Ghosh P. Calculus-II 2021

Textbook in PDF format

Course Objectives: The objective of the course to study applications of differentiability in Mean value theorems and also to find the surface area and volumes of solids of revolutions.
Unit 1:
Algebra of differentiable functions, Caratheodory's theorem and chain rule of differentiation; Relative extrema, Interior extremum theorem, Rolle's theorem, Lagrange's and Cauchy's mean-value theorem and its applications, Intermediate value property of derivatives - Darboux's theorem.
Unit 2:
Taylor polynomial, Taylor's theorem with Lagrange form of remainder, Application of Taylor's theorem in error estimation; Relative extrema, and to establish a criterion for convexity; Taylor's series expansions of simple trigonometric and exponential functions.
Unit 3:
Reduction formulae, Beta and Gamma functions, Quadratures and rectifications of curves.
Unit 4:
Volumes and surfaces of solids of revolutions, Pappus theorem, Double and triple integrals, Change of order of integration, Drichlet's and Liouville's integral formulae.
Course Learning Outcomes:
Understanding the concept of mean value theorems.
The applications of mean value theorem and Taylor's theorem.
To find the surface area and volumes of solids of revolutions