Numerical Methods
for Calculus & Differential Equations
B'11 Course Information

Info
MA3457/CS4033 Mon, Tue, Thu, Fri: 2 pm Section B01



Course Information | Homework Assignments | Mini-Projects | Test Preview | Announcements & Hints




Instructor: TA:

Vadim V. Yakovlev

Office: SH104C
Phone: x 5495
E-mail: vadim@wpi.edu

William Sanguinet

Office: SH201
Phone: x5546
E-mail: wcsanguinet@wpi.edu

Classes & Office Hours:

Monday Tuesday Wednesday Thursday Friday
Lectures
@ HL154
2:00-2:50 pm 2:00-2:50 pm - 2:00-2:50 pm 2:00-2:50 pm
Conferences
@ HL154
- - 2:00-2:50 pm - -
Office Hours *) 3:00-3:50 pm (I) 1:00-1:50 pm (TA) - 4:00-4:50 pm (I) 1:00-1:50 pm (TA)
____________
*) Also by appointment


Course Objectives:

The course's primary goal is to introduce the students to a wide range of numerical algorithms related to problems in Calculus and Differential Equations, explain their fundamental principles and illustrate their applications.

Upon completing the course the students will be able to apply numerical procedures to solve applied problems and, when applying the algorithms to particular practical scenarios, control their performance.

Main Topics: Course Contents:
  1. Interpolation
  2. Approximation
  3. Numerical Integration
  4. Initial Value Problems
  5. Boundary Value Problems
  • MATLAB Computation related to 1 to 5
Four 1-hour lectures a week
One 1-hour conference a week
Daily homework assignments
Five Topic Quizzes
Four Mini-Projects
Two Midterms
The Final (including comprehensive MATLAB test)
Useful Sources:

Text:

R.L. Burden and J.D. Faires, Numerical Analysis, 9th Edition, Brooks/Cole, 2011.

Further Reading:

Reference lists for Topics 1 to 5

Course Web Page:

http://www.wpi.edu/~vadim/NM_I/B11_Info.html

Grading Scheme:

The 100% course grade is based on:

Topic Quizzes (20%, 5 times, 4% each),
Mini-Projects (20%, 4 Projects, 5% each),
Midterms (30%, 1st - 15%, 2nd - 15%),
Final Exam (30%, Part 1 - 15%, Part 2 - 15%).

Point ranges derived to percents for grades are given by:

Percentage 90 80 - 90 70 - 80 < 70
Grade A B C NR

Homework & Quizzes:

Each topic covered in the course is illustrated by a number of applied problems to be solved at home. The list of recommended problems can be found on the Homework Assignments page.

Papers with the homework problems are not handed in, so each student should take a personal responsibility for doing sufficient study and practice.

In the end of each course section, there will be a 15 min quiz composed from the homework problems assigned in the preceding classes. Using notes will be allowed when doing the quiz.

Mini-Projects:

Work on each course topic will be accompanied by a short project (to be completed by the end of each part of the course; the printed copies are due by the Project Days in accordance with the Schedule of Events.)

The projects are not supposed to be extended and complex, but their presence in the course is essential: they should familiarize students with practical use of MATLAB for solving applied problems. This work will be done in pairs as independent studies: to complete the projects, additional reading and practicing may be necessary.

The project descriptions and tasks can be found on the Mini-Projects page.

Midterms & Final Exam:

There will be two Midterms covering Topics 1 to 3. The Final Exam will consist of two parts (each one of 1 hour length):

(I) Part I is similar to Midterms and covers Topics 4 and 5.

(II) Part II involves practical MATLAB work and covers the subjects from the entire course. (This test will take place in a computer lab immediately following Part I.

The Midterms and the First part of the Final are open book & open notes events. The use of calculators is allowed; however, it is critical to show all major steps of the solution on paper. Two days prior to the test, its description will appear on the Test Preview page.
Bonuses & Other Policies:

There will be opportunities to earn bonus points. Each Midterm and the Final contains a bonus problem. Also, the outstanding Projects can be awarded bonus points at the instructor's discretion.

Students are responsible for learning the basics of MATLAB on their own. Supportive material will be provided as a handout presuming that corresponding discussion of MATLAB technicalities will take up our class time.

IMPORTANT: No make up of the missed Quizzes and Midterms will be possible and no late Project submissions will be accepted unless there is a legitimate reason which can be documented (an illness or another unavoidable emergency).

All important information which becomes available during the course (including answers to FAQ) will be posted on the Announcements & Hints page.
Accommodations:

If you need course adaptations or accommodations because of a disability, the related arrangements should done as soon as possible. Those students who believe that they may need accommodations in this class but don't have appropriate documentations, are encouraged to contact the Disability Services Office located in the Student Development and Counseling Center, x4908.

Academic Dishonesty:

WPI's Academic Honesty policy, definitions and examples of academic dishonesty, and other info on the subject (including explanations of the steps that will be taken if students are suspected of violating the policy) can be found at: http://www.wpi.edu/offices/policies/honesty/. If you are ever unsure as to whether your intended actions are considered academically honest or not, please see your instructor.

Syllabus & Schedule of Events:

Week 1: Interpolation: Polynomial interpolation (Largange & Newton polynomials). Sources of errors. MATLAB computation. Week 2: Interpolation(cont'd): Numerical differentiation, including Richardson scheme. Approximation: Method of least squares. Orthogonal systems. Week 3: Approximation (cont'd): MATLAB computation. Numerical integration: The definite integral. Week 4: Numerical integration (cont'd): Trapezoidal rule. Romberg algorithm. Adaptive Simpson scheme. Week 5: Numerical integration (cont'd): MATLAB computation. Initial value problem: Analytical and numerical techniques. Taylor series. Week 6: Initial value problem (cont'd): Runge-Kutta method. MATLAB computation. Boundary value problem: Shooting method. Week 7: Boundary value problem (cont'd): Finite-difference discretization. MATLAB computation.

Course Information | Homework Assignments | Mini-Projects | Test Preview | Announcements & Hints

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Last modified: Wed, Nov 9, 2011