MAT 341  Applied Real Analysis   LEC 02, Fall 2021 

MW 2:40-4:00pm Earth&Space 131

Instructor: Ljudmila Kamenova
Office: Math Tower 3-115
Office hours: MW 1:30-2:30pm
MLC hours: M 4-5pm (online)

Grader: Yulun Xu, e-mail: Yulun.Xu@stonybrook.edu
Grader's office: Math Tower S-240A
Grader's office hours: on the web card

The Instructor may be reached by e-mail at kamenova@math.stonybrook.edu.


Description: Partial differential equations of mathematical physics: the heat, wave, and Laplace equations. Solutions by techniques such as separation of variables using orthogonal functions (e.g., Fourier series, Bessel functions, Legendre polynomials). D'Alambert solution of the wave equation.

Prerequisites: C or higher in the following: MAT 203 or 205 or 307 or AMS 261; MAT 303 or 305 or AMS 361

Advisory Prerequisite: MAT 200 or MAT 250

Syllabus: Course Syllabus


Required book: David L. Powers, Boundary Value Problems and Partial Differential Equations, 6th edition, Academic Press, 2009


Grading Policy: Grades will be computed using the following scheme: Homework -- 30%, Midterm 1 -- 20%, Midterm 2 -- 20%, Final -- 30%.


Exams:


Schedule and Homework: (No late homework is accepted) Each week's homework assignment is usually due at the beginning of Monday's lecture (2:40 pm) of the following week, unless Monday is a holiday.
 

Week   Date Sections Assignment
1   Aug. 23  
Aug. 25  
1.1 Periodic functions and Fourier series
1.2 Arbitrary period and half-range expansions
HW 1 (due Aug. 30)
1.1: 1abc, 2ad, 4, 7b, 8
1.2: 1, 7, 10b
2 Aug. 30  
Sept. 1  
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. 6  
Sept. 8  
LABOR DAY
1.5 Operations on Fourier series, 2.1 Heat equation: derivation and boundary conditions
HW 3 (due Sept. 13)
1.5: 2, 5, 8, 9
Ch. 1 Misc.: 19, 20
2.1: 2, 8
4   Sept. 13  
Sept. 15  
2.2 Steady state temperatures
2.3 Example: fixed end temperatures
HW 4 (due Sept. 20)
2.2: 3, 6, 7
2.3: 6, 8
5 Sept. 20  
Sept. 22  
2.4 Example: insulated bar
2.5 Example: different boundary conditions
HW 5 (due Sept. 27)
2.4: 4, 5, 8
2.5: 4, 5, 6
6 Sept. 27  
Sept. 29  
MIDTERM 1 (1.1-1.5, 2.1-2.3)
2.6 Example: convection
HW 6 (due Oct. 4)
2.6: 7, 9, 10
7 Oct. 4  
Oct. 6  
2.7 Sturm--Liouville problems  
2.8, 2.9 Expansion in series of eigenfunctions, generalities  
HW 7 (due Oct. 13)
2.7: 1, 3abc, 7
2.8: 1,3
8 Oct. 11  
Oct. 13  
FALL BREAK
1.9 Fourier transform, 2.10 Semi-infinite rod
HW 8 (due Oct. 18)
1.9: 1abc, 3a, 5a
2.10: 3, 4
9 Oct. 18  
Oct. 20  
3.1 The vibrating string
3.2 Solution of the vibrating string problem
HW 9 (due Oct. 25)
3.1: 3
3.2: 3, 4, 5, 7
10 Oct. 25  
Oct. 27  
3.3, 3.4 d'Alembert's solutions, generalities
4.1 Potential equation (Laplace's equation)
HW 10 (due Nov. 1)
3.3: 1, 2, 5
Ch. 3 Misc.: 4, 5, 31, 32
11 Nov. 1  
Nov. 3  
4.2 Potential in a rectangle
MIDTERM 2 (2.4-2.9, 1.9, 2.10, 3.1-3.3)
HW 11 (due Nov. 8)
4.1: 1, 2, 6
4.2: 5, 6
12 Nov. 8  
Nov. 10  
4.3 Further examples for a rectangle
4.4 Potential in unbounded regions
HW 12 (due Nov. 15)
4.3: 1a, 2b
4.4: 4a, 5ab
13 Nov. 15  
Nov. 17  
4.5 Potential in a disk
5.3 Two-dimensional heat equation
HW 13 (due Nov. 22)
4.5: 1, 4
5.3: 5, 7abc, 10
Nov. 22  
Nov. 24  
In-class office hours
THANKSGIVING BREAK
14 Nov. 29  
Dec. 1  
4.6 Classification and limitations  
Final exam review, part 1
Practice problems
4.6: 5, 7, 8  
15 Dec. 6  
 
Final exam review, part 2  
 
Dec. 8   Final Exam
5:30-8:00pm
Cumulative
All sections included in Midterms 1, 2
plus 4.1-4.5, 5.3


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