APPLIED CALCULUS

Syllabus

Module: 1. Differential Calculus
Functions, graph of functions, New functions from Old functions,
Limit of a function, Continuity, Limits at infinity, Derivative as a function,
Maxima and Minima of functions of single variable, Mean value theorem,
Effect of derivates on the shape of a graph.
Activities: Visualization of the functions, Maxima and Minima of a
function using open source software, Solving of Competitive Examination
questions (Ex. GATE).

Module: 2. Functions of several variables
Partial derivatives, Chain rule, Total derivative, Maxima and minima
of functions of two variables, Method of Lagrange’s Multipliers,
Application problems in engineering.
Activities: Partial Derivatives with two or three variables, Maxima
and Minima of a function using-source software, Solving of Competitive
Examination questions (Ex. GATE).

Module: 3. Integral Calculus
Fundamental theorem of Calculus, Indefinite integrals and the Net
Change Theorem, Improper integrals, Arc Length, Area of Region, Area
of surface of revolution.
Activities: Definite and Indefinite Integrals, Determination of Area,
Solving of Competitive Examinations (Ex. GATE).

Module: 4. Multiple Integrals
Iterated integrals and Fubini’s theorem, Evaluation of double integrals,
change of order of integration, change of variables between Cartesian and
polar co-ordinates, evaluation of triple integrals-change of variables
between Cartesian and cylindrical and spherical co-ordiantes.
Activities: Double integrals and triple integrals using open-source
software, solving of Competitive Examination questions (Ex. GATE).