Calculus II
Description

Taylor-Maclaurin Theorem. Taylor polynomials, Lagrange formula for the remainder, use of Taylor polynomials in approximating.
Antiderivatives and Indefinite integral. Definition, basic properties, integration by change of variable, integration by parts, integration of rational functions, integration of basic types of functions.
Definite integral (Riemann Integral). Definition, properties, integrable functions, mean value theorems for definite integrals, inequalities between definite integrals, Fundamental Theorem of Calculus, change of variables in definite integrals.
Applications of definite integrals. Calculation of areas, volumes of revolution and arc lengths, functions.
Line integrals. Vector functions, parametric representation of curves, line integrals.
Improper integrals. Types of improper integrals and their calculation, basic properties, convergence criteria for improper integers of nonnegative functions (comparison test, limit test, etc.), absolute integrability of improper integrals, change of variables in improper integrals.

In order to highlight the special educational and didactical aspects of a course, special emphasis is given on the historical evolution and scientific development of the subject as well as on its applications in technology and/or other sciences.

Division: Pure Mathematics
Instructors:


Program of Studies:
Undergraduate Studies
Semester: B
ECTS: 8
Hours per week (Lec/Tut/L): 3/2/0
Code: PM105
Course type: Core
Erasmus students: Yes




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