# Remus Radu

Institute for Mathematical Science
Stony Brook University

office: Math Tower 4-103
phone: (631) 632-8266
e-mail: remus.radu@stonybrook.edu

MAT 341: Applied Real Analysis
Spring 2017
Schedule & Homework

# Schedule

The PDF version of the schedule is available for print here.

 Date Topic Section Assignments Due date Jan 24 An introduction to Fourier series 1.1 1.1: 1abc, 2ad, 4, 7b, 8 HW1 Due Jan 31 Jan 26 Determining Fourier coefficients; Examples 1.2 1.2: 1, 7c Jan 31 Even & odd extensions Convergence of Fourier series 1.2, 1.3 1.2:10b, 11b HW2 Due Feb 7 Feb 2 Uniform convergence of Fourier series 1.3, 1.4 1.3:1abd, 2ad, 6 Feb 7 Fourier sine & cosine series Basic operations on Fourier series 1.4, 1.5 1.4: 1ae, 2, 3ab, 5bc page 120: 19, 20 [use a=3] HW3 Due Feb 14 Feb 9 no class (snow storm) Feb 14 Differentiation of Fourier seriesThe heat equation 1.5, 2.1 1.5: 2, 5, 9 2.1: 2, 9 HW4Due Feb 23 Feb 16 The heat equationSteady-state & transient solutions 2.1, 2.2 2.2: 2, 6 Feb 21 Fixed-end temperatures 2.3 2.3: 8 [use a=pi] Feb 23 Insulated bar; ExamplesReview 2.4 2.3: 6 2.4: 4 [use a=pi], 5, 8 HW5Due Mar 9 Feb 28 Midterm 1 (2:30-3:50pm) Covers 1.1-1.5, 2.1-2.3 -- Solutions Practice exams: Fall 2015 (Solutions) and Spring 2015 (Solutions) Mar 2 Different boundary conditions 2.5 2.5: 4, 5 [use a=pi], 6 Mar 7 Eigenvalues and eigenfunctionsConvection 2.6, 2.7Notes 2.6: 7, 9, 10 HW6Due Mar 23Problem 3c Mar 9 Sturm-Liouville problems 2.7 2.7: 1, 3abc, 7 Mar 14 no class (Spring break) Mar 16 no class (Spring break) Mar 21 Series of eigenfunctions & examplesFourier integral & applications to PDEs 2.8, 1.9 2.8: 1 [use b=2]1.9: 1ab, 3a HW7Due Mar 30 Mar 23 Semi-infinite rodThe wave equation 2.10, 3.1 2.10: 3, 4 Mar 28 The wave equation 3.2 3.2: 3, 4, 5, 7 HW8Due Apr 6 Comments Mar 30 D'Alembert's solution; Examples 3.3, 3.4 3.3: 1, 2, 5 Apr 4 The wave equation: generalizationsLaplace's equation 3.4, 4.1 page 255: 18page 257: 31 HW9Due Apr 20 Comments Apr 6 Dirichlet's problem in a rectangleExamples & Review 4.2, 4.3 4.1: 2 4.2: 5 [use a=1, f(x)=sin(3pix)]4.2: 6 Apr 11 Midterm 2 (2:30-3:50pm) Covers 2.4-2.8, 2.10, 1.9, 3.1-3.4 -- Solutions Practice exams: Fall 2015 (Solutions) and Spring 2015 (Solutions) Extra practice problems Apr 13 Potential in a rectangle; ExamplesPotential in unbounded regions 4.3, 4.4 4.3: 2b4.4: 4a, 5ab HW10Due Apr 27 Apr 18 Polar coordinatesPotential in a disk 4.1, 4.5Notes 4.1: 64.5: 1 Apr 20 Dirichlet problem in a disk; Examples 4.5 4.5: 4 Apr 25 Two-dimensional heat equation 5.3, 5.4Notes 5.3: 1, 7c [use a=b=pi] HW11Due May 4 Apr 27 Problems in polar coordinatesBessel's equation 5.5, 5.6 5.4: 5 May 2 Temperature in a cylinderApplications: symmetric vibrations 5.6, 5.7 5.6: 3 [use a=1]page 371: 1 May 4 Examples & Review 5.7 May 15 Final Exam (11:15am-1:45pm) -- in class, Melville Library E4315 The final is cumulative and covers: 1.1-1.5, 1.9, 2.1-2.8, 2.10, 3.1-3.4, 4.1-4.5, 5.3-5.6 Practice exams: Fall 2015 and Spring 2015.

Last updated January 2017