General Course Information

Lecture time and location:  TR 9:30am-10:45am, Boggs B5
Instructor:   Victor Vilaça Da Rocha
Email:  vrocha3 AT math.gatech.edu
Office hours:   Monday & Wednesday 2-3pm (Clough 248), or by appointment.
Class webpage:  http://people.math.gatech.edu/~vrocha3/2552D.html

Click here for the syllabus, where you can find the grading scheme and class policy.

Studios and TA office hours 
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

Where to get help

There are several resources available when you want some help outside of lecture and recitation:

Schedule and Homework Assignments

Midterm1-practice-Fall2019
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) A (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.
Week 17 04/30
T
Final Exam. Good luck everyone.