Welcome to the webpage for Math 305: Sturm-Liouville Theory with Physics Applications.
Useful and fun links:
Desmos graphing calculator
Two traveling waves passing through each other in a wave tank
Standing waves on a vibrating string demo
Dolphins chasing bubble rings (really complicated traveling wave)
Standing waves on string Desmos sheet
Here is the COURSE SYLLABUS.
Reading notes:
Homework assignments (problems given in the chapters listed above):
Homework 1 assigned Wednesday, January 18th. Due Monday, January 23rd at the SQRC by SQRC closing time. Homework for this course should take about six to nine hours per week. If an assignment is appearing to exceed this time frame please let me know as soon as you can so we can strategize the best way to balance the pace of this course.
Exe 1.1.1, Exe 1.2.1, Exe 1.3.1, Exe 1.4.1, Exe 1.4.2, Exe 1.4.3
Homework 2 assigned Monday, January 23rd. Due Monday January 30th at the SQRC by SQRC closing time. Please read all of Chapter 1 of the text. This assignment focuses on Sections 1.5-1.8, so close reading of these sections is important.
Exe 1.4.4, 1.4.5, 1.4.6 (this one is optional), 1.5.1, 1.5.2, 1.5.3, 1.5.4, 1.5.5, 1.5.6, 1.7.1
Homework 3 assigned Monday, January 30th. Due Monday February 6th at the SQRC by SQRC closing time. Read Sections 1.5-1.10 of Chapter 1 of the text carefully. Begin to read first section of Chapter 2.
Exe 1.5.7, 1.10.3, 2.1.1, 2.1.2
Homework 4 assigned Monday, February 6th. Due Monday February 13th at the SQRC by SQRC closing time. Read Chapter 2 of the text carefully.
Exe 1.10.4, 2.1.3, 2.1.4, 2.2.2, 2.3.1, 2.3.2 (optional), 2.5.3
Homework 5 assigned Monday, February 20th. Due Monday February 27th at the SQRC by SQRC closing time. Read Chapter 2 of the text carefully, including Section 2.7. You are welcome to bring questions about Section 2.7 to class (and office hours of course!).
Exe 2.5.1, 2.6.1, 2.6.5, 2.8.1 in addition to:
Bonus Problem 1: Compute the modulus and complex conjugate of: 2-3i and e^(πi/4).
Bonus Problem 2: The seventh line on page 80 of the text states e^(ikπx) form an orthogonal sequence in L2([-1,1]). Please confirm that this is true. Be careful to note that the inner product being used here is given in the beginning of Example 2.23. In
particular we are looking at L2([-1,1]) as containing complex valued functions, and so the inner product changes slightly.
Bonus Problem 3: Please use the first five standing waveforms obtained in the Dirichlet IBVP for the Wave Equation on [-1, 1] to
approximate the solution to this IBVP, assuming the initial position displaces the string upward into a perfectly semi-circular arch
and initial velocity is zero. (Initially problem was stated with space domain [-L,L]. Please use [-1,1] instead.)
Homework 6 assigned Tuesday, February 28th. Due Monday March 6th at the SQRC by SQRC closing time. Read of Chapter 2 as needed as well as Sections 3.1-3.4 of the text carefully. Do a first reading (so look for the big picture only) of Sections 3.5 and 3.6.
Exe 2.10.1, 3.1.1 (1)(2) only, 3.2.1, 3.2.2, 3.3.1
Homework 7 assigned Monday, March 13th. Due Monday March 20th at the SQRC by SQRC closing time. Read of Chapter 3 as needed.
Exe 3.4.1, 3.4.2, 3.6.1, 3.6.2, 3.6.3
Homework 8 assigned Monday, March 20th. Due Monday April 3rd at the SQRC by SQRC closing time. Read Section 6.1 and 6.3.
Exe 6.1.1, 6.1.2, 6.3.1, 6.3.2, 6.3.3
Homework 9 assigned Wednesday, April 5th. Due Monday April 17th at the SQRC by SQRC closing time. Please read Section 6.1 and 6.3 as needed.
Exe 6.3.4 and the problems from class that are posted HERE.
Homework 10 assigned Monday, April 17th. Due Monday April 24th at the SQRC by SQRC closing time. Please read Chapter 4 of the text.
Exe 4.3.1, Exe 4.5.1 and the problems that are posted HERE.