AML702 Applied Computational Methods

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Course info

Credit: 3 Units (3-0-2).

Instructor: Dr. Md Rushdie Ibne Islam, Email: rushdie@am.iitd.ac.in, Office: 4B-19 (Block IV, top floor).

Class timings:

• Lecture: Tuesday, Thursday, Friday; 11 AM – 11:50 AM; LT-IV
• Practical: Monday; 3 PM - 5 PM; Optimization Lab

TAs: Naveen and Saurabh Singh.

Office hours: Either stop by instructor's office (for quick discussion) or take an email appointment (for longer discussion).

Important note: Please include APL702 (without space) in the subject line for all email communications related to this course.

Syllabus

• Part I: Introduction and Fundamentals
  • Course plan and introduction to computational methods.
  • MATLAB fundamentals and programming with MATLAB.
  • Round-off and truncation errors.
• Part II: Numerical Methods for Algebra and Calculus
  • Finding roots of functions.
  • Numerical solution of linear algebraic equations:
    • Gauss elimination.
    • LU and Cholesky factorization.
    • Iterative methods.
  • Numerical solution of non-linear equations.
  • Eigenvalue problems.
  • Numerical integration:
    • Newton-Cotes formulas.
    • The trapezoidal rule.
    • Simpson’s rule.
  • Numerical differentiation using the finite difference method.
• Part III: Differential Equations and Applications
  • Solution of ordinary differential equations:
    • Initial value problems.
    • Boundary value problems.
  • Solution of partial differential equations (brief overview).
  • Control volume method (brief overview).

References

• Primary
  • Chapra, S.C. Applied Numerical Methods with MATLAB for Engineers and Scientists.
  • Moin, P. Fundamentals of Engineering Numerical Analysis.
• Additional
  • Dahlquist, G. and Bjorck, A. Numerical Methods.

Grading

• Quiz: 15% (5% x 3)
• Minor: 20%
• Major: 30%
• Programming assignments: 35% (5% x Top 7)

If a student decides to audit the course, the passing grade will be 40%. Additionally, the student must write minor and major exams, and the attendance must be greater than or equal to 75% in lectures and tutorials separately.

Quizzes, minor and major

• Three quizzes will be conducted; one (quiz #1) before and other two (quiz #2) after the minor exam. Exact date, time and place will be notified later.
• Minor and major exams will be scheduled based on the institute timetable.

Homework

• Homework will be assigned almost every week. These will not be graded. Hence, submission is not necessary.
• Students are strongly encouraged to try the homework problems.

Attendance

• Students are strongly encouraged to attend all the lectures sessions. Attendance will be recorded for each lecture session. If a student's attendance is less than 75%, the student will be awarded one grade less than the actual grade that he/she has earned. For example, a student who has got an A grade but has attendance less than 75% will be awarded an A (-) grade. However, please note that there are no marks for attendance.
• In case of absence due to unforeseen circumstances, such as medical reasons, the student must inform the instructor via email within a week from the date of absence.
• If a student cannot appear for an exam due to medical reasons, a medical certificate needs to be produced from IIT Delhi hospital for consideration of time extension or re-exam.