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

After learning the course the students should be able to:

- evaluate exponential, trigonometric and hyperbolic functions of a complex number
- 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.
- determine whether a real-valued function is harmonic or not. Find the harmonic conjugate of a harmonic function.
- understand the properties of Analytic function.
- evaluate a contour integral with an integrand which have singularities lying inside or outside the simple closed contour.
- recognize and apply the Cauchy’s integral formula and the generalized Cauchy’s integral formula.
- classify zeros and singularities of an analytic function.
- find the Laurent series of a rational function.
- write a trigonometric integral over [0, 2π] as a contour integral and evaluate using the residue theorem.
- distinguish between conformal and non conformal mappings.
- find fixed and critical point of Bilinear Transformation.
- calculate Finite Differences of tabulated data.
- find an approximate solution of algebraic equations using appropriate method.
- find an eigen value using appropriate iterative method.
- find an approximate solution of Ordinary Differential Equations using appropriate iterative method.