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
Spring 2022
Schedule & Homework

Schedule

Dates Sections covered and assigned reading
 Homework
Jan 31, Feb 2 & 4 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 2 Following problems in Powers, 6th edition (page:number format): 55:1(a,b,c),2(a,d), 56:4,7(a,b); 63:1; 64:7,10(a,b),11(a,b); 109:1,2. Due: Feb 9.
Feb 7, 9 & 11 Convergence and uniform convergence of Fourier series. Basic operation on Fourier series. Ch.1, §§1.3-1.4.
HW 3 70:1(a,b,d),2(a,d),5,6; 77:1(a,e); 78 2,3(a,b),4,5(b,c). Due: Feb 16.
Feb 14,16 & 18 The heat equation. Steady-state and transient solutions. Fixed-end temperatures and separation of variables. Ch.2, §§2.1-2.3.
HW 4 133:2; 139:2; 140:6; 148:2,6,8. Due: Feb 23.
Feb 21,23 & 25 Insulated bar and different boundary conditions. Summary of separation of variables method. Ch.2, §§2.4-2.5.
HW 5 154:2,4,5; 155:8; 162:4,5,6. Due: Mar 2
Feb 28, Mar 2 & 4 Example: Convection. Eigenvalues and eigenfunctions. Ch.2, §§ 2.6-2.7.
March 4, Midterm 1 in class.
Covers Ch. 1, §§1.1-1.4, 1.10 and Ch. 2, §§2.1-2.5.

HW 6 169:7,9,10; 174:1.
Due Mar 9
Mar 7, 9 & 11 Sturm-Liouville problems & relation to Fourier series. Series of eigenfunctions, examples. Fourier integral.
Ch 1, §§1.9 and Ch 2, §§2.7-2.8.
HW 7 104:1(a,b),3(a); 175:3(b,c),7; 178:1.
Due Mar 23
Mar 21, 23 & 25 Fourier integral & applications to PDEs. Semi-infinite and infinite rod.
Ch 2, §§2.10-2.11.
HW 8 187:3,4; 194:2,3,5.
Due Mar 30
Mar 28, 30 & Apr 1 Wave equation, D'Alembert solution. Solution in unbounded regions.
Ch 3, §§3.1-3.3 & §3.6.
HW 9 224-225: 3,4,5,7; 233-234: 1,2,5,7; 247: 1,2,3.
Due: Apr 6
Apr 4, 6 & 8 Laplace's equation. Dirichlet problem in a rectangle.
Ch 4, §§4.1-4.2.
April 8, Midterm 2 in class.
Covers Ch. 2, §§2.7-2.8, 2.10-2.11, Ch. 3, §§3.1-3.3.
HW 10 263: 1-6; 269: 5,6.
Due: Apr 13
Apr 11, 13 & 15 Laplace equation in a rectangle and in unbounded regions. Polar coordinates and Dirichlet problem in a disk.
Ch 4, §§ 4.3-4.5.
HW 11 263:6; 276: 2(b); 281: 4(a), 5(a,b); 293: 1,4.
Due: Apr 20
April 18, 20 & 22 Two-dimensional heat equation: double series solution. Problems in polar coordinates. Bessel equation.
Ch. 5, §§5.2-5.5
HW 12 321-322: 5,7; 324: 5; 330: 4,6.
Due: Apr 27
Apr 25, 27 & 29 Fourier-Bessel series and heat equation in cylinder. Vibrations of a circular membrane.
Ch. 5, §§5.6-5.7.
HW 13 335-336: 3,5,7; 343-344: 2,7.
Due: May 4
May 2, 4 & 6 Spherical coordinates and Legendre polynomials. Review.
Ch. 5, §5.9.
Extra Credit HW 361: 6-9.
Due: May 9.