of Mathematical Analysis
Sokolovská 83, 4th floor, room K479
On maternity leave since February 14, 2013.
Program of Winter Semester 2012/13:
I. Introduction. Elements of mathematical logic and set theory. Real numbers.
II. Sequences. Limits.
III. Functions of one real variable. Limits, continuity, derivatives. Investigation of a function.
Tuesday January 15
Wednesday January 23
Tuesday January 29
Tuesday February 5
Tuesday February 12
Students are supposed to enroll for exam terms in SIS.
There will be one more term (the last one) at the beginning of Summer Semester:
Friday February 22, 3:30 p.m., in Opletalova, O109 - the examiner will be Tomáš Bárta (teacher of the Czech parallel). See SIS for details.
Test Jan 15
Test Jan 23
Test Jan 29
Test Feb 5
Only the students who have fulfilled credit requirements (see below) can approach exam on Mathematics I.
The exam starts with a written part - test 120 min. approx. (4 calculus problems: limit of a sequence, limits and continuity of functions, derivative, investigation of a function and its graph). To pass this part, at least half of maximum points is necessary. If a student passes the written part with 1/2 to 2/3 of maximum points and fails in the oral part, he/she must pass the written part at next term again. With 2/3 or more, no repetition of the written part is needed.
The oral part (theory as read during the lectures) is either the same day or the day after the written part (according to actual number of students who passed the written exam). It involves definition of a key notion - its correct formulation is necessary for passing the oral part - another definition and formulation of two theorems, one of them with proof. At the written part, students can use written/printed materials, no electronic devices are allowed. At the oral part, no materials are allowed, students have about 30 min. to prepare themselves. Detailed oral exam requirements (list of key notions, definitions, theorems and proofs) here.
Lecture notes (supplemented during the course), final version Dec 25, 2012; Jan 13: proofs of Theorems 3.1 and 3.2 added on demand.
Limits to practise: Homework problems with answers, two more.
Credit requirements: There were three written tests (up to 30 min) on basic 'high-school' calculus on seminars: Oct 17, Nov 7, Nov 28. Topics of the third test: (in)equations with parameter, analytic geometry (expression of lines and planes, distance between a point and a line/plane, planar curves in R^2: elipse, parabola, hyperbola), limit of a sequence (basic difficulty). Sample test 3 with solutions here. Sample test 2 here. Sample test 1 here. For credit, students have to pass at least two tests. Further, a correct solution of a homework problem involving current topics of the course is required. Homework problems were submitted November 29. Those who have no exercise on the list assigned are asked to choose a free one and let me know by e-mail. Students have to perform a correct solution before entering the exam.
First test evaluation
Second test evaluation
Third test evaluation. The test with results here
Test retake (Dec 14)
Skills and knowledge necessary for understanding higher mathematics
The text involves a series of exercises which are recommended to be done at the beginning of the course. Answers
Links to archives of the course materials:
by Miroslav Zelený
by Ondřej Kalenda - exercises
A.C. Chiang: Fundamental Methods of Mathematical Economics
B. P. Demidovich: Problems in Mathematical Analysis (also in Czech and Russian)
W. Rudin: Principles of Mathematical Analysis
V. Hájková, M. Johanis, O. John, O. F. K. Kalenda, M. Zelený, Matematika, Matfyzpress, 2006 and 2012 (in Czech; pdf here - pp. 1-118 for Mathematics 1)
Brief lecture notes published here
Any introductory book on mathematical analysis
Archiv příkladů Ondřeje Kalendy
Archiv příkladů Pavly Pavlíkové (dole na stránce)
Index of /~history/ Mathematicians