Numerical Methods for Calculus and Differential
Equations
MA3457/CS4033 - 2016 B term
Lecture and Homework Schedule
The following lecture schedule is tentative. It is expected that we will follow
it rather closely, but there will be minor deviations from time to time.
Note: There may be topics covered in conference that are not listed in
the lecture listing below.
|
Lecture |
Date |
Topic
|
Files/Homework
|
|
1 |
Tu
Oct 25 |
Introduction to MA3457/CS4033 |
Learn Matlab |
|
Conf |
We
Oct 26 |
Conference – PIC Math Industrial Case Study Videos |
Homework 1 due Wed Nov
2nd |
|
2 |
Th
Oct 27 |
Errors, Condition Number, Error Propagation |
|
|
3 |
Fr
Oct 28 |
Condition Number, Error Propagation |
|
|
|
|
|
|
|
4 |
Mon
Oct 31 |
Taylor Polynomials and Big Oh notation |
|
|
5 |
Tu
Nov 1 |
Interpolation Interpolation vs Approximation |
Demonstration - polygui.m
and polyinterp.m |
|
6 |
We
Nov 2 |
The
Lagrange Interpolation Problem -- Lagrange's formulation Homework 1 due |
|
|
7 |
Th
Nov 3 |
Proof of Uniqueness of
Solution to Lagrange Interpolation Problem. |
|
|
8 |
Fr
Nov 4 |
Discrepancy
between a function and its L. I. Polynomial |
Homework 2 due Thurs
Nov 10 |
|
. |
. |
. |
|
|
9 |
Mo
Nov 7 |
Splines |
|
|
10 |
Tu
Nov 8 |
Linear, Quadratic and Cubic
Splines |
|
|
Conf |
We
Nov 9 |
Plotting the Lagrange Interpolating Polynomial: An example LagIntPoly_gauss.m |
|
|
11 |
Th
Nov 10 |
Homework 2 due |
|
|
12 |
Fr
Nov 11 |
Homework 3 due Wed Nov
16 |
|
|
. |
. |
|
|
|
13 |
Mo
Nov 14 |
“Best Fit” to data |
|
|
14 |
Tu
Nov 15 |
Discrete Least Squares |
|
|
15 |
We
Nov 16 |
Discrete Least Squares
Polynomial Fit Normal Matrices, Ill-conditioning Homework 3 due |
|
|
16 |
Th
Nov 17 |
Loglinear fit |
Homework 4 due Wed Nov 30 |
|
Conf |
Fr
Nov 18 |
Review for Exam 1 |
|
|
. |
. |
|
|
|
17 |
Mo
Nov 21 |
Exam 1 covering material up to and
including that of lecture #15 (not including Log Linear Fit) |
|
|
18 |
Tu
Nov 22 |
|
|
|
. |
. |
|
|
|
19 |
Mo
Nov 28 |
Orthogonal Functions |
|
|
20 |
Tu
Nov 29 |
Numerical Quadrature |
Section 4.3 Homework 5 due Wed Dec 7 |
|
Conf |
We
Nov 30 |
Homework 4 due Estimating Order of Convergence by Using Polynomials |
|
|
21 |
Th
Dec 2 |
Composite Trapezoid Rule, Composite Simpson's Rule, Error
Formulae |
Section 4.4 |
|
22 |
Fr
Dec 2 |
Estimating Order of Convergence Analytically and Experimentally |
|
|
. |
. |
|
|
|
23 |
Mo
Dec 5 |
Numerical Differentiation |
|
|
24 |
Tu
Dec 6 |
Deriving numerical schemes for first and second derivatives |
|
|
25
|
We
Dec 7 |
Homework 5 due Numerical Methods for ODEs ODEs and Intro to Euler’s Method |
Homework 6 due Wed Dec 14 |
|
26 |
Th
Dec 8 |
Euler’s Method Watch in class “Creating More Realistic
Animation for Movies” Segment I https://youtu.be/z8wlEsSnpQY Segment II https://youtu.be/TwHiZvLz1mA first 8 mins |
|
|
27 |
Fr
Dec 9 |
Midpoint Rule, Modified Euler |
|
|
. |
. |
|
|
|
28 |
Mo
Dec 12 |
Local Truncation Error – Euler,
Midpoint, Modified Euler |
|
|
29 |
Tu
Dec 13 |
Higher Order ODEs, Systems of
ODEs, Miscellany |
|
|
|
We
Dec 14 |
Homework 6 due |
|
|
|
Th
Dec 15 |
EXAM II Exam 2 covering material from lecture #16 up to and including
lecture #29 |
|