Ghosh P. Calculus-I 2021

Textbook in PDF format

Course Objectives: It is a basic course on the study of real valued functions that would develop an analytical ability to have a more matured perspective of the key concepts of calculus, namely, limits, continuity, differentiability and their applications.
Unit 1:
Functions, types, domain and range, Limits of functions, Sequential criterion for limits, Divergence criteria, Limit theorems, One-sided limits, Infinite limits and limits at infinity.
Unit 2:
Continuous functions, Sequential criterion for continuity and discontinuity, Algebra of continuous functions, Properties of continuous functions on closed and bounded intervals; Uniform continuity, Non-uniform continuity criteria, Uniform continuity theorem.
Unit 3:
Differentiability of functions, Successive differentiation, Leibnitz’s theorem, Partial differentiation, Jacobians, Euler’s theorem on homogeneous functions, proof and applications.
Unit 4:
Tangents and normals, Envelopes and Evolutes, Curvature, Asymptotes, Singular points, Curve tracing.
Course Learning Outcomes:
To have a rigorous understanding of the concept of limit of a function.
The geometrical properties of continuous functions on closed and bounded intervals.
The applications of mean value theorem and Taylor’s theorem