Numerical Methods - Tilley WPI - MA3457-CS4033

MA 3457/CS 4033 - Numerical Methods for Calculus and Differential Equations

B-Term 2019

Prof. B.S. Tilley

Department of Mathematical Sciences

Worcester Polytechnic Institute

Instructor: Prof. B.S. Tilley

Department of Mathematical Sciences

Worcester Polytechnic Institute

Office: SH 105A

TA: Evan Witz

e-mail: tilley@wpi.edu

Tilley Home Page

Phone: (508) 831-6664

Office Hours: MRF 1:00-1:50 or by appt.

email: ewitz@wpi.edu

Course Description: This course provides an introduction to modern computational methods for differential and integral calculus and differential equations. Topics covered include: interpolation and polynomial approximation, approximation theory, numerical differentiation and integration, numerical solutions of ordinary differential equations. Error analysis will be emphasized throughout. Undergraduate credit may not be earned for both this course and for MA 3255/CS 4031.

Prerequisites: Recommended background: MA 2051. An ability to write computer programs in a scientific language is assumed. In our class, we will be using MATLAB for numerical computations and coding labs.

Installation instructions for Matlab at WPI

System Requirements for Matlab

Recommended Text: Numerical Analysis, Tenth Edition, R.L. Burden, D.J. Faires, A.M. Burden (ISBN-13: 978-1305253667 ) (2015)

Course Organization

The course content is organized in the following themes

Calculus: Interpolation, Lagrange polynomials, splines, orthogonal polynomials, numerical differentiation, quadrature techniques
Ordinary Differential Equations: Forward Euler, Multistep Methods, Runge-Kutta, Adaptive Time-Stepping

To learn the material fully, we apply the following methods

Theory: Extending concepts from analysis and linear algebra to algorithms intended to approximate their computational analogues. Requires mathematical proof and rigor.
Practice: Developing scripts in MATLAB to implement these algorithms and verify that the results are consistent with the mathematical theory.

Classroom Culture

During class, please silence/turn off all cell phones. Laptops will be needed to work on the laboratory assignments at times during class, but otherwise laptops and tablet should be turned off. Side discussions and comments should be kept to a minimum, and should not be disruptive to other students during the class.

Course Grades and Policies

Grades will be determined based on homework assignments, coding projects and three in-class exams

Homework & Labs: 50%: These assignments will be a combination of written assignments along with programming assignments (labs). The labs will be uploaded onto Canvas (https://canvas.wpi.edu), and the format for the labs are MATLAB Scripts. Written homework will be turned in during class. All written assignments should be neatly written or typed (e.g. LaTeX or Microsoft Word). Illegible problems will receive no credit. Due dates for assignments can be found on the Canvas course site. Late assignments will not be accepted.
Two Exams: 50% Two in-class exams will take place at the dates below. The topics are the specific themes described above. Note that Exam 3 is on the final day of class, so plan accordingly. Plane tickets leaving for the break is not a sufficient reason to miss or reschedule Exam 2.
- Exam 1 (25%): November 11, 2019
- Exam 2 (25%): December 13, 2019
Grading Policy Students have two business days to contact the instructor about potential errors in grading any assignment (homework, labs, exams) after receiving their graded work. Beyond this time, the grade on that assignment is final.
Make-Up Exam Policy Make-up for Exam 1 requires permission from the instructor at least two days prior to the exam, at which time a date for the make-up exam will be agreed upon by the student and instructor. No make-up exams are allowed after the scheduled exam is given (see the dates above). Students who cannot attend Exam 2 at the time above due need to inform the instructor at least two days prior to the exam. If the instructor feels that the reason to miss the exam is a valid one, the student will receive an incomplete (I) for the course, and the make-up will be taken in Spring 2020.
Accommodations: Reasonable accommodations will be made for students with verifiable disabilities. Students with disabilities who need to utilize accommodations in this class are encouraged to contact the Office of Disability Services (ODS) as soon as possible to ensure that such accommodations are implemented in a timely fashion. This office can be contacted via email: DisabilityServices@wpi.edu, via phone: (508) 831-4908, or in person: 124 Daniels Hall. If you have approved accommodations, please request your accommodation letters online through the Office of Disability Services Student Portal.

Academic Integrity and WPI Policies

All students are expected to be familiar with and adhere to WPI’s policy on academic integrity (i.e., no cheating, fabrication, facilitation, or plagiarism). Please refer to the WPI Academic Honesty Policy within the Student Code of Conduct (https://www.wpi.edu/about/policies/academic-integrity). Academic integrity violations will be prosecuted according to the university’s policy. For more details as to what constitutes academic dishonesty, please see https://www.wpi.edu/about/policies/academic-integrity/dishonesty.

Students are responsible to complying with all of WPI's policies at https://www.wpi.edu/about/policies

Course Schedule (updated frequently)