Contents
Introduction to functions: mathematical and physical meaning, graphs, and function types.
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. Applicationproblems (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 the 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. Operator, gradient, divergence, and curl with their application.