Mathematical Analysis II 0600-MS1-1AM2#a
Ćwiczenia (CW) Rok akademicki 2018/19

Learning outcomes and verification methods:

Understands the notion of Riemann integral of function of one variable and has mastered basic techniques of integration. - Quizzes Test/ midterm exam Homework presentation of solutions continous evaluation

Can define all elementary functions and knows their basic properties. - Quizzes Test/ midterm exam Homework presentation of solutions continous evaluation

Knows the notion of a sequence of mappings and understands relationships between the notions of pointwise convergence, uniform convergence, and almost uniform convergence. - Quizzes Test/ midterm exam Homework presentation of solutions continous evaluation

Knows how to use notions, theorems and methods of differential calculus of functions of one variable to the analysis of function giving rationalizations of correctness of his solutions. - Quizzes Test/ midterm exam Homework presentation of solutions continous evaluation

Contents of the course

Differentiation of function of one variable. Interpretation of derivative and applications. Differentials of higher order. Taylor formula. Extrema of a function. Convexity. Generalized sequences. Riemann integral. Basic theorem of intergral and differential calculus. Methods of integration. Logarithm function and its properties. Exp function of real and complex variable. Trigonometric and hyperbolic functions. Intergrals on non-compact sets. Euler's gamma function. Length of an arc of a function in R^n. Banach principle. Sequences of mappings. Pointwise convergence, uniform convergence and almost uniform convergence. Differentiation and integration of functional series. Power series.

Teaching methods: exercises, consultations, studying literature, home works, discussions in groups.