# Maths - 4 (2140001) Old Code : 140001

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
The 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:

• 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, 2p] 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.

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.