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Math 115: Homework

Written homework will generally be due on Monday in class. You are encouraged to discuss the homework with other members of the class, but you will be expected to write up your solutions without any assistance. It is appropriate to acknowledge the assistance of others. I will reserve the right to refuse to accept late homework for any reason.

Your homework will be grading for both correctness and clarity; you should follow the Math department's homework guidelines when writing up your solutions. Poor presentation on your homework (and exams) may result in loss of credit.
Week #8

    Reading:
    1. We will now begin studying Partial Differential Equations and using the second book: here is the first chapter:
      Chapter 1: An Introduction to Partial Differential Equation
    2. Chapter 2: The Diffusion Equation and Chapter 5: Solving the Diffusion Equation via Separation of Variables
      are both relevant for the lecture on Wednesday, March 7th. 
MAPLE:

Notes and MAPLE Worksheet for MAPLE Lab on Monday (3/11)
MAPLE Worksheet on solving the diffusion equation via separation of variables from Wednesday (3/13)
Homework (Due Wed. 3/27 in class):
Solutions (will be posted by Wed. 3/27):
Week #9
    Reading:
This week we will study Fourier Series; there are three chapters that are relevant:
MAPLE:


Homework (Due Wed. 4/3 in class):
Solutions (will be posted by Wed. 4/3):
Week #10
    Reading:
This week we will study Separation of Variables for the Heat and wave Equations:
MAPLE:


Homework (Due Mon. 4/8 in class):
Solutions (will be posted by Mon. 4/8):
Week #11
    Reading:
- This week on Monday we will look at Complex Fourier Series, which leads naturally to a discussion of the Fourier Transform.
- The lecture on Wednesday, April 10th is cancelled.
- We will have a make-up lecture on Thursday, April 11th from Noon-1:10 PM on Sprague Third.
- We will discuss some properties of the Fourier Transform, including transforms of δ-functions, solutions of ODE's, Green's Functions, Transfer Functions and Convolutions.
Homework (Due Mon. 4/15 in class):
Solutions:
Week #12
    Reading:
This week on Monday we will solve the Heat Equation via the Fourier Transform.
This week on Wednesday we will solve the Wave equation via the Fourier Transform and derived the d'Alembert solution.
    MAPLE Worksheets:
d'Alembert Solution to the Wave Equation
Homework (Due Mon. 4/22 in class):
Solutions (To be posted on Mon. 4/22) :
Midterm #2: The second midterm was available on Wednesday, April 24th and wasdue on Monday, April 29th in class.
  • The exam was a four hour take-home with an optional break.
  • You could use any class materials distributed during the course, and your own notes.
  • You could use this Table of Fourier Transforms.
  • You could NOT use any internet resources other than the course website.
  • You could use Mathematica, MAPLE or Wolfram Alpha for calculations.
The exam covered the topics for Weeks 8-12 -  basically Separation of Variables, Fourier Series and the Fourier Transform.
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