"Differential and Integral Calculus 3". School of Mathematical Sciences. (Ya. Yakubov)

1. Euclidean space. Functions in Euclidean space.
2. Partial derivatives. Directional derivatives. Differentiability. Fermat theorem. Continuous differentiability.
3. Chain rule. Level curves. Gradient perpendicular to level curves. Higher-order partial derivatives. The mixed partial derivatives theorem. Taylor expansion. Classification of critical points.
4. Inverse function theorem. Open mapping theorem. Lagrange multipliers method. Implicit function theorem.
5. Rectangles (boxes). Negligible sets. Riemann integral. Darboux sums and Darboux integrals. Lebesgue theorem.
6. Jordan measurable sets. Fubini theorem. Diffeomorphism. Change of variables in the Riemann integral. Improper integral. Parameter-dependent integrals.