Course: Numerical Methods
Course Information:
When: MW 4:30pm - 5:45pm (EST)
Where: Wilmeth Active Learning Center 2087
Zoom: https://purdue-edu.zoom.us/j/9874334092?pwd=MVRVcHhjQXFac0VYUHcwUzdHK2tFUT09
Instructor: Pan Li
Office Hour of Pan Li: Mon. & Wed. 5:45pm-6:15pm, Wilmeth Active Learning Center 2087 (after the lectures on Mon. & Wed.)
Teaching Assistants and the Office Hours:
Adarsh Barik, abarik@purdue.edu;
Office Hour: Mon. 3:00 - 4:00pm; in-person TA hours at HAAS G72
Ji Hun Hwang, hwang102@purdue.edu;
Office Hour: Fri. 9 - 10am; Zoom link: https://purdue-edu.zoom.us/j/2426186420
Shu Li, li3916@purdue.edu;
Office Hour: Wed. 9:15 - 10:15pm; in-person TA hours at HAAS G72
Deepak Maurya, dmaurya@purdue.edu;
Office Hour: Wed. 2:15 - 3:15pm; in-person TA hours at HAAS G72
Textbook:
Numerical Methods by Anne Greenbaum and Tim Chartier
Content:
This course is a introductory course on numerical computation.
Topics include (tentative):
Basics (Chapters 1-5)
Introduction and Mathematical modeling (1-2) (Coding examples)
Readings: Chapter 1 and Appendices A & B of the textbook
Introduction to software for numerical computation (Julia) (1-2) (Chapter 2) (install tutorial) (Coding examples)
Readings: Chapter 2 of the textbook and Tutorial on Julia (Chapter 1-5 and plotting)
[Homework 1: Mathematical Modeling + Julia]
Floating-point computation (2) (Chapter 5)
[Sep 6. No class]
Monte Carlo methods (1) (Chapter 3) (Coding examples)
Newton's method for root finding, bisection search, fixed-point iteration (2) (Chapter 4) (Coding example)
[Homework 2: Floating-point + MC methods + Netwon]
Midterm I on Sep. 29 (covers 1-5)
Linear system (Chapters 6,7,12)
Gaussian elimination and its complexity, LU factorization, pivoting (2) (Chapter 7.1 - 7.3) (Coding example)
Conditioning and error in linear systems (2) (Chapter 6, Chapter 7.4 - 7.5) (Coding example)
[Homework3: Linear systems, Conditioning, error]
[Oct 11. No class]
QR factorization and least squares (1) (Chapter 7.6)
Iterative methods to solve linear systems and Conjugated gradient descent (2) (Chapter 12.2)
Eigenvalues problems (1-2) (Chapter 12.1)
[Homework4: QR, LS, iterative methods, eigenvalues]
Midterm II on Nov. 10 (covers 6-11)
Numerical calculus (Chapters 8-11, some 13, 14)
The Vandermonde form and the interpolating polynomial (1-2) (Chapter 8.1 - 8.3).
Chebyshev and spline interpolation (1-2) (Chapter 8.5 - Chapter 8.6)
Numerical integration: Newton-Cotes, piecewise integration (1) (Chapter 10.1-10.2)
[Homework 5: interpolation, newton-cotes]
Numerical integration: Gaussian Quadrature (1) (Chapter 10.3)
[Nov 24. No class]
Numerical Methods for ODE: Euler's methods, midpoint, Runge-Kutta (1) (Chapter 11.1, 11.2)
Numerical Methods for ODE: Local truncation error and convergence (1) (Chapter 11.1, 11.2)
[Homework 6: numerical integration and ODE]
Midterm III on Dec. 8 (covers parts of 12-17)
Prerequisite:
Students should get at least C, suggested B, in the following (or equivalent) course categories.
Evaluation
Homework: 6% * 6 = 36%
The due of a homework will be Friday 11:59 pm, next week after the homework gets released.
Late submission is allowed. The late due is the first monday 11:59 pm after the Friday due. Late submission can only get 80% credit.
Quizzes (3% * 4 = 12%)
Three midterms (20% + 20% + 12% = 52%, in-class exam)
Scribing Lecture Notes / Commenting on HWs (3% bonus)
Survey (1% bonus)
Grading
The anticipated grade ranges are
A+---95% +
A --- 87 - 95%
B --- 70 - 86%
C --- 55 - 69%
D --- 40 - 55%
F --- 0 - 40%
These may be adjusted downward by up to 10% to achieve a reasonable grade distribution. They also may be minor upward adjustments.
Homeworks
Homework 1 Mathematical Modeling + Julia [Due Sep 10]
Homework 2 [Release due Sep 13] [Due Sep 24]
Homework 3 [Release due Oct 04] [Due Oct 22]
Homework 4 [Release due Oct 25] [Due Nov 05]
Homework 5 [Release due Nov 08] [Due Nov 19]
Homework 6 [Release due Nov 22] [Due Dec 3]