- Topology in $\mathbbR^n$ : Open sets, closed sets, compact sets, Heine-Borel theorem, path connectedness in $\mathbbR^n$.
- Differential Calculus : Directional derivatives and its drawbacks, total derivative, comparison with differentiability on $\mathbbR$, chain rule and its applications, $C^k$ functions, mixed derivatives, Taylor's theorem, smooth functions with compact supports, inverse function theorem, implicit function theorem and the rank theorem, examples, maxima and minima, critical point of the Hessian, constrained extrema and Lagrange's multipliers, examples.
- Integral Calculus : Line integrals, behaviour of line integral under a change of parameter, independence of path, conditions for a vector field to be a gradient, concept of potential and its construction on convex sets, multiple Riemann integrals, Fubini's theorem, change of variables, integration by parts.
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