Introduction to Engineering Mathematics (AHT-003)

About Course

COURSEOBJECTIVES:

The objective of this course is to familiarize the prospective engineers with techniques of applied
mathematics. It aims to equip the students with standard concepts, tools and mathematical
software sat an intermediate level that will serve them well towards tackling mathematical
problem and applications that they would find useful in their disciplines. Mainly, the objectives
are:
1. To introduce the notion of differential calculus and their related properties and applications.
2. To present the notion of integral calculus and their properties.
3. To familiarize with applications of differential and integral calculus.
4. To develop the essential tool of vector calculus to deal with higher order problems.
5. To comprehend the idea of matrices and their applications in solving the system of equation

COURSE OUTCOMES(s):At the end of this course, the students will be able:

1. To visualize and conceptualize the engineering problems.
2. To model the engineering problem mathematically using theory of calculus and matrices.
3. To determine the solution of the studied engineering problem from application point of view.
4. To validate the solution.
5. To implement the solution for engineering problem.

                                                       Syllabus

Unit- 1*: Calculus I
Limit, continuity & differentiability, Rolle’s theorem, Mean-value theorems, Expansion of
functions by Maclaurin’s and Taylor’s for one variable, Taylor’s theorem for function of two
variables, Partial differentiation, Maxima &minima (two and three variables), Method of
Lagranges multipliers.

Unit 2*: Calculus II
Definite integral and its properties, Curve tracing, Multiple (double & triple) integral, Change
the order of the integration, Change of variables, Beta and Gamma functions and their properties.
.
Unit 3: Calculus III 
Jacobians, Approximation of error, Applications of definite integrals to evaluate surface areas
and volumes of revolutions; Centre of mass, Centre of gravity.

Unit4: Vector Calculus
Vector and its properties; Scalar and vector point function; Differentiation of vectors; Gradient,
Geometrical meaning of gradient, Directional derivative, Divergence and curl, Line integral,
Surface integral and Volume integral, Gauss divergence, Stokes and Green theorems (without
proof).

Unit 5*: Matrices 
Matrix and their types and properties, Rank of a matrix, Consistency of system of linear
equations, Solution of simultaneous linear equations by elementary transformations, Eigen
values & Eigen vectors, Cayley-Hamilton theorem and its applications to find inverse,
Diagonalization of matrices.