Welcome to the B05/B06 section of Math 20D!
General information
The discussions will focus on the mathematical part of the course. Should you have any questions regarding the MATLAB component, you should ask them during the office hours or address them to the MATLAB tutors. Their schedule is available on Canvas.
All Zoom links are available under the "Zoom LTI PRO" section on Canvas.
- Main course website
- https://www.math.ucsd.edu/~natamam/WI21math20d/
- Discussions (on Zoom)
- B05: Tue. 12:00 - 12:50
- B06: Tue. 13:00 - 13:50
- Office hours (on Zoom)
- Mon. 16:00 - 18:00
- Extra office hours (on Zoom)
- Mon., Mar. 15. 16:00 - 18:00
- Contact
-
For most questions regarding course content, homework, and
administrative details, you are encouraged to use the
"Discussion" section on Canvas.
You can also send me an email at
apal (at) ucsd (dot) edu
. Please include "MATH 20D" in your subject line.
Schedule
The schedule will be updated as the quarter progresses. Please click on the date to download the notes for that day. Most references are to the textbook "Fundamentals of Differential Equations" (9ed) by Nagel, Saff, Snider (abbreviated "NSS").
Please inform me if you notice any typos / mistakes in the notes.
- Jan. 12
- Classification of differential equations, solutions to
separable equations and linear equations.
NSS 1.1, 1.2, 2.2, 2.3. - Jan. 19
- Exact equations, integrating factors, homogeneous
linear equations.
NSS 2.4, 2.5, 4.2. - Jan. 26
- Complex and repeated roots, undetermined coefficients.
NSS 4.3, 4.4. - Feb. 02
- Undetermined coefficients, superposition principle, variation of parameters.
NSS 4.4, 4.5, 4.6.
Problems: MIT 18.03 2C-7(a)(e), 2D-1 - Feb. 09
- Organised by Saeed (check email for Zoom link)
- Feb. 16
- Organised by Saeed (check email for Zoom link)
- Feb. 23
- The Laplace transform, its properties, the inverse
transform, solving linear IVPs using the Laplace transform.
NSS 7.2, 7.3, 7.4, 7.5.
Problems: MIT 18.03 3A-10(c), 3B-1(a)(c)(d) - Mar. 02
- Discontinuous functions, convolutions, Dirac delta.
NSS 7.6, 7.8, 7.9.
Problems: MIT 18.03 3C-1(b)(c), 3C-4, 3C-5, 3D-1, 3D-4(a)(b). - Mar. 09
- Power series and series solutions, matrices.
NSS 8.2, 8.3, 9.1, 9.3.
Problems: MIT 18.03 6A-1(d), 6A-2(c), 6A-3(a), 6B-1(a), 6B-2(c), 6C-2.
Resources
Additional Remarks
The following remarks are not directly relevant to the course. You are definitely encouraged to take a look at the links you find interesting.
- A proof of existence of integrating factors can be found here. See also: notes from Jan. 19.
- A biography of Laplace at MacTutor History of Mathematics Archive is available here.