Math 413 - Numerical Analysis - Fall 2014
Instructor: Christopher Sadowski
Email: csadowski at ursinus dot edu
Office: Pfahler Hall 101L
Office Hours: T, Th 3:00 - 4:00 and by appointment.
Location: Pfahler Hall 109
Text: Numerical Analysis, Ninth Edition, by Richard L. Burden and J. Douglas Faires
Grading:
-20% Homework and Maple Assignments
-20% Midterm 1
-20% Midterm 2
-40% Final Exam
Exams:
Midterm 1 will be held on Tuesday, 9/30/14.
Midterm 2 will be held on Tuesday, 11/11/14
Midterm 2 solutions
Final Exam will be held on Friday/ 12/12/14 in the usual classroom.
Homework and Maple Labs: There will be weekly homework assigned. Some assignments will involve Maple programming. Students can request Maple to be installed on their laptops at Myrin Library Tech Support. A helpful introduction to Maple can be found here: http://www.math.rutgers.edu/courses/251/maple_new/maple0.html
Homework 1 (due 9/4/14):
Section 1.1: 1, 5, 8, 15
Section 2.1: 1, 7, 10, 12
Homework 2 (due 9/11/14):
Section 2.2: 1abc, 2abc, 5, 17, 20
Section 2.3 20abde (use both Newton's method and the secant method and compare your results. The secant method requires numbers p0 and p1. Use the p1 you obtained with Newton's method for this).
Future homeworks and assignments will be sent out by email.
Syllabus (subject to change as the course progresses):
Week 1: 8/26, 8/28
Section 1.1 Review of Calculus
Section 2.1: The Bisection Method. Code discussed in class can be found here.
Please see comments at the top of code for instructions.
Week 2: 9/2, 9/4
Section 2.2: Fixed Point Iteration
Section 2.3: Newton's Method and Its Extensions
Week 3: 9/9, 9/11
Section 2.4: Error Analysis For Iterative Methods
Section 3.1: Interpolation and the Lagrange Polynomial
Week 4: 9/16, 9/18
Section 3.1 continued
Section 3.3: Divided Differences
Week 5: 9/23, 9/25
Section 3.4: Hermite Interpolation
Section 3.5 Cubic Spline Interpolation
Week 6: 9/30, 10/2
Midterm 1, Covering everything up to and including 3.3
Section 3.5 Cubic Spline Interpolation continued
Week 7: 10/6, 10/9
Section 4.1 Numerical Differentiation
Section 4.2 Richardson Extrapolation
Week 8: 10/16
Section 4.3: Elements of Numerical Integration
Week 9: 10/ 21, 10/23
Section 4.3 continued
Section 4.4: Composite Numerical Integration
Week 10: 10/28, 10/30
Section 4.5: Romberg Integration
Section 4.6: Adaptive Quadrature
Week 11: 11/4, 11/6
Section 4.7 Gaussian Quadrature
Section 4.9 Improper Integrals
Week 12: 11/11, 11/13
Midterm 2 will be on 11/11/14.
Week 13: 11/18, 11/20
Section 5.1 The Theory of Initial Value Problems
Section 5.2 Euler's Method
Week 14: 11/24
Section 5.3: Taylor Methods
Week 15: 12/2, 12/4
Section 5.4: Runge-Kutta Methods