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Mathematical Analysis 2 | Summer semester 2021/2022
| exercises Tuesday | 10:45 - 12:15 | EB129
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Some MS's materials
partial derivatives - brief sketch
Credits
A maximum of 30 points can be obtained from the credits. The minimum number
of points required for credit is 10. A maximum of 15 points can be obtained
on the basis of a successfully completed and submitted project. Examples from
the submitted project will be corrected and the student will be briefly informed
of those examples in which he/she made major errors. The student
may then submit corrections to these examples within 4 days. This opportunity
to correct significantly defective examples from the project cannot be repeated. Further
15 points can be obtained from one test. This test cannot be repeated. Personal
participation in the exercises is compulsory for full-time students.
Individual study plans
Students who submit confirmation of an approved individual study plan by
March 7, 2022 will engage in an independent study of the core course literature
or recommended resources. They will also immediately arrange a schedule of
consultations with the lecturers (B. Krajc and M. Sadowská). Attendance at consultations
is mandatory, and specific questions are expected from students who
have covered the material according to the attached schedule for full-time study.
Project and test submission dates are also mandatory for students with an individual
study plan.
How the semester will proceed
Projects will be assigned to students by February 21, 2022. Sample exam assignments
will be published by February 21, 2022. Solved projects will be submitted
by May 6, 2022. The form of processing and submission of projects will be
announced. The credit test will take place on May 3, 2022.
The test cannot be repeated. If the student fails to appear on the specified date
for a serious reason, then the test may be taken on May 10, 2022 by arrangement
with M. Sadowská.
Basic study literature
Differential Calculus (DC)
Integral Calculus (IC)
Mathematical Analysis 1 (prerequisity)
Other recommended sources
MIT course
L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973
Schedule of lectures
1. Functions of multiple variables, limits, continuity (up to Section 3.2 in DC)
2. Partial derivatives, directional derivatives (up to Section 4.3 in DC)
3. Differentials, gradients (up to Section 4.5, Section 4.6 will be omitted in DC)
4. Taylor’s theorem (Section 5, Section 6 will be omitted in DC)
5. Local extremes (up to Section 7.1 in DC)
6. Global extremes (up to Section 7.2 in DC)
7. Double integral over measurable sets (up to page 9 in IC)
8. Fubini’s theorem (up to page 14 in IC)
9. Substitution in the double integral (up to page 23 in IC)
10. Applications of the double integral (up to Chapter 4.2, Chapters 4.3, 4.4
will be omitted in IC)
11. Triple integral over intervals (up to page 33) 11.Triple integral over measurable sets (up to page 43) 12.Substitution in the triple integral (up to page
53)
13. Some applications of triple integrals (up to page 58, Section 8.2 will be omitted)
14. Reserve
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