Mathematical Analysis I

Short Description

Course Sections and Topics
Section	Topics within the section
Sequences and Limits	Sequences. Limits of sequences Limits of sequences. Limits of functions Limits of functions. Continuity. Hyperbolic functions
Differentiation	Derivatives. Differentials Mean-Value Theorems l’Hopital’s rule Taylor Formula with Lagrange and Peano remainders Taylor formula and limits Increasing / decreasing functions. Concave / convex functions
Integration and Series	Antiderivative. Indefinite integral Definite integral The Fundamental Theorem of Calculus Improper Integrals Convergence tests. Dirichlet’s test Series. Convergence tests Absolute / Conditional convergence Power Series. Radius of convergence Functional series. Uniform convergence