### 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'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:
• Midterm 1 -- Monday, September 27, in class

• Midterm 2 -- Wednesday, November 3, in class

• Final -- Wednesday, December 8, 5:30pm-8:00pm in Earth&Space 131

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 series1.4 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 DAY1.5 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, 64.2: 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, 2b4.4: 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, 45.3: 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 CumulativeAll sections included in Midterms 1, 2plus 4.1-4.5, 5.3

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