Location & Time

MWF 1.25 AM-2.15 PM
218A Hosler Building

Instructor

Kamesh Madduri
Office hours:
MWF 2.30 PM-3.30 PM (343E IST,
Skype: madduri.psu)
Appointment (cal)

TA

Diman Tootaghaj
Office hours:
Tue 8.30 AM-9.30 AM,
Th 11.30 AM-12.30 PM (338E IST)

Important Dates

Aug 27. First class
Sep 07. HW1 posted
Sep 14. HW1 due
Sep 19. HW2 posted
Sep 26. HW2 due
Sep 28. Midterm 1
Oct 17. HW3 posted
Oct 24. HW3 due
Nov 02. HW4 posted
Nov 05. Midterm 2
Nov 12. HW4 due
Dec 03. HW5 posted
Dec 10. HW5 due
Dec 19. Final exam

Overview

This class introduces students to key topics in numerical analysis, with emphasis on the computational mathematics behind numerical methods and on proving theorems. CMPSC/MATH 451 is a related course that has a significant overlap with topics studied in CMPSC/MATH 455 and CMPSC/MATH 456. Students may obtain credit for either this class or CMPSC/MATH 451, but not both.

Topics

Floating Point Arithmetic, Approximations in Scientific Computing, Non-linear equations in one variable, Linear Systems: Direct Methods, Polynomial Interpolation, Piecewise Polynomial Interpolation, Numerical Differentiation, Numerical Integration.

Syllabus

Last updated Oct 11. pdf icon

Schedule

Lecture 1, Aug 27
Course Logistics
Introduction to Scientific Computing
Lecture 2, Aug 29
Taylor's theorem
Types of error
Lecture 3, Aug 31
Analyzing algorithms
Problem conditioning
Lecture 4, Sep 5
Floating-point systems
Lecture 5, Sep 7
Rounding unit
Roundoff error accumulation
Octave tutorial
Lecture 6, Sep 10
IEEE standard
Cancellation error
More Octave examples
Lecture 7, Sep 12
Non-linear equations: Introduction
Interval bisection
Lecture 8, Sep 14
Fixed point iteration
Lecture 9, Sep 17
Order of convergence
Newton's method
Examples
Lecture 10, Sep 19
Secant method
Octave examples
Lecture 11, Sep 21
Secant method order of convergence
Lecture 12, Sep 24
HW1 discussion
Multiple roots
Lecture 13, Sep 26
Function minimization using Newton's method
Linear Systems Introduction
Lecture 14, Oct 1
Matrices Review
Vector and Matrix Norms
Lecture 15, Oct 3
Midterm 1 discussion
Lecture 16, Oct 5
Midterm 1 discussion (continued)
Special classes of matrices
Operation counts
Lecture 17, Oct 8
Forward and Backward substitution
Gaussian Elimination
Lecture 18, Oct 10
Gaussian Elimination (continued)
Examples
Lecture 19, Oct 12
GE with Pivoting
Octave Linear Systems tutorial
Lecture 20, Oct 15
Octave code for Gaussian Elimation
GE with Complete pivoting
Uniqueness of GE
Lecture 21, Oct 17
Cholesky decomposition
Example
Lecture 22, Oct 19
Sparse matrices, banded systems
Error analysis, Matrix conditioning
Lecture 23, Oct 22
Linear systems exercises
Lecture 24, Oct 24
Linear systems exercises
Lecture 25, Oct 26
Interpolation: Introduction
Monomial Basis
Lecture 26, Oct 31
Lagrange Interpolation
Newton's basis
Lecture 27, Nov 2
Divided Differences
Lecture 28, Nov 5
Review for Midterm exam 2
Lecture 29, Nov 7
Midterm exam 2 solutions
Lecture 30, Nov 9
Error in polynomial interpolation
Chebyshev interpolation
Lecture 31, Nov 12
Piecewise linear interpolation
Piecewise cubic interpolation
Lecture 32, Nov 26
Review of piecewise interpolation
Cubic spline interpolation
Lecture 33, Nov 28
Numerical Differentiation, finite difference schemes
Richardson extrapolation
Lecture 34, Nov 30
Numerical Integration, Quadrature rules
Newton-Cotes quadrature rules
Lecture 35, Dec 3
Precision of Newton-Cotes rules
Composite quadrature
Octave tutorial
Lecture 36, Dec 5
Clenshaw-Curtis quadrature
Gaussian quadrature
Lecture 37, Dec 7
Adaptive quadrature
Romberg integration
Octave examples
Lecture 38, Dec 10
Review lecture
Lecture 39, Dec 12
Review lecture
Lecture 40, Dec 14
Review lecture

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.



Last updated: