Location & Time

Section 1: MWF 2.30 PM-3.20 PM
167 Willard Building
Section 2: MWF 1.25 PM-2.15 PM
365 Willard Building

Instructor

Kamesh Madduri
Office hours:
TR 12 PM-1.30 PM (343E IST)
Appointment (cal)

TA

Hongyuan Zhan
Office hours:
MWF 10 AM-11 AM (350 IST)

Important Dates

Jan 11. First class
Feb 08. HW1 due
Feb 17. HW2 due
Feb 24. Exam 1
Mar 23. HW3 due
Apr 01. HW4 due
Apr 04. Exam 2
Apr 13. HW5 due
Apr 22. HW6 due
May 04. Final exam

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 February 7. pdf icon

Schedule

Lecture 1, Jan 11
Course Logistics
Lecture 2, Jan 13
Types of error
Taylor's theorem
Asymptotic notation for error
Lecture 3, Jan 15
Asymptotic notation
Criteria for assessing numerical methods
Lecture 4, Jan 20
Problem conditioning
Floating-point systems
Lecture 5, Jan 22
Floating-point systems
Rounding rules
Lecture 6, Jan 25
IEEE floating-point standards
Rounding unit
Lecture 7, Jan 27
Octave tutorial
Lecture 8, Jan 29
Octave tutorial
Lecture 9, Feb 1
Error in floating-point arithmetic
Cancellation error
Nonlinear equations: Introduction
Lecture 10, Feb 3
Interval bisection
Fixed point iteration
Lecture 11, Feb 5
Fixed point theorem
Order of convergence
Lecture 12, Feb 8
Newton's method
Lecture 13, Feb 10
Secant iteration
Java applets
Lecture 14, Feb 12
Octave code
Lecture 15, Feb 15
Linear independence
Vector norms
Lecture 16, Feb 17
Matrix norms
Special classes of matrics
Operation counts
Lecture 17, Feb 19
Backward and forward substitution
Gaussian Elimination
Lecture 18, Feb 22
Review for exam 1
Lecture 19, Feb 24
Exam 1
Lecture 20, Feb 26
Elimination matrices
LU decomposition
Lecture 21, Feb 29
GE with Partial and Complete Pivoting
Lecture 22, Mar 2
Gauss-Jordan elimination
Review: Numerical computations in practice
Lecture 23, Mar 4
Exam 1 solutions discussion
Octave code for linear systems
Lecture 24, Mar 14
LU Factorization uniqueness
Cholesky decomposition
Lecture 25, Mar 16
Sparse matrices
Error and matrix conditioning
Lecture 26, Mar 18
Monomial basis
Lagrange basis
Lecture 27, Mar 21
Newton basis
Divided differences
Lecture 28, Mar 23
Interpolation applets
Error in polynomial interpolation
Lecture 29, Mar 25
Chebyshev interpolation
Interpolation Octave tutorial
Piecewise polynomial interpolation: Introduction
Lecture 30, Mar 28
Piecewise hermite interpolation
Cubic spline interpolation
Lecture 31, Apr 1
Exam 2 review
Lecture 32, Apr 4
Exam 2
Lecture 33, Apr 6
Numerical Differentiation
Lecture 34, Apr 11
Integration: Introduction
Newton-Cotes quadrature
Lecture 35, Apr 13
Clenshaw-Curtis quadrature
Composite quadrature
Java applets
Lecture 36, Apr 15
Adaptive quadrature
Octave code
Exam 2 solutions discussion
Lecture 37, Apr 18
IVP ODEs: Introduction
Lipschitz continuity
Lecture 38, Apr 20
ODE solution stability
Forward Euler method
Backward Euler method
Lecture 39, Apr 22
ODE Error analysis
Runge-Kutta methods
Lecture 40, Apr 25
ODEs Octave code
Java applets
Exercises
Lecture 41, Apr 27
Final exam review
Lecture 42, Apr 29
Final exam review

Textbook

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

Prerequisites

MATH 230 or MATH 231; Three credits of programming.

Class material

Lecture notes and homework assignments will be posted on Canvas.



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