Math 331: Fourier Series and Boundary Value Problems

Lectures: MWF 14:00-14:50 in CAMP 177
Instructor: Carmeliza Navasca, (cnavasca@clarkson.edu), SC 391
Office Hours: MW 15:00-14:00, F 12:00-13:00, 13:00-14:0

Objectives:
(1) to learn Fourier series as solutions to boundary value problems
(2) to learn how to solve a variety of boundary value problems both analytically (and numerically)

Course Info

Textbook: David Powers, Boundary Value Problems, Fifth Edition, Elsevier.

Prerequisites: Math 231 and Math 232.

Grading Scheme: 10% hw, 10% quiz, 10% project, 20% midterm 1, 20% midterm 2, 30% final exam

Participation: Class participation (e.g. asking questions and participating in discussions) is encouraged. Your interaction will be considered when assigning borderline grades.

Homework: Weekly assignment will be assigned every Monday and will be collected the following Monday at the beginning of class. No late hw will be accepted. However, one homework grade will be dropped.

Quiz: There will be a weekly quiz on Monday. The lowest quiz grade will be dropped.

Project: There will be a project. The project entails advanced topics which can be done in groups of two or more.

Exam: The two midterms are scheduled on February 24 and April 6. There is one comprenhensive exam TBA. No make-up exam will be given unless you have proper documentation. No shows on exams will result on an F grade.

Handouts and Other Info: All other info can be found at moodle.

Reading and Blogging: To acheive our objectives, you must read the sections ideally before lecture. To encourage this activity, you must blog about the reading material weekly. Your blog must have at least three sentences summarizing the sections read and at least one question on something you find unclear, complicated or puzzling.

Course Syllabus

Week 0: Jan 13
Introduction


Week 1: Jan 16-20
0.1 ODE: Homogeneous Linear Equations
0.2 ODE: Nonhomogeneous Linear Equations
0.3 ODE: Intro to boundary value problems

Week 2: Jan 23-27
1.1 Fourier Series and Integrals: Periodic Functions and Fourier Series
1.2 Fourier Series and Integrals: Arbitrary Period and Half-Range Expansions
1.3 Fourier Series and Integrals: Convergence of Fourier Series
1.4 Fourier Series and Integrals: Uniform Convergence

Week 3: Jan 30-Feb 1-3
1.5 Fourier Series and Integrals: Operations on Fourier Series
1.8 Fourier Series and Integrals: Numerical Determination of Fourier Coefficients
1.9 Fourier Series and Integrals: Fourier Integrals

Week 4: Feb 6-10
2.1 Heat Equation: Derivation and Boundary Conditions
2.2 Heat Equation: Steady-State Temperature
2.3 Heat Equation: Fixed End Temperature

Week 5: Feb 13-17
2.4 Heat Equation: Insulated Bar
Winter Break!

Week 6: Feb 20-24
2.7 Heat Equation: Sturm-Liouville Problems
Review
Midterm Exam I

Week 7: Feb 27-29-Mar 2
2.10 Heat Equation: Semi-Infinite Rod
2.11 Heat Equation: Infinite Rod
3.1 Wave Equation: The Vibrating String

Week 8: Mar 5-9
3.2 Wave Equation: Solution of the Vibrating String Problem
3.3 Wave Equation: d'Alembert's Solution
3.4 Wave Equation: 1-D Wave Equation

Week 9: Mar 12-16
3.5 Wave Equation: Estimation of Eigenvalues
3.6 Wave Equation: in Unbounded Regions
4.1 Potential Equation: Potential Equation

Week 10: Mar 19-23
Spring Break!

Week 11: Mar 26-30
4.2 Potential Equation: Potential in a Rectangle
4.3 Potential Equation: More example for a Rectangle
4.4 Potential Equation: Potential in Unbounded Regions

Week 12: Apr 2-6
4.5 Potential Equation: Potential in a Disk
Review
Midterm Exam II

Week 13: Apr 9-13
5.1 Higher Dimensions and Other Coordinates: 2-D Wave Equation
5.2 Higher Dimensions and Other Coordinates: 3-D Wave Equation
5.3 Higher Dimensions and Other Coordinates: 2-D Heat Equation

Week 14: Apr 16-20
7.1 Numerical Methods: Boundary Value Problems
7.2 Numerical Methods: Heat Problems
7.3 Numerical Methods: Partial Differential Equations

Week 15: Apr 23-27
Projects