Location & Time

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

Instructor

Kamesh Madduri
Office hours:
MW 1.30PM-2.30PM (343E IST)
F 1.30PM-2.30PM (Skype,
ID madduri.451.officehours)
Appointment (cal)

TA

Ping Chi
Office hours:
TTh 1.00PM-2.00PM (338E IST)

Important Dates

Aug 22. First class
Sep 02. HW1 given out
Sep 02. HW1 due
Sep 16. HW2 given out
Sep 23. HW2 due
Sep 26. Midterm exam 1
Oct 07. HW3 given out
Oct 14. HW3 due
Oct 26. HW4 given out
Oct 31. Midterm exam 2
Nov 04. HW4 due
Nov 14. Extra-credit HW given out
Nov 21. HW5 given out
Nov 30. Extra-credit HW due
Dec 05. HW5 due

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

Approximations in Scientific Computing, Floating Point Arithmetic, Systems of Linear Equations, Linear Least Squares, Non-linear Equations, Interpolation, Numerical Integration, Numerical Differentiation, Initial Value Problems for ODEs.

Syllabus

Last updated Sep 19. pdf icon

Schedule

Lecture 1, Aug 22
Course Logistics
Introduction to Scientific Computing
Error Analysis
Lecture 2, Aug 24
Error Analysis
Sensitivity and Conditioning
Review
Lecture 3, Aug 26
Floating-point systems
IEEE-754 standard
Lecture 4, Aug 29
Floating-point computations
Octave tutorial
Lecture 5, Aug 31
Octave tutorial (continued)
Linear systems introduction
Vector Norms
Lecture 6, Sep 2
Matrix Norms and Condition Number
Error Bounds
HW 1 online
Lecture 7, Sep 7
Transformations
Triangular systems
Forward and Back substitution
Lecture 8, Sep 9
Gaussian Elimination
HW 1 due
Lecture 9, Sep 12
LU Factorization with Partial Pivoting
Exercises
Lecture 10, Sep 14
HW1 discussion
Linear systems with Octave
Lecture 11, Sep 16
Octave examples continued
Gauss-Jordan elimination
HW 2 online
Lecture 12, Sep 19
Solving modified systems
Special types of linear systems
Lecture 13, Sep 21
Linear systems software
Non-linear systems: Introduction
Lecture 14, Sep 23
Review of floating-point arithmetic
Lecture 15, Sep 26
Review of linear systems
Midterm Exam 1
Lecture 16, Sep 28
Midterm Exam solutions discussion
Non-linear systems: conditioning
Lecture 17, Sep 30
Convergence rate
Intermediate value theorem
Interval Bisection
Lecture 18, Oct 3
Fixed-point iterations
Newton's method
Lecture 19, Oct 5
Newton's method convergence theorems
Secant method
Lecture 20, Oct 7
Inverse Quadratic Interpolation
Linear Fractional Interpolation
Dekker's method, Brent's method
HW3 online
Lecture 21, Oct 10
Non-linear equations: exercises, Halley's method
Octave code
Lecture 22, Oct 12
Non-linear equations, exercises
Non-linear systems: Fixed-point, Newton method
Lecture 23, Oct 14
Secant updating methods: Broyden method
Lecture 24, Oct 17
Interpolation: Introduction
Basis functions, monomial basis, Horner evaluation
Lecture 25, Oct 19
Lagrange Interpolation
Newton Interpolation
Lecture 26, Oct 21
Divided differences
Orthonormal polynomials
Legendre polynomials
Lecture 27, Oct 24
Chebyshev points
Piecewise polynomial interpolation
Lecture 28, Oct 26
Hermite cubic, cubic splines
Octave examples for polynomial interpolation
Lecture 29, Oct 28
Octave examples for polynomial, spline interpolation
Review of non-linear systems
Lecture 30, Oct 31
Review of Interpolation
Midterm exam 2
Lecture 31, Nov 2
Numerical Quadrature: Introduction
Method of Undetermined Coefficients
Lecture 32, Nov 4
Newton-Cotes Quadrature
Clenshaw-Curtis Quadrature
Lecture 33, Nov 7
Midterm exam 2 discussion
Gaussian Quadrature
Lecture 34, Nov 9
Progressive Gaussian Quadrature
Composite Quadrature
Adaptive Quadrature
Octave code: Newton-Cotes rules
Lecture 35, Nov 11
Octave code: Composite and Adaptive Quadrature
Other Integration Problems
Lecture 36, Nov 14
Numerical Differentiation
Richardson Extrapolation
Lecture 37, Nov 28
ODEs: Introduction
Lecture 38, Nov 30
ODEs: Existence, Uniqueness
Lecture 39, Dec 2
ODEs: Stability
Euler's method
Lecture 40, Dec 5
Backward Euler method
Stiff ODEs
Lecture 41, Dec 7
Runge-Kutta methods
Numerical Integration: Review
Lecture 42, Dec 9
Review for final exam

Textbook

Michael Heath, Scientific Computing: An Introductory Survey, second edition, Mc-Graw Hill Higher Education, 2002.

Prerequisites

Three credits of programming; MATH 230 or MATH 231.

Class material

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



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