Math course description Essay
Derivatives and differentials: Differentiation formulas and rules, chain rule, implicit differentiation, higher derivatives, preferential. 4. Mean value theorem: Mean value theorem of differentials, L hospital rule, Taylor formula. 5. Infinite integrals: Interrogatives and infinite integrals, substitution rule, integration by parts. 6. Definite integrals: Definition and properties of definite integral, criteria of existence of definite integrals, fundamental theorem of calculus, substitution rule, integration by parts, improper integrals. 7.
Applications of differentiation and integration: Maximum and minimum values, curve sketching, arc length and differential of arc length, curvature, applications of integration.
8. Differential equations: First-order differential equations, some integral higher-order differential equations, linear differential equations. 9. Multivariate differential calculus: Partial derivatives and higher partial derivatives, total differentials, chain rule, implicit differentiation, applications of partial derivatives to geometry, Taylor formula and extreme values, directional derivatives and gradients. 0. Multivariate integral calculus: Definition of Riemann integrals, double integrals, triple integrals, line integrals, surface integrals, applications of Riemann integrals.