Basic Calculus 1 (Jan 2023)

This contains the details of the tutorial sessions (2 hours each) conducted during this course.

Tutorial 1: Absolute value function, functions: domain, range, composition, inverse; and plotting graphs

Tutorial 2: Composite function, inverse function, limits, epsilon-delta formulation, and sandwich theorem

Tutorial 3: Left-hand limit, right-hand limit, limits at infinity, infinite limit. Some algebraic computations of limits

Tutorial 4: Continuity, EVT, IVT, properties of continuity, problems on epsilon-delta for continuity

Tutorial 5: Differentiation, tangents, differentiability, and corresponding problems

Tutorial 6: Application of derivatives: critical points, maxima-minima, increasing decreasing functions, Rolle’s theorem and LMVT

Tutorial 7: Problems on differential calculus: critical points, curvatures, graphs plotting, Rolle’s theorem, LMVT, and single variable optimization problems

Tutorial 8: Application of derivatives: Concavity, extremas, inflexion, approximation using differentials, L-Hopitals rule. Introduction to indefinite integrals.

Tutorial 9: Reimann Integral, limit of a sum, Properties of definite integrals, some substitution tricks, area under a curve, newton-lebnitz theorem

Tutorial 10: Integration by parts, partial fractions, area, Newton lebnitz, fundamental theorem of calculus, definite integrals

Tutorial 11: Definite Integrals, Volume by rotation: Slicing method, disk method, washer method; reduction formula; Visualization using GeoGebra

Tutorial 12: Cylindrical methods for calculating volumes, the surface area of rotation (surface integrals), and the length of curves and line integrals. Definite integrals and substituion

You can get the tutorial materials here, and the video lectures in this youtube link. Certificate