Applied Calculus

Introduction to functions: Mathematical and physical meaning, graphs and types of function.

Introduction to limits: Theorems of limits and their applications to functions. Right hand and left hand limits. Continuous and discontinuous functions and their applications.

Derivatives: Introduction to derivatives. Geometrical and  physical meaning of derivatives. Partial derivatives and their geometric significance. Application       problems (rate of change, marginal analysis). 

Higher Derivatives: Leibnitz theorem, Rolle’s theorem,Mean value theorem. Taylors and Maclaurins series.

Evaluation of limits using L’ Hospital’s rule: Indeterminate forms (0/0), (∞/∞), (ox∞), (∞-∞), 1^∞, ∞⁰, 0⁰.

Application of Derivatives: Asymptotes, curvature and radius of curvature, differentials with application.

Application of partial Derivatives: Euler’s theorem, total differentials; maxima and minima of function of two variables.

Integral Calculus: Methods of integration by substitution and by parts. Integration of rational and irrational algebraic functions. Definite integrals, improper integrals. Gamma and Beta functions; reduction formulae.

Application of Integral Calculus: Cost function from marginal cost, rocket flights; area under curve.

Vector Calculus: Vector differentiation and vector integration with their physical interpretation and applications.Ñoperator, gradient, divergence and curl with their application.