Math 305: An introduction to partial differential equations with applications to physics
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
Particular solution to the IBVP for the WE with Dirichlet BC.
Video with beautiful visual description of the Fourier transform
Here is the COURSE SYLLABUS.
Reading notes:
Old Chapter from previous version of text -- source for project ideas.
Old Chapter 6 -- Section 6.2 and Section 6.4 and are both good project options.
Homework assignments (problems given in the chapters listed above):
Homework 1 assigned Wednesday, January 17th. Due Wednesday, January 24th 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. Also, to receive full credit for a problem please show your work.
Problems: The exercises on this page and Exe 1.4.1, Exe 1.4.2, Exe 1.4.3
Homework 2 assigned Wednesday, January 24th. Due Wednesday, January 31th at the SQRC by SQRC closing time. To receive full credit for a problem please show your work.
Reading: Please read Chapter 2 of the course notes, posted above.
Problems: Exe 1.4.4, Exe 1.4.5, Exe 2.2.1, Exe 2.3.1, Exe 2.3.2, Exe 2.3.3, Exe 2.4.1
Homework 3 assigned Wednesday, January 31rd. Due Wednesday, February 7th at the SQRC by SQRC closing time. To receive full credit for a problem please show your work.
Reading: Please read Chapters 2 and 3 of the course notes, posted above.
Problems: The exercises on this page and Exe 2.5.2, Exe 3.1.1, Exe 3.1.2
Homework 4 assigned Thursday, 8th. Due Wednesday, February 14th at the SQRC by SQRC closing time. To receive full credit for a problem please show your work.
Reading: Please read Chapter 3 of the course notes, posted above.
Problems: The exercise on this page and Exe 3.2.1, 3.2.2, 3.2.3, 3.2.4, 3.2.5, 3.3.4, 3.3.5.
Homework 5 assigned Thursday, Feb 15th. Due Wednesday, February 28th at the SQRC by SQRC closing time. To receive full credit for a problem please show your work.
Reading: Please read Chapter 3 of the course notes, posted above.
Problems: Exe 3.4.1, 3.4.2, 3.4.3, 3.4.4, 3.5.1, 3.6.1.
Homework 6 assigned Friday, March 2nd. Due Wednesday, March 7th at the SQRC by SQRC closing time. To receive full credit for a problem please show your work.
Reading: Please read Chapter 4 of the course notes, posted above. Play with http://www.falstad.com/fourier/Fourier.html.
Problems: Exe 3.7.1, 3.7.2, 3.8.1, 3.8.2.
Homework 7
Reading: Please read Chapters 3 and 4 of the course notes as needed.
Problems: Exe 4.1.1, 4.2.2. Also please show that the little Fourier transform is linear, and
that f(f-1(c))=c. (Here f denotes the little Fourier transform. Here is the solution key to HW 7.
Homework 8 assigned Wednesday, March 21st. Due Wednesday, April 4th at the SQRC by SQRC closing time. To receive full credit for a problem please show your work.
Reading: Please read Chapter 4 of the course notes as needed.
Problems: Exe 4.3.1, 4.3.2, 4.3.3, 4.4.1, 4.4.2. Here is the solution key to HW 6, please feel free to
refer to it for the Fourier series needed in Exe 4.3.2.
Homework 9 assigned Friday, April 5th. Due Wednesday, April 18th at the SQRC by SQRC closing time. To receive full credit for a problem please show your work.
Reading: Please read Chapters 4 and 8 of the course notes as needed.
Problems: Exe 4.5.1, 4.5.2, 4.5.3, 4.6.1, 4.6.2, 8.2.1. Here is the solution key to HW 9.
Homework 10 No new problems today, however please read Chapters 8 and 9.