CE F324 Numerical Analysis

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Course info

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

Instructor: Dr. Md Rushdie Ibne Islam, Email: rushdie.islam@pilani.bits-pilani.ac.in, Office: 1212-A (FD-I, first floor).

Class timings:

• Lecture: Monday, Wednesday (12.00 - 12.50 PM); Thursday (3.00 - 3.50 PM); 6103 (NAB)

TAs: Will be announced later.

Office hours: Wednesday (5.00 PM - 6.00 PM).

Important note: Please include CEF324 (without space) in the subject line for all email communications related to this course.

Syllabus

• Part I: Errors in Computation
  • Source and types of errors, error propagation.
  • Floating-point representation, rounding error, and floating-point arithmetic.
• Part II: Roots of Nonlinear Equations
  • Direct and iterative methods, order of convergence.
  • Iterative methods for solving systems of nonlinear equations.
• Part III: Linear Systems of Equations
  • Direct and iterative methods, rate of convergence.
  • Condition number and ill-conditioned systems.
• Part IV: Interpolation and Approximation
  • Lagrange and Newton divided difference interpolation.
  • Errors in interpolation, least square and uniform approximations.
• Part V: Numerical Differentiation
  • Differentiation using interpolation formulas.
• Part VI: Numerical Integration
  • Newton-Cotes formulas and Gauss quadrature rules.
• Part VII: Numerical Solutions of ODEs
  • Taylor, Euler, and Runge-Kutta methods.
  • Application to initial value problems.
• Part VIII: Numerical Solutions of PDEs
  • Classification of PDEs: elliptic, parabolic, and hyperbolic.
  • Finite difference method (FDM) for Laplace, Poisson, heat, and wave equations.
  • Stability, consistency, boundary and initial conditions, implicit and explicit schemes.
• Part IX: Optimization
  • Problem definition, simplex method, duality.
  • Transportation problems, line search, constrained and unconstrained optimization.
• Part X: Monte Carlo Method and Simulation
  • Random digits and pseudo-random numbers.
  • Applications of Monte Carlo methods and variance reduction.
• Please see course handout for details.

References

• Primary
  • G. Dahlquist and A. Bjorck, Numerical Methods, First Edition (Reprint), Dover Publications, 2003.
• Additional
  • K. E. Atkinson, An Introduction to Numerical Analysis, First Edition, John Wiley & Sons, 1978.
  • P. Moin, Fundamentals of Engineering Numerical Analysis, First Edition, Cambridge University Press, 2010.

Grading

• Quiz (Best 2 out of 4): 20%
• Assignments: 20%
• Mid semester exam: 25%
• Comprehensive exam: 35%

Quizzes, mid semester and comprehensive exams

• Four quizzes will be conducted. Exact date and time will be notified later.
• Mid semester and comprehensive exams will be scheduled based on the institute timetable.

Make-up policy

• If the student is unable to appear for the Regular Examination due to genuine exigencies, the student must refer to the procedure for applying for Make-up Examination. No make up for the assignments.
• Academic honesty and integrity are to be maintained by all the students throughout the semester and no type of academic dishonesty is acceptable.