvalues. Note on repeated eigenvalues. Section 6.3: Example. |
Sec 6.3: #1, 4, 5, 9, 10, 16, 21. (You may use online calculators to find eigenvalues for 3x3 matrices, but you should find eigenvectors yourself using row reduction.) Sec 6.4: #1, 3, 4, 6. Studio worksheet 10 (Mon) and solution. |
02/13 R |
First part of the Lecture: Nondefective Matrices with Complex Eigenvalues. | Sec 6.4. Section 6.4: Example. |
Special Studio worksheet (Midterm review) (Wed) and solution. | |
02/13 R |
Midterm 1 in lecture (Covers lectures and studios on 01/06-02/11) | Midterm1-practice-Fall2019A (long) list of practice problems with solutions. Midterm and solution. |
||
Week 7 | 02/18 T |
Introduction to Second order linear equations. Linear homogeneous equation with constant coefficients. | Sec 4.1,
4.2,
4.3. Note on the reduction of order (Sec 4.2). |
Sec 4.1: #3, 5, 9, 11, 16, 17, 21; Sec 4.2: #5, 11, 15, 25. Sec 4.3: #2, 6, 7, 11, 13, 19, 21, 23, 25, 29, 30, 31, 36, 43, 47, 51. Studio worksheet 11 (Mon) and solution. |
02/20 R |
Mechanical vibrations. | Sec 4.4. | Sec 4.4: #1, 3, 5, 6, 7, 8, 11, 12, 13, 17, 18, 19. Studio worksheet 12 (Wed) and solution part 1 and part 2 (phase portraits and solutions). |
|
Week 8 | 02/25 T |
Method of undetermined coefficients. | Sec 4.5. | Sec 4.5: #1-5, 13, 15, 18, 26, 27, 37. Studio worksheet 13 (Mon) and solution. |
02/26 W |
Quiz 3 in studio (Covers lectures and studios on Sec 6.1,6.3-6.4 and Sec 4.1-4.4) | Quiz 3: Sections D1,D2 and solution, Section D3 and solution. | ||
02/27 R |
Method of undetermined coefficients (cont.), Forced vibrations. | Sec 4.5, 4.6. |
Sec 4.5: #7, 17, 21, 27(a). Sec 4.6: #5, 9, 12, 15, 16, 17. Studio worksheet 14 (Wed) and solution. |
|
Week 9 | 03/03 T |
Variation of parameters. | Sec 4.7. Lecture Notes: Example 1 and Example 2. |
Sec 4.7: #3, 7, 10, 11, 19, 23.
Studio worksheet 15 (Mon) and solution. |
03/05 R |
Definition and properties of the Laplace Transform. | Sec 5.1. | Sec 5.1: #3, 7, 13, 15, 16, 19, 21, 23. Studio worksheet 16 (Wed) and solution. |
|
Week 10 | 03/10 T |
Properties of the Laplace Transform and Inverse Laplace Transform. | Sec 5.2, 5.3. | Sec 5.2: #1, 5, 7, 9, 11a, 19, 21.
Sec 5.3: #3, 9, 10, 11, 13, 14, 15, 18, 19, 21, 23. Studio worksheet 17 (Mon) and solution. |
03/11 W |
Quiz 4 in studio (Covers lectures and studios up to Sec 5.1) | Quiz 4: Section D1 and solution, Section D2 and solution, Section D3 and solution. | ||
03/12 R |
Solving differential equations with Laplace transform, Laplace transform for discontinuous and periodic functions. | Sec 5.4, 5.5. |
Sec 5.4: #1, 2, 3, 5, 10, 12, 13, 18. Sec 5.5: #2, 8, 9, 11, 14, 15, 21, 22, 23. Studio worksheet 18 (Wed) and solution. |
|
Week 11 | No class (Spring break). | |||
Week 12 | Training week for online Lectures & Extended Spring Break. | |||
Week 13 | 03/31 T |
Laplace transform for periodic functions, Differential equations with discontinuous forcing functions. | Sec 5.5, 5.6. | Sec 5.6: #1, 2, 4, 6, 7(no need to draw the graphs for these two questions), 12, 15.
Studio worksheet 19 (Mon) and solution (available soon). |
04/02 R |
Autonomous Systems. Stability. Almost Linear Systems | Sec 7.1, 7.2. |
Sec 7.1: #3, 7 (find critical points only). Sec 7.2: #25, 26. Studio worksheet 20 (Wed) (available soon) and solution (available soon). |
|
Week 14 | 04/07 T |
Almost Linear Systems (cont). | Sec 7.2. | Sec 7.2: #1, 3, 7.
Studio worksheet 21 (Mon) (available soon) and solution (available soon). |
04/07 T |
Midterm 2 in lecture's time |
Formula sheet for the Laplace Transform. A (long) list of practice problems with solutions. Midterm and solution (available soon). |
||
04/09 R |
Competing species. | Sec 7.3. |
Sec 7.3: #1, 2, 3, 5 (part a-d and f), 17 Studio worksheet 22 (Wed) (available soon) and solution (available soon). |
|
Week 15 | 04/13 M |
Quiz 5 in Studio's time | ||
04/14 T |
Predator-prey systems. | Sec 7.4. | Sec 7.4: #1, 3, 11(a,b), 14, 15.
Studio worksheet 23 (Mon) (available soon) and solution (available soon). |
|
04/16 R |
Numerical approximations: Euler's method. Accuracy of numerical methods. | Sec 8.1 and 8.2 (No more slides). |
Sec 8.1: #3, 6 Sec 8.2: #7, 16 Studio worksheet 24 (Wed) (available soon) and solution (available soon). |
|
Week 16 | 04/21 T |
Last class. | Final Reviews. |
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Week 17 | 04/30 T |
Final Exam. Good luck everyone. |