Mathematical analysis II.1
General data
Course ID: | 1000-113bAM3b |
Erasmus code / ISCED: |
11.1
|
Course title: | Mathematical analysis II.1 |
Name in Polish: | Analiza matematyczna II.1 (potok 2) |
Organizational unit: | Faculty of Mathematics, Informatics, and Mechanics |
Course groups: |
Obligatory courses for 2nd grade JSEM Obligatory courses for 2nd grade JSIM (3I+4M) Obligatory courses for 2nd grade JSIM (3M+4I) Obligatory courses for 2rd grade Mathematics |
ECTS credit allocation (and other scores): |
(not available)
|
Language: | Polish |
Main fields of studies for MISMaP: | mathematics |
Type of course: | obligatory courses |
Short description: |
Many-variable differential calculus, measure and integration theory. |
Full description: |
Linear and topological structure of Euclidean spaces; transformations, continuity. Calculus in several variables: directional derivative, differentiability, higher-order derivatives, symmetry od the second and higher order differentials, Taylor's formula, the implicit function theorem, local extrema. Manifolds in R^n, tangent spaces, local parametrizations and maps, manifolds defined by a system of equations, normal vectors. Constrained maxima and minima, Lagrange multipliers with examples.The concept of measure; outer measure and Caratheodory's theorem. Lebesgue measure; measurable functions, Lebesgue integral. Lebesgue monotone convergence theorem, Lebesgue bounded convergence theorem, the Fatou lemma. Fubini's theorem, change of variables under the integral. |
Bibliography: |
M.Spivak, Modern Approach to Classical Theorems of Advanced Calculus W.A. Benjamin, L.Bers, Calculus W.Rudin, Principles of Mathematical Analysis, McGraw-Hill Science Engineering W.Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966. xi+412 pp. |
Copyright by University of Warsaw.