Location & Time

Section 1: MWF 11.15AM-12.05PM
Section 2: MWF 12.20PM-01.10PM
110 Walker Building

Instructor

Kamesh Madduri
Office hours:
MWF 1.30 PM-2.30 PM (343E IST)
Appointment (cal)

TA

Yu-Hsuan Kuo
Office hours:
TR 4.00 PM-5.00 PM (339 IST)

Important Dates

Aug 26. First class
Sep 16. HW1 due
Sep 30. HW2 due
Oct 02. Exam 1
Oct 28. HW3 due
Nov 04. HW4 due
Nov 04. Exam 2
Dec 06. HW5 due
Dec 09. HW6 due
Dec 13. Exam 3

Overview

This class introduces students to key ideas behind numerical computation, with emphasis on the implementation of common numerical methods. CMPSC/MATH 455 is a related course that covers a subset of the topics that we will study in this class. Students may obtain credit for either this class or CMPSC/MATH 455, but not both.

Topics

Floating Point Arithmetic, Approximations in Scientific Computing, Nonlinear equations in one variable, Linear Systems: Direct Methods, Polynomial Interpolation, Piecewise Polynomial Interpolation, Numerical Differentiation, Numerical Integration, Initial Value Problems for ODEs.

Syllabus

Last updated October 28. pdf icon

Schedule

Lecture 1, Aug 26
Course Logistics
Introduction to Scientific Computing
Lecture 2, Aug 28
Error types
Taylor series
Asymptotic notation
Lecture 3, Aug 30
Error bounds
Criteria for assessing numerical methods
Lecture 4, September 4
Problem conditioning
Floating-point systems
Lecture 5, September 6
IEEE floating-point standards
Rounding rules
Lecture 6, September 9
Octave tutorial
Rounding unit
Avoiding roundoff error
Lecture 7, September 11
Floating-point arithmetic
Cancellation error
Lecture 8, September 13
Nonlinear equations: Introduction
Iterative methods
Interval bisection
Lecture 9, September 16
Fixed-point iteration
Order of convergence
Lecture 10, September 18
Rate of convergence
Newton's method
Secant iteration
Lecture 11, September 20
Function minimization
Nonlinear equations: Octave programs
Lecture 12, September 23
Linear systems: Introduction
Linear independence
Lecture 13, September 25
Vector and matrix norms
Lecture 14, September 27
Special classes of matrices
Orthogonal matrices
Lecture 15, September 30
Operation counts
Forward and backward substitution
Lecture 16, October 2
Exam 1 review
Exam 1 (evening)
Lecture 17, October 4
Gaussian elimination
Lecture 18, October 7
Gaussian elimination (continued)
LU decomposition
Lecture 19, October 9
Gaussian Elimination with pivoting
Lecture 20, October 11
Exam 1 solutions discussion
Lecture 21, October 14
Cholesky factorization
Lecture 22, October 18
Gauss-Jordan Elimination
Octave programs
Lecture 23, October 21
Octave programs
Sparse matrices
Relative Error and Matrix Conditioning
Lecture 24, October 23
Polynomial Interpolation: Introduction
Monomial basis
Lagrange basis
Lecture 25, October 25
Newton basis
Divided differences
Lecture 26, October 28
Error in polynomial interpolation
Lecture 27, October 30
Interpolation with derivative values
Piecewise polynomial Interpolation: Introduction
Lecture 28, November 1
Hermite cubic interpolation
Cubic splines
Lecture 29, November 4
Exam 2 review
Exam 2 (evening)
Lecture 30, November 6
Piecewise polynomial interpolation exercises
Lecture 31, November 8
Exam 2 solutions discussion
Numerical differentiation: Introduction
Lecture 32, November 11
Finite difference schemes for computing derivative
Richardson extrapolation
Lecture 33, November 13
Numerical Integration: Introduction
Newton-Cotes quadrature
Lecture 34, November 15
Deriving quadrature rules
Error in quadrature rules
Lecture 35, November 18
Clenshaw-Curtis quadrature
Gaussian quadrature
Composite quadrature
Lecture 36, November 22
Adaptive quadrature
Octave examples
Lecture 37, December 2
Romberg Integration
Multidimensional Integration
Lecture 38, December 4
ODEs: Introduction
Stability, Global error
Lecture 39, December 6
Lipschitz continuity
Euler's methods
Lecture 40, December 9
Runge-Kutta methods
Lecture 41, December 11
ODE exercises
Lecture 42, December 13
Exam 3 review

Textbook

Uri M. Ascher and Chen Greif, A First Course in Numerical Methods, SIAM, 2011.

Prerequisites

MATH 220; MATH 230 or MATH 231; Three credits of programming (CMPSC 201 or CMPSC 202 or CMPSC 121).

Class material

Presentations, lecture notes, and homework assignments will be posted on Angel.



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