Unit 1

Functions – domain, range, graphs of elementary functions, limits – left limit, right limit, continuity, definition of derivative, derivative as rate of change, implicit differentiation.

Unit 2

Extreme values of functions, critical points, graphing with 𝑦′ and 𝑦′′, asymptotes, optimization problems, linearization and differentials, L’Hospital’s Rule. Riemann sums and definite integrals (just some elementary examples, not the proof), Area, Fundamental theorem of Calculus.

Unit 3

Area between curves, Volumes of solids of revolution – washer method and cylindrical shell method, Length of plane curves, Areas of surfaces of revolution, Moments and centres of Mass.

Unit 4

Sequences, Infinite series as a limit of sequence, Integral test, Comparison tests, Ratio and Root tests, Alternating Series, Absolute and Conditional convergence.

Unit 5

Power series, Taylor and Maclaurin Series, Error estimates, Applications of Power Series.

Course Outcome:
CO1: Understand the elementary functions and concepts of limit, continuity, derivative and integral
CO2: Study techniques of differentiation and use it in optimisation problems and curve sketching
CO3: Defining Integral as a sum and review integration techniques
CO4: Use of integrals for the computation of areas, volumes and arc length
CO5: Discuss some basic concepts in the theory of infinite series with some insight to Power series.

Evaluation Pattern: As in the rules for Assessment Procedure (R.14)

Skills and Employability: Mathematics being a language of all physical sciences and being a speciality in itself, the entire contents of this course, tutorials and assignments lays mathematical foundation for many mathematics, physics and engineering courses and builds skills required for a career as an educator in schools, colleges and universities, as a researcher, and as a communicator of mathematics in general.

Thomas and Finney, Calculus and Analytic Geometry, 11th edition, Pearson.

N. Piskunov, Differential and Integral Calculus Vol. I and II, CBS Publishers.