This document provides information about an Advanced Calculus and Numerical Methods course. The goal of the course is to provide students with foundational knowledge of integral calculus, vector calculus, partial differential equations, and numerical methods. Key outcomes include applying concepts like multiple integration and change of variables to compute areas and volumes, understanding multivariate calculus applications like solenoidal and irrotational vectors, formulating and solving physical problems with partial differential equations, and applying numerical methods to model engineering phenomena. The course content has applications in areas like heat transfer, fluid flow, elasticity, and electrodynamics. Students will be evaluated through assignments, quizzes, seminars, and an in-class test.

1. ADVANCED CALCULUS AND
NUMERICAL METHODS
(21MAT21)
Expectation Setting Session
P. RAJENDRA

2. What is ACNM?
The goal of the course ADVANCED CALCULUS AND NUMERICAL
METHODS is to facilitate the students with a concrete foundation of
integral calculus, vector calculus, partial differential equations and
numerical methods enabling them to acquire the knowledge of these
mathematical tools.

3. Outcomes of learning ACNM
1. Apply the concept of change of order of integration and change of
variables to evaluate multiple integrals and their usage in computing the
area and volume.
2. Illustrate the applications of multivariate calculus to understand the
solenoidal and irrotational vectors and also exhibit the inter dependence of
line, surface and volume integrals.
3. Formulate physical problems to partial differential equations and to obtain
solution for standard practical PDE’s.
4. Apply the knowledge of numerical methods in modelling of various
physical and engineering phenomena.
5. Solve first order ordinary differential equations arising in engineering
problems.

4. Applications of Advanced Calculus and
Numerical Methods (ACNM)
* Partial differential equations are used to mathematically formulate,
and thus aid the solution of, physical and other problems involving
functions of several variables, such as the propagation of heat or
sound, fluid flow, elasticity, electrostatics, electrodynamics, etc.
*Numerical methods are used to solve complex heat transfer
problems involving mechanisms such as conduction, convection,
radiation, or a combination of them.
* Applications of Integral Calculus include computations involving area,
volume, arc length, center of mass, work, and pressure.

5. Teaching aids and Evaluation
• Chalk and duster
• Workbook, Assignments, and IAT’s
• Quiz and Seminars