Math 377: Numerical Methods

Lectures: MWF 13:00-13:50 in TAC 208
Laboratory: F 14:00-14:50 in Snell 241
Instructor: Carmeliza Navasca, (cnavasca@clarkson.edu), SC 391
Office Hours: MW 9:30-10:00, 12:00-13:00 and F 11:00-13:00

Objectives:
(1) to learn the basics of numerical analysis which entails understanding why numerical methods work and their limitations
(2) to acquire computational experience

Course Info

Textbook: John H. Mathews and Kurtis D. Fink, Numerical Methods Using Matlab, Fourth Edition, Prentice Hall.

Prerequisites: Math 231, Math 232 and some knowledge of Matlab.

Grading Scheme: 15% hw, 5% quiz/blog, 10% mini project, 20% midterm 1, 20% midterm 2, 30% final exam

Participation: Class participation (e.g. asking questions and participating in discussions) is encouraged. Your interaction will be considered when assigning borderline grades.

Homework: Weekly assignment will be collected every Friday at the beginning of class. Some problems will require some amount of Matlab programming. No late hw will be accepted. However, two hw grades will be dropped.

Quiz: There will be quizzes. Some will be announced. The lowest quiz grade will be dropped.

Project: There will be several mini projects. The projects which are computational in nature can be done in groups of two or more.

Exam: The two midterms are scheduled on Oct 6 and Nov 8. There is one comprenhensive exam TBA. No make-up exam will be given unless you have proper documentation. No shows on exams will result on an F grade.

Handouts and Other Info: All other info can be found at moodle.

Reading and Blogging: To acheive our objectives you must read the sections ideally before lecture. To encourage this activity, you must blog about the reading material weekly. Your blog must have at least three sentences summarizing the sections read and one question on something you find unclear.

Course Syllabus


Week 1: Aug 23-27
1.1 Review of Calculus
1.2 Binary Numbers
1.3 Error Analysis
Matlab Tutorial

Week 2: Aug 30-Sept 3
2.1 Iterative Nonlinear Equation Solver
2.2 Bisection Method
2.3 Initial Approximation and Convergence Criteria

Week 3: Sept 6-10
2.4 Newton-Raphson and Secant Method
4.1 Taylor Series

Week 4: Sept 13-17
4.2 Introduction to Interpolation
4.3 Lagrange Approximation
4.4 Newton Polynomials

Week 5: Sept 20-24
5.1 Least-Squares LIne
5.2 Methods of Curve Fitting
5.3 Interpolation by Spline Functions

Week 6: Sept 29-Oct 1
Fall Recess
6.1 Approximating the Derivative
6.2 Numerical Differentiation Formulas

Week 7: Oct 4-Oct 8
Review
Midterm 1
7.1 Introduction to Quadrature

Week 8: Oct 11-Oct 15
7.2 Composite Trapezoidal and Simpson's Rule
7.3 Recursive Rules
7.4 Gauss-Legendre Integration

Week 9: Oct 18-Oct 22
9.1 Introduction to Differential Equations
9.2 Euler's Method
9.3 Heun's Method
9.4 Taylor Series Method

Week 10: Oct 25-Oct 29
9.5 Runge-Kutta Methods
9.6 Predictor-Corrector Methods
3.1 Introduction to Vectors and Matrices

Week 11: Nov 1-Nov 5
3.2 Gaussian Elimination and Pivoting
3.6 Iterative Methods for LInear Systems
Review

Week 12: Nov 8-Nov 12
Midterm 2
10.1 Hyperbolic Equations
10.2 Parabolic Equations

Week 13: Nov 15-Nov 19
11.1 Homogeneous Systems: Eigenvalue Problem
11.2 Power Method
11.3 Jacobi's Method

Week 14: Nov 22
Review
Thanksgiving Break

Week 15: Nov 29-Dec 3
Work on Project