Leon Takhtajan


Department of Mathematics
Stony Brook University

office: Math Tower 5-111
phone: (631) 632-8287
e-mail: leon.takhtajan@stonybrook.edu

MAT 341.02: Applied Real Analysis
Fall 2022
Schedule & Homework

Schedule

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Dates Sections covered and assigned reading
 Homework
All problems are from Powers, 6th edition, in page:number format
Week 1:
Aug 22-26 		Introduction to Fourier series. Examples. Fourier sine and cosine series. Complex form of Fourier series (pp. 108-109). Ch. 1, §§ 1.1-1.2 and § 1.10.
HW 1 55:1(a,b,c),2(a,d), 56:7(a,b); 63:1; 64:7(a,b,c*),10(a,b); 109:1,2. Due: Aug 31.
Week 2:
Aug 29-Sep 2 		Convergence and uniform convergence of Fourier series. Basic operation on Fourier series. Ch.1, §§1.3-1.4.
HW 2 70:1(a,b,d),2(a,d),5,6; 77:1(a,e),2,3(a,b),4,5(b,c). Due: Sep 7.
Week 3: Sep 5-9
 Basic operation on Fourier series, cont. The heat equation. Steady-state and transient solutions. Ch.1, § 1.5 & Ch.2, §§2.1-2.2.
HW 3 70:7*, 82-83:2,5,9,10; 133:2; 140:5,6. Due: Sep 14.
Week 4:
Sep 12-16 		Fixed-end temperatures and separation of variables. Insulated bar and different boundary conditions. Ch.2, §§2.3-2.5.
HW 4 148:6,8; 154:2,4,5; 155:8; 162:4,5,6. Due: Sep 21
Week 5:
Sep 19-24 		Example: Convection. Summary of separation of variables method. Eigenvalues and eigenfunctions. Ch.2, §§ 2.6-2.7.
HW 5 169:7,9,10; 174:1.
Due: Sep 28
Week 6: Sep 26-30 Sturm-Liouville problems & relation to Fourier series. Series of eigenfunctions, examples. Fourier integral. Ch 1, §§1.9 and Ch 2, §§2.7-2.8.
Sep 28, Midterm 1 in class.
Covers Ch. 1, §§1.1-1.5, 1.10 and Ch. 2, §§2.1-2.5.

HW 6 104:1(a,b),3(a); 175:3(b,c),7; 178:1,3; 179:7.
Due: Oct 5
Week 7: Oct 3-7 Fourier integral & applications to PDEs. Semi-infinite and infinite rod.
Ch 2, §§2.10-2.11.
HW 7 187:3,4; 193-194:2,3,5.
Due Oct 12
Week 8: Oct 10-14 Wave equation, D'Alembert solution.
Ch 3, §§3.1-3.3.
HW 8 224-225: 3,4,5,7; 233-234: 1,2,5,7.
Due: Oct 19
Week 9: Oct 17-21 Wave equation in unbounded regions. Laplace's equation. Dirichlet problem in a rectangle.
Ch. 3, §3.6 & Ch 4, §§4.1-4.2.
HW 9 247: 1,2,3; 263: 1-6; 269: 5,6.
Due: Oct 26
Week 10: Oct 24-28 Laplace equation in a rectangle and in unbounded regions. Polar coordinates and Dirichlet problem in a disk.
Ch 4, §§ 4.3-4.5.
HW 10 276: 2(b); 281: 4(a), 5(a,b); 293: 1,4.
Due: Nov 7
Week 11: Oct 31 - Nov 4 Dirichlet problem in a disk cont. Two-dimensional heat equation: double series solution. Problems in polar coordinates. Ch. 5, §§5.2-5.4.
Nov 2, Midterm 2 in class.
Covers Ch. 2, §§2.6-2.7, 2.10-2.11 and Ch. 3, §§3.1-3.3, 3.6.

HW 11 321-322: 5,7,10; 324: 5.
Due: Nov 14
Week 12: Nov 7-11 Two-dimensional heat equation: double series solution. Problems in polar coordinates and Bessel equation.
Ch. 5, §§5.3-5.5.
HW 12 330: 4,6; 335-336: 3,5,7; 343-344: 2,7.
Due: Nov 21
Week 13: Nov 14-18 Bessel equation. Fourier-Bessel series and heat equation in cylinder. Vibrations of a circular membrane.
Ch. 5, §§5.5-5.7.
HW 13 371-372: 5,6,8,9.
Due: Nov 28
Week 14: Nov 28 - Dec 2 Spherical coordinates and Legendre polynomials.
Ch. 5, §5.9.
HW 14 361: 6-9.
Due: Dec 5