MATHEMATICS 1 — WS 2017/18

Office hours:

upon request (see my timetable and suggest me some days and times via e-mail)
my office is in Sokolovská 83, 2nd floor, behind the glass door opposite to the staircase

News

Exam D. Problems and handwritten solutions. One student passed the exam, 9 in total.

Exam C. Problems and handwritten solutions. Four students passed the exam, 8 in total.

Exam B. Problems and handwritten solutions. One student passed the exam.

Exam A. Problems and handwritten solutions. Three students have passed the exam.

The exams are held

written parts on Mondays 8.1., 15.1., 22.1., 5.2. and 12.2. at 9:00 - 10:30 AM.
oral parts on the following Tuesdays.
8.1. and 9.1. in Opletalova.
All other dates in Sokolovska 83, Prague 8 (the building where is my office), the written part in room K3 (together with course ODE2), the oral part in K2 (together with the czech course Matematika 1). Both rooms are in the 2nd floor.

Basic information
Exams
Lecture
Exercises
Beamer presentation to download

Basic information

Lecture - Wendesday and Thursday 9.30 - 10.50, O105 (Bárta)

Seminar - Thursday 11.00 - 12.20, O105 (Bárta)

Exercises - Wendesday 11.00 - 12.20, O105 (Vlasák)

Prerequisities. Knowledge of 'high school mathematics' is required, see this document for details. Seminar Introductory mathematics is intended for improving such skills.
Literature. Script to download (WORK IN PROGRESS, last update 22.11.2017).

Exams and grading

midterm test: 10 points
homeworks: 20 points (10 homeworks, 2 points each)
final exam: 90 points (50 points written exam, 40 points oral exam)

Students will be admitted to the oral exam only if the score from the first part (midterms, homeworks and written exam together) is at least 50 points. To pass the exam successfully, at least 20 points from the oral exam are required.

Grading: The total score is obtained as the sum of the points from the oral part and the first part, where the score of the first part is reduced to 60 if it exceeds 60. The final grade depends on the total score as follows.

70-75.5 points ... "E"
76-81.5 points ... "D"
82-87.5 points ... "C"
88-93.5 points ... "B"
94-100 points ... "A"

Midterm test takes part approximately in the half of the semester. Students are asked to compute a limit of a sequence within 30 minutes. Literature is allowed, electronic devices are prohibited. There are two attempts, the better result is taken into account. Here are the sample midterm test, 1st Midterm test and 2nd Midterm test including solutions and grading.

Final Exam takes part in the examination period at the end of the semester. Students have three attempts to pass the final exam. It consists of a written part and oral part.

Written part. Students have 90 minutes to solve problems on limit of a function, derivatives, investigation of a function. Lecture notes and other materials are allowed, electronic devices are prohibited. A sample test is available here.
Oral part follows typically the day after the written exam. The oral part tests understanding the definitions and theorems and ability to apply them. Each student should prepare answers within approximately 40 minutes. During the oral part only pencil and paper are allowed. Then the student should present answers and should answer additional questions. Here is a sample question.

See exam details for more details concerning both parts, as well as general exam rules and the requirements (list of required definitions, theorems and proofs).

Lecture

Here is the beamer presentation to download and the list of definitions and theorems for printing (last update November 15, 2017).

Preliminary plan of lectures:

1. lecture: INTRODUCTION - sets, statements and predicates, quantifiers
2. lecture: methods of proofs
3. lecture: REAL NUMBERS, infimum, supremum
4. lecture: Supremum theorem
5. lecture: integer part, Archimedes property, roots, density of Q
6. lecture: SEQUENCES, LIMIT, uniqueness of limit
7. lecture: arithmetics of limits, ordering, sandwich theorem
8. lecture: infinite limit, extending theorems to infinite limits
9. lecture: limit of monotone sequence, Theorem of Bolzano and Weierstrass
10. lecture: FUNCTION, LIMIT of function, continuity, one-sided and infinite limits
11. lecture: arithmetics of limits, division by positive zero
12. lecture: limit of composite function
13. lecture: Heine Theorem, limit of monotone function, intermediate value theorem
14. lecture: image of interval, attaing of extrema, continuity of inverse function, ELEMENTARY FUNCTIONS, logarithm
15. lecture: properties of logarithm, exponential, trigonometric functions
16. lecture: inverse trigonometric functions, DERIVATIVE, arithmetics of derivatives
17. lecture: derivative of composite function, inverse function, elementary functions, neccessary condition for local extremum
18. lecture: Rolle and Lagrange Theorem, sign of derivative and monotonicity
19. lecture: L'Hospital rule
20. lecture: Examples to L'Hospital rule
21. lecture: convex and concave function,
22. lecture: inflexions
23. lecture: investigation of functions
24. lecture: asymptotes

Seminar and exercises

Homeworks with solutions. HW1, HW2, HW3, HW4, HW5, HW6, HW7, HW8, HW9, HW10.

Recomended problems.

Some further problems to practice from the web pages of Kristyna Kuncova:

160 limits, some with results
some f^g limits with solutions here
derivatives with results, usually there are some problematic points but you can ignore them
investigation of function with solutions, in czech but you can understand the formulae for f', f'' and graphs.

Some past exam problems (from previous years) you can find here and here (click on year numbers). However, these problems can be more difficult than the midterm limit.

Preliminary plan:

1. week: statements and predicates
2. week: suprema and infima
3. week: limits of sequences, rational functions, roots, exponentials, factorials
4. week: limits of sequences, sandwich theorem, integer parts
5. week: limits of sequences, midterm test
6. week: limits of functions, trics from sequences
7. week: limit of composite functions, elementary functions
8. week: functions f^g, Heine theorem
9. week: continuity and derivatives
10. week: derivatives
11. week: investigation of functions
12. week: investigation of functions