1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2019/2020
4. Computer science and econometrics - pierwszego stopnia z tyt. licencjata
5. Analiza matematyczna 2

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Analiza matematyczna 2 - opis przedmiotu

Cel przedmiotu

To acquaint students with differential methods of examining extrema and the convexity of a function, with the notions of the primitive function and Riemann integral. The emphasis is placed on mastering calculating techniques, in particular those of integrating, and also on applications of differential and integral calculus. The next aim is to transfer basics of differential calculus on functions in several variables.

Wymagania wstępne

Zapisz zmiany

Mathematical Analysis 1.

Zakres tematyczny

Lecture

1. Number series (3 godz.)

● Real series and their convergence ● Series with non-negative terms. Comparison tests. Cauchy’s and d’Alembert criteria of convergence ● Absolute and conditional convergence ● Operations on series

2. Differential calculus of functions of several variables (8 godz.)

● Directional and partial derivatives, gradient ●  Partial derivatives  of   composite functions  ● Derivatives of higher order ● Applicability of  partial derivatives, local and global extrema 

3. Indefinite integral (6 godz.)

● Primitive function ● Elementary formulas of  integral calculus, integration by parts and by substitution

4. Riemann integral (5 godz.)

● Riemann integral and area. Basic properties of integral. Mean value theorem for integrals  Newton-Leibniz fundamental theorem of calculus and its consequences Całka Riemanna i jej podstawowe własności ● Applications in geometry and economics ● Improper integral

5. Integral calculus of functions of several variables (8 godz.)

● Definition and properties of  multiple integrals in 2 and 3 dimensions ● Iterated integrals and Fubini theorem ● Applicability of multiple integrals

Class 

1. Number series (3 godz.)

● Real series and their convergence ● Series with non-negative terms. Comparison tests. Cauchy’s and d’Alembert criteria of convergence ● Absolute and conditional convergence ● Operations on series

2. Differential calculus of functions of several variables (8 godz.)

● Directional and partial derivatives, gradient ●  Partial derivatives  of   composite functions  ● Derivatives of higher order ● Applicability of  partial derivatives, local and global extrema 

3. Indefinite integral (6 godz.)

● Primitive function ● Elementary formulas of  integral calculus, integration by parts and by substitution

4. Riemann integral (5 godz.)

● Riemann integral and area. Basic properties of integral. Mean value theorem for integrals  Newton-Leibniz fundamental theorem of calculus and its consequences Całka Riemanna i jej podstawowe własności ● Applications in geometry and economics ● Improper integral

5. Integral calculus of functions of several variables (8 godz.)

● Definition and properties of  multiple integrals in 2 and 3 dimensions ● Iterated integrals and Fubini theorem ● Applicability of multiple integrals

Metody kształcenia

Traditional lecture; class where students, leaded by the teacher, solve exercises and discuss; team-work completed with a written composition; work over a book; making use of internet.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

1. Verifying the extent of preparation of students and their activity during the classes.

2. Two  colloquias with problems of various degree of difficulties, allowing to verify if students attained learning outcomes at the very least.

3. Written compositions elaborated a material indicated by the lecturer and prepared by  students.

4. Exam with indicated point ranges.

The final grade is the mean of those of the class 40% and exam 60%. A necessary condition to enter the exam is a positive grade of the classes. A necessary condition to pass the course is a positive grade of the exam.

 

Literatura podstawowa

In English:

1. W. F. Trench, Introduction to Real Analysis, Library of Congress Cataloging-in-Publication, Free Hyperlinked Edition 2.04 December 2013

http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF

2.  M. Gemes, Zolt́an Szentmikĺossy, Mathematical Analysis – Exercises I, E ̈otv ̈os Loŕand University Faculty of Science, http://etananyag.ttk.elte.hu/FiLeS/downloads/4a_GemesSzentm_MathAnExI.pdf

In Polish:

1. W. Kołodziej, Analiza matematyczna, PWN, W-wa,2009.

2. W. Rudin, Podstawy analizy matematycznej, PWN, W-wa, 2009.

4. M. Gewert, Z. Skoczylas, Analiza matematyczna 2, Oficyna Wydawnicza GIS, Wrocław 2005.

Literatura uzupełniająca

1. J .Banaś, Podstawy matematyki dla ekonomistów, WNT, W-wa, 2005.

3. M.L.Lial, R.N.Greenwell, N.P.Rithey, Calculus with Applications, Boston, 2012

4. R. Rudnicki, Wykłady z analizy matematycznej, PWN, W-wa, 2006.

2. J. Banaś, S.Wędrychowicz, Zbiór zadań z analizy matematycznej, WNT, W-wa,2004

5. W. Krysicki, L. Włodarski, Analiza matematyczna w zadaniach, cz. I/II,PWN,W-wa,2008.

6. W. Sosulski, J. Szajkowski, Zbiór zadań z analizy matematycznej, Red. Wyd. Nauk Ścisłych i Ekonomicznych, UZ, 2007.

 

Uwagi

Zmodyfikowane przez dr Alina Szelecka (ostatnia modyfikacja: 21-11-2020 06:10)