Homework
MATH 6702
Date Chapter.Section/Topics or Page/Problems
M Jan 6 Lecture 1: Introduction: ordinary derivatives
Assignment 1 Due Friday January 24
W 8 Lecture 2: convexity
M 13 Lecture 3: partial derivatives
Assignment 2 Due Friday January 31
W 15 Lecture 4: partial derivatives and
the structure of ordinary differential equations
M 20 Holiday
Assignment 3 Due Friday Febuary 7
W 22 cold/snow day
M 27 Lecture 5: ordinary differential equations and
partial differential equations
Assignment 4 Due Friday Febuary 21
W 29 Lecture 6: clean up day...
higher order ODE and systems
axially symmetric solutions of Laplace's equation
questions---asking your own questions
M Feb 3 Lecture 7: Green's function(s) and integration
Assignment 5 Due Friday Febuary 28
W 5 Lecture 8: Convolution with a fundamental solution
M 10 Lecture 9: Regularity for convolution integrals
W 12 Lecture 10: Laplacian of convolution with the fundamental solution
Assignment 6 Due Friday March 14
M 17 Lecture 11: Laplacian of convolution with the fundamental solution (continued)
W 19 Lecture 12: The boundary value problem (intro)
M 24 Lecture 13: Green's function: The boundary value problem
(overview of Cauchy-Kowalevski theorem)
Assignment 7 Due Friday March 28
W 26 Lecture 14: Green's corrector function
symmetry and Green's solution
M Mar 3 Lecture 15: Green's solution of Poisson's equation (continued)
Green's function for the ball (n > 2) (intro)
W 5 Lecture 16: Green's function for the ball (n > 2) (continued)
average values of harmonic functions (mean value property)
M 10 Lecture 17: avarage values and maximum principle(s)
W 12 Lecture 18: strong maximum principle
Assignment 8 Due Friday April 4
M March 17 Holiday
W March 19 Holiday
M 24 Lecture 19: derivation of the heat equation
W 26 Lecture 20: 1-D heat equation, some solutions
Assignment 9 Due Friday April 11
M 31 Lecture 21:
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F April 25 Final Exam 11:20-2:10
Final Assignment Due Friday April 25
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=====================Old Schedule Spring 2023======================
Assignment 2 Due Wednesday February 1
Assignment 3 = Exam 1 Due Wednesday February 8
W 18 Lecture 3: differentiability and continuity
M 23 Lecture 4: multivariable power series
Assignment 4 Due Wednesday February 15
W 25 Lecture 5:
Assignment 5 Due Wednesday February 22
M 30 Lecture 6: continuous (partial) differentiability (C^1) implies continuity
Assignment 6 = Exam 2 Due Wednesday March 1
W Feb 1 Lecture 7: Full differentiability for functions of several variables
modeling the slinky (preliminaries---step zero)
M 6 Lecture 8: What we didn't do:
continuous (partial) differentiability implies full differentiability
modeling the slinky (preliminaries)
What we actually did:
Directional derivatives, parameterized curves, and
first order PDE (also a review of ODE)
W 8 Lecture 9: What we didn't do:
First Order Quasilinear PDE
Method of Characteristics
What we actually did:
Started talking about integration...along with
weak derivatives and compactly supported functions
M 13 Lecture 10: smooth compactly supported functions
and hopefully some PDE
Assignment 7 Due Wednesday March 8
W 15 Lecture 11: Lagrange multipliers (graphs, level sets, parameterized curves, etc.)
Slinky data (coil measurements) taken so far (Mathematica notebook)
Slinky data (coil measurements) taken so far (pdf format)
M 20 Lecture 12: no lecture
Assignment 8 Due Wednesday March 15
W 22 Lecture 13: d'Alembert's solution via the method of characteristics
Assignment 9 Due Wednesday March 29
M 27 Lecture 14: Integration (definition)
W Mar 1 Lecture 15: Integration (Fubini's theorem and change of variables)
Assignment 10 Due Wednesday April 5
M 6 Lecture 16: Special integrands
The divergence and the divergence theorem
Assignment 11 Due Wednesday April 12
W 8 Lecture 17: Derivation of the heat equation(s)
M 13 Lecture 18: Philosophy and integration
Assignment 12 Due Wednesday April 17
W 15 Lecture 19: canceled (?)
M 20 Spring Break
W 22 Spring Break
M 27 Lecture 19: Laplace's equation
Derivation via calculus of variations
Assignment 13 Due Wednesday April 22
W 29 Lecture 20:
M Apr 3 Lecture 21: Calculus of variations
W 5 Lecture 23:
M 10 Lecture 24:
W 12 Lecture 25:
Final Assignment Due Wednesday May 3
M 17 Lecture 26:
W 19 Lecture 27:
M 24 Lecture 28 (last lecture):
F Apr 28 Final Exam 11:20-2:10
Th May 4 Game Over