MAT 341-02 - Applied Real Analysis - Fall 2020
The class meets every Monday and Wednesday 2:40-4:00pm on the Zoom platform. Access is here or through Blackboard.
Course information
| Office hours: | Monday 1:00-2:00pm |
| Wednesday 4:00-5:00pm | |
| or by appointment | |
| Office hours will be held on Zoom: | |
| https://stonybrook.zoom.us/j/2482038879?pwd=TDVGcUU4UXhlNHEvdllnckdBb2VpZz09 | |
| You also have the option to come to my office (Math Tower 4101B). | |
| Teaching Assistant: | Jiahao Hu |
| Textbook: | David Powers, Boundary Value Problems and Partial Differential Equations, 6th ed., Elsevier (Academic Press), 2010. |
| The 5th edition is also fine. |
Course links
| Zoom meeting room: | https://stonybrook.zoom.us/j/94180284321?pwd=a1dINEEvRlhEK3grb29xQkdjS1oyQT09 |
| Password 199493 | |
| Video lectures: | https://drive.google.com/drive/folders/1Ieu5Po1lRvn0V50x6Bk3DY76FkK9Miqs?usp=sharing |
| Gradescope: | https://www.gradescope.com/ |
| Piazza: | https://piazza.com/class/kcz8dqglw5n20m |
Course schedule and assignments
Each week’s homework assignment is due at the beginning of Monday’s lecture (2:40 pm) of the following week.
| Week | Date | Sections | Assignment |
| 1 | Aug. 24 Aug. 26 |
1.1 Periodic functions and Fourier series 1.2 Arbitrary period and half-range expansions |
HW 1 1.1: 1abc, 2ad, 4, 7b, 8 1.2: 1, 7, 10b |
| 2 | Aug. 31 Sept. 2 |
1.3 Convergence of Fourier series 1.4 Uniform convergence |
HW 2 (due Sept. 8) 1.3: 1abd, 2ad, 5, 6 1.4: 1ae, 2, 3ab, 5bc |
| 3 | Sept. 9 |
1.5 Operations on Fourier series 2.1 Heat equation: derivation and boundary conditions |
HW 3 1.5: 2, 5, 8, 9 Ch. 1 Misc.: 19, 20 2.1: 2, 8 |
| 4 | Sept. 14 Sept. 16 |
2.2 Steady state temperatures 2.3 Example: fixed end temperatures |
HW 4 2.2: 3, 6, 7 2.3: 6, 8 |
| 5 | Sept. 21 Sept. 23 |
2.4 Example: insulated bar 2.5 Example: different boundary conditions |
HW 5 (due Sept. 30) 2.4: 4, 5, 8 2.5: 4, 5, 6 |
| 6 | Sept. 28 Sept. 30 |
MIDTERM 1 (1.1-1.5, 2.1-2.3) 2.6 Example: convection |
HW 6 2.6: 7, 9, 10 |
| 7 | Oct. 5 Oct. 7 |
2.7 Sturm--Liouville problems 2.8, 2.9 Expansion in series of eigenfunctions, generalities |
HW 7 2.7: 1, 3abc, 7 2.8: 1,3 |
| 8 | Oct. 12 Oct. 14 |
1.9 Fourier transform 2.10 Semi-infinite rod |
HW 8 1.9: 1abc, 3a, 5a 2.10: 3, 4 |
| 9 | Oct. 19 Oct. 21 |
3.1 The vibrating string 3.2 Solution of the vibrating string problem |
HW 9 3.1: 3 3.2: 3, 4, 5, 7 |
| 10 | Oct. 26 Oct. 28 |
3.3, 3.4 d'Alembert's solutions, generalities 4.1 Potential equation (Laplace's equation) |
HW 10 3.3: 1, 2, 5 Ch. 3 Misc.: 4, 5, 31, 32 |
| 11 | Nov. 2 Nov. 4 |
4.2 Potential in a rectangle MIDTERM 2 (2.4-2.9, 1.9, 2.10, 3.1-3.4) |
HW 11 4.1: 1, 2, 6 4.2: 5, 6 |
| 12 | Nov. 9 Nov. 11 |
4.3 Further examples for a rectangle
4.4 Potential in unbounded regions |
HW 12 4.3: 1a, 2b 4.4: 4a, 5ab |
| 13 | Nov. 16 Nov. 18 |
4.5 Potential in a disk 5.3 Two-dimensional heat equation |
HW 13 4.5: 1, 4 5.3: 5, 7abc, 10 |
| Nov. 23 Nov. 25 |
THANKSGIVING BREAK |
||
| 14 | Nov. 30 Dec. 2 |
4.6 Classification and limitations Final exam review, part 1 |
Suggested problems 4.6: 5, 7, 8 |
| 15 | Dec. 7 |
Final exam review, part 2 |
|
| Dec. 9 | Final Exam
5:30-8:00pm |
Cumulative All sections included in Midterms 1, 2 plus 4.1-4.5, 5.3 |
Exams
Midterm I: Monday, September 28, 2:40-4:00pm. (Online)
Practice exams from previous semesters:
Practice 1 (Solutions)
Practice 2 (Solutions)
Practice 3 (with solutions)
Practice 4 (Solutions)
Practice 5 (with solutions)
Midterm II: Wednesday, November 4, 2:40-4:00pm. (Online)
Practice exams from previous semesters:
Practice 1 (Solutions)
Practice 2 (Solutions)
Practice 3 (with solutions)
Final: Wednesday, December 9, 5:30-8:00pm. (Online)
Practice exams from previous semesters:
Practice 1
Practice 2
Practice 3
Practice 4
Practice 5 (Solutions)