- Differentiation: Definition and basic properties, higher order derivatives, Leibnitz's theorem on successive differentiation.
- Mean Value Theorems: Rolle's theorem, Lagrange's and Cauchy's mean value theorems, Taylor's theorem, computation of Taylor's series.
- Maxima and minima: Maxima and minima of a function of one variable, saddle points, applications.
- Integration: Riemann integral viewed as an area, partitions, upper and lower integrals, Riemann integrability of a function, basic properties of Riemann integrals, mean value theorems for Riemann integrals, fundamental theorem of calculus, change of variable formula and integration by parts, improper Riemann integral. Beta and Gamma functions.
- Sequence of functions Uniform convergence, convergence and continuity. Weierstrass approximation theorem.
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