MATHEMATICS 1 — WS 2017/18
- 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
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.
- 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
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.
- midterm test: 10 points
- homeworks: 20 points (10 homeworks, 2 points each)
- final exam: 90 points (50 points written exam, 40 points oral exam)
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.
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).
- 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.
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.
Some further problems to practice from the web pages of Kristyna Kuncova:
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.
- 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