Instructor: Nelson Castaneda Office: Marcus White 111

Phone: 832-2851

E-mail: castanedan@ccsu.edu

Office Hours: Tuesdays and Thursdays 12 – 1 PM. We can meet at a different time if necessary.

Major Goals: This course introduces students to the basic methods of Numerical Analysis. We study algorithms to find approximate solutions to problems from Calculus, Differential Equations and other areas of mathematics. This course serves also as an introduction to scientific computation using MATLAB. Graduate students are required to complete and additional project.

Credits: 3

Prerequisite: Math 221 and CS 152, or permission of the instructor.

Section: Class meets MTWR from 1 PM to 3 PM in NC - 22405

Topics Considered: Nonlinear Equations, Interpolation and Polynomial Approximation, Curve Fitting, Numerical Differentiation and Integration, Numerical Solutions of Ordinary Differential Equations.

Textbook: Numerical Methods using MATLAB by J. H. Mathews and K. D. Fink, Fourth Edition, Pearson.

Exams: There will be two non-cumulative in-class tests, several MATLAB projects and a final exam. The two tests are worth 100 points each and will be given on July 13 and July 27. The final exam is cumulative and worth 150 points. The date of the final exam is Thursday, August 5 from 1 PM to 3 PM.

Homework: A list of homework problems will be handed out. Homework will not be collected but will be discussed in class.

Projects: A few MATLAB projects will be assigned during the semester. They are worth 100 points total. In addition to this, Graduate Students will submit a special final project worth 100 points at the end of the semester.

Grade: There is a total of 450 points possible for undergraduate and 550 points for graduate students. To earn an A- you must score at least 90% of the points, to earn a B- at least 80%, to earn a C- at least 70%, and to earn a D- at least 60%.

Chapter 1. Preliminaries

1.1 Review of Calculus : 2, 3, 6, 12

1.2 Binary Numbers: 1 - 5, 7, 8, 13

1.3 Error Analysis: 1, 2, 3, 5, 8, 9, 10, 12

Chapter 2. Solution of Nonlinear Equations f(x) = 0

2.1 Iteration for Solving x=g(x): 1, 3, 8, 10

2.2 Bracketing Methods for Locating a Root: 1 - 5

2.3 Initial Approximation and Convergence Criteria: 1, 3, 5

2.4 Newton-Raphson and Secant Methods: 2, 5, 6, 11, 13, 18, 21

Chapter 4. Interpolation and Polynomial Approximation

4.1 Taylor Series and Calculation of Functions: 1, 2, 3, 5, 9, 10

4.2 Introduction to Interpolation: 1, 2

4.3 Lagrange Approximation: 1, 3, 5

4.4 Newton Polynomials: 1, 3, 5

Chapter 5. Curve Fitting

5.1 Least-Square Line: 1, 2, 8

5.2 Methods of Curve Fitting: 1, 3, 6

5.3 Interpolation by Spline Functions: 1, 3, 5, 7

5.4 Fourier Series and Trigonometric Polynomials: 1, 3, 6, 7

Chapter 6. Numerical Differentiation

6.1 Approximating the Derivative: 1, 3, 5, 6

6.2 Numerical Differentiation Formulas: 1, 4, 6 – 8, 14

Chapter 7. Numerical Integration

     7.1 Introduction to Quadrature: 1, 3, 4, 5

     7.2 Composite Trapezoidal and Simpon’s Rule: 1 – 3, 6, 9

     7.3 Recursive Rules and Rombert Integration: 1, 3, 5

     7.4 Adaptive Quadrature: 1

Chapter 9. Solution of Differential Equations

     9.1 Introduction to Differential Equations: 1 – 9, 13, 14

     9.2 Euler’s Method: 1, 3, 5, 7

     9.3 Heun’s Method: 1, 3, 6, 7

     9.4 Taylor Series Method: 1, 3, 5, 9

     9.5 Runge-Kutta Methods: 1, 3, 5, 7

2. In the event of a weather emergency, which requires curtailment or cancellation of classes, listen to WTIC (1080 AM) or call 832-3333 for the "general snow message." In the event that I am prevented from traveling to campus and must cancel class, I will place an "extended absence greeting" on my office phone, 832-2851.

3. Last day to drop the class is October 18. Withdrawal forms are available in the

Enrollment Center, Willard Hall. Cessation of attendance, notice to the instructor, or telephone calls to the Enrollment Center are not considered official notice of a student’s intention to withdraw from the course.