Complex Variables and Numerical Methods (2141905)  

5
Credit
3 + 2 + 0
Lect + Tuto + Pract
Teaching Scheme
70 + 20 + 10
ESE + PA + ALA
Theory Marks
30 + 0 + 20
ESE + OEP + PA
Practical Marks
ESE - End Semester Examination, PA - Progress Assessment, ALA - Active Learning Assignments, OEP -Open Ended Problem


Prerequisite

As a pre-requisite to this course students are required to have a reasonable mastery over
multivariable calculus, differential equations and Linear algebra

Rationale

Mathematics is a language of Science and Engineering.

Course Outcome

After learning the course the students should be able to:

  1. evaluate exponential, trigonometric and hyperbolic functions of a complex number
  2. define continuity, differentiability, analyticity of a function using limits. Determine where a function is continuous/discontinuous, differentiable/non-differentiable, analytic/not analytic or entire/not entire.
  3. determine whether a real-valued function is harmonic or not. Find the harmonic conjugate of a harmonic function.
  4. understand the properties of Analytic function.
  5. evaluate a contour integral with an integrand which have singularities lying inside or outside the simple closed contour.
  6. recognize and apply the Cauchy’s integral formula and the generalized Cauchy’s integral formula.
  7. classify zeros and singularities of an analytic function.
  8. find the Laurent series of a rational function.
  9. write a trigonometric integral over [0, 2π] as a contour integral and evaluate using the residue theorem.
  10. distinguish between conformal and non conformal mappings.
  11. find fixed and critical point of Bilinear Transformation.
  12. calculate Finite Differences of tabulated data.
  13. find an approximate solution of algebraic equations using appropriate method.
  14. find an eigen value using appropriate iterative method.
  15. find an approximate solution of Ordinary Differential Equations using appropriate iterative method.

Active Learning

Preparation of power-point slides, which include videos, animations, pictures, graphics for better understanding theory and practical work – The faculty will allocate chapters/ parts of chapters to groups of students so that the entire syllabus to be covered. The power-point slides should be put up on the web-site of the College/ Institute, along with the names of the students of the group, the name of the faculty, Department and College on the first slide. The best three works should submit to GTU.