Friday, 19 04 2019

Differential Calculus and Mathematical Analysis


Differential Calculus and Mathematical Analysis
Lesson Code:  22Υ101
Level:  Undergraduate
Semester:  1ο



Real numbers. Axioms of R. Basic topological concepts to R. Functions of one variable. Continuity at a point. Continuity in an interval. Derivative. Differential of a function. Derivative of a composite function and higher order derivatives. Basic theorems of differential calculus. Iterative methods for solving equations. Extremum points. Taylor expansions. Taylor Series. Uniform convergence of sequence and series of functions. Indefinite integrals. Riemann integral. Basic theorems of integral calculus. Areas. Smooth curves. Length of a curve. Numerical integration. Sequences. Sequence convergence. Cauchy criterion. Monotonous sequences. Series of numbers. Convergence criteria. Absolute and conditional convergence. Alternating series. Rearrangements of series. Product of series. Power series and radius of convergence. Improper integrals. Basic convergence criteria. Absolute convergence. Conditional convergence.



Perdios Efstathios 

Kalantonis Vasileios