• Real number system, definitions of sequence and convergence, bounded sequences, Cauchy sequence, infinite series, absolute and conditional convergence
• Limit, continuity, uniform continuity, differentiability, mean value theorems, Taylor’s theorem, Taylor’s series, power series, maxima and minima.
• Functions of several variables, limit, continuity, differentiability, gradient, directional derivatives, chain rule, Taylor’s theorem, Maxima and minima,
and method of Lagrange multipliers.
• Riemann integral, fundamental theorems of calculus, improper integrals, Multiple integrals.
• Text books and references:
1: K. A. Ross, Elementary Analysis: The Theory of Calculus, Springer, 2nd Edition, 2013.
2: Walter Rudin, Principles of Mathematical Analysis, 3rd edition, Mc Graw Hill 2023.
3: S. R. Ghorpade and B. V. Limaye, A course in Calculus and Real Analysis, Springer, 2006.
4: S. R. Ghorpade and B. V. Limaye, A course in Multivariable Calculus and Analysis, Springer,2010.
• For lecture notes and practise problems: Click Here