CS 323: Numerical Analysis and Computing

Time: 3:50 pm - 5:10 pm, every Tuesday and Thursday

Place: PH Pharmacy Building (William Levin Hall), Room 111

Recitation:

No recitation first week

Instructor: Peng Zhang

Office: Hill 444

Email: pz149@rutgers.edu

Office hours: Thursday 5:30 pm - 6:30 pm or by appointment

TA: Adarsh Srinivasan

Email: as4100@scarletmail.rutgers.edu

Recitation PTL: Sharath Punna

Email: sharath.punna@rutgers.edu

Grader: Parth Goel

Email: pg514@scarletmail.rutgers.edu

Course Description:

This course is an introduction to numerical analysis. During this course, we will learn the concept of error and why we need to analyze and predict it; we will study numerical methods for the basic problems of numerical analysis; we will implement numerical algorithms using programming languages (e.g., MATLAB).

Prerequisites:

Calculus, linear algebra, high-level programming language

Programming languages:

Matlab (You may get a free license at https://www.mathworks.com/academia/tah-portal/rutgers-university-354167.html#get)

Textbook:

Elementary Numerical Analysis, 3rd edition, by Kendall Atkinson, Weimin Han

Additional references:

Numerical Algorithms, Justin Solomon (http://people.csail.mit.edu/jsolomon/share/book/numerical_book.pdf)

Grading:

Written homework and programming projects: 50%

Midterm exam: 25%

Final exam: 25%

Schedule:

9/6: Introduction, a brief intro to MATLAB (Ref: Appendix D of [AH])

9/8: The Taylor polynomial (Ref: Chp 1 of [AH]). HW1 is out, due on Sept 22

9/13: Storing numbers in computers (Ref: Chp 2.1 of [S], Chp 2.1 of [AH])

9/15: machine epsilon, rounding and chopping, errors (Ref: Chp 2.1.2 and Chp 2.2 of [AH])

9/20: sources of error, propagation of error (Ref: Chp 2.2 and 2.3 of [AH])

9/22: error propagation of function evaluation and summation (Ref: Chp 2.3, 2.4 of [AH]). HW 1 is due, HW2 is out, due on Oct 6

9/27: root finding: the Bisection method (Ref: Chp 3.1 of [AH])

9/29: root finding: Newton's method (Ref: Chp 3.2 of [AH])

10/04: root finding: the Secant method (Ref: Chp 3.3 of [AH])

10/06: root finding: fixed point iterations (Ref: Chp 3.4 of [AH]). HW2 is due, HW3 is out, due on Oct 20

10/11: linear algebra review (Ref: Chp 1.2 of [S])

10/13: matrices, solvability of systems of linear equations (Ref: Chp 1.3 and Chp 3.1 of [S])

10/18: matrix inverse, Gaussian elimination (Ref: Chp 3.1 and 3.2 of [S])

10/20: encode row operations, Gaussian elimination (Ref: Chp 3.3 and 3.4 of [S]). HW3 is due, HW4 is out, due on Nov 3

10/25: LU factorization (Ref: Chp 3.5 of [S])

10/27: in-class Midterm

11/01: LU factorization, Tridiagonal systems (Ref: Chp 3.5 of [S], Chp 6.4.1 and Chp 6.4.2 of [AH])

11/03: Error in solving systems of linear equations (iterative refinement, sensitivity analysis) (Ref: Chp 6.5 of [AH]) (A good reading material on iterative refinement) HW4 is due, HW5 is out, due on Nov 17

11/08: iterative methods (Ref: Chp 6.6 of [AH])

11/10: least squares data fitting (Ref: Chp 7.1 of [AH], Chp 4.1.2 and 4.1.3 of [S])

11/15: polynomial interpolation (Ref: Chp 4.1.1 -- 4.1.3 of [AH], Chp 13.1 of [S])

11/17: divided differences (Ref: Chp 4.1.4 -- 4.1.6 of [AH]) HW5 is due, HW6 (optional) is out, due on Dec 1

11/22: error in polynomial interpolation (Ref: Chp 4.2, 4.4, 4.5, 4.6 of [AH])

11/24: Thanksgiving holiday, no class

11/29: pairwise polynomial interpolation/spline interpolation (Ref: Chp 4.3 of [AH])

12/01: numerical integration: the trapezoidal rule (Ref: Chp 5.1 of [AH])

12/06: Simpson's rule, error formula (Ref: Chp 5.1.2 and 5.2 of [AH])

12/08: Gaussian quadrature (Ref Chp 5.3 of [AH])