### Mathematical Analysis II NMAI055

**Time and place:** Wednesday at 9:00 (lecture) and at 10:40 (tutorial) in S11

**Tutorial organization and credit: ** At each tutorial a set of homework will be issued, due for the next lecture. You are expected to attempt to solve all homework and write your solution of each part on a separate sheet of paper. One part of the homework will submitted to be marked for credit and the solution of the remaining homework will be discussed during the tutorial. Any homework submitted late will score 0%. If you are unable to attend the lecture and want to submit homework, you can to submit all parts of homework before the lecture.
To obtain credit from the tutorial, you need to meet the following conditions

- score at least 50% in the test at the end of the term,
- to score average 60% of credit from homework, three lowest marks/undelivered homeworks will not be considered into this average.

**
Test from tutorials:** 27.5. 2019 at 9:30 in S11 (building at Malostranske namesti). Time: 90 minutes. Topics: primitive functions, integrals and their applications, multivariable functions - continuity, partial and directional derivatives, total differential, tangent plane, extrema (including constrained), implicit functions. Any written/printed materials allowed, no electronics.

**
Resit for the test from tutorials:** 3.6. 2019 at 9:00 in S10 (building at Malostranske namesti).

**Exam:** You must obtain credit from the tutorial to be able to take the exam. You must register in SIS to take the exam. Exam dates are: 30.5., 6.6., 17.6. and 21.6. (21.6. is not reccommended for the first attempt). ** Last exam attempt is September 19.** Exam description and list of exam requirements. The exam will be written and will have a form similar to the practice exam.

** Materials:** Lecture notes. For recommended study materials see the syllabus, you might also find useful notes by Aleš Pultr.
Collection of questions and exercises, some with solutions, I highly reccommend: Margit Gémes, Zoltán Szentmiklóssy: Mathematical Analysis - Exercises I.
Another collection of problems (with solutions) you migt find useful.
Learn methods of calculating integration by hand, even though computers can do it for you: this integral calculator provides also detailed calculaction and graph of the function. Use it for practicing, but don't worry too much if it uses tricks you did not learn.
Flowchart for differentiation and integration.

**Covered material:**

- 20.2. lecture: Antiderivatives: definition and properties, antiderivatives of elementary functions. Lecture notes.
- 20.2. tutorial: Taylor polynomial and its applications. Tutorial and homework problems. Solution.
- 27.2. lecture: Calculating primitive functions by parts and by substitution. Examples of primitive functions which cannot be expressed by elementary functions. Primitive function of every rational function can be expressed by elementary functions. Lecture notes.
- 27.2. tutorial: Calculating primitive functions by parts, gluing primitive functions. Tutorial and homework problems.
- 6.3. lecture: Riemann sum and integral. Lecture notes.
- 6.3. tutorial: Simple substitutions (from last week) and partial fractions. Tutorial and homework problems.
- 13.3. lecture:Riemann integrable functions, integrability criterion. Lecture notes.
- 13.3. tutorial: Substitutions. Tutorial and homework problems.
- 20.3. lecture: Fundamental theorems of calculus. Substitution and per partes for definite integral. Newton integral. Lecture notes.
- 20.3. tutorial: Definite integral. Tutorial and homework problems.
- 27.3. lecture: Applications of integral. Lecture notes.
- 27.3. tutorial: Applications of integral. Tutorial and homework problems.
- 3.4. lecture: Multivariable calculus - introduction. Lecture notes.
- 3.4. tutorial: Multivariable calculus. Tutorial and homework problems.
- 10.4. lecture: Multivariable calculus - Fubini theorem, partial derivatives and total differential. Lecture notes. Multivariate calculus pictures.
- 10.4. tutorial: Multivariable calculus. Tutorial and homework problems.
- 17.4. lecture: Multivariable calculus - calculating total diferential and partial derivatives. Lecture notes.
- 17.4. tutorial: Multivariable calculus. Tutorial and homework problems.
- 24.4. lecture: Multivariable calculus - partial derivatives of higher order, extremes of multivariable functions. Lecture notes.
- 24.4. tutorial: Multivariable calculus - partial derivatives of higher order, extremes of multivariable functions. Tutorial problems. Homework (due 15.5.).
- 1.5. no lecture/tutorial (public holiday)
- 8.5. no lecture/tutorial (public holiday)
- 15.5. lecture: Implicit functions and Lagrange multipliers.Lecture notes.
- 15.5. tutorial: Implicit functions and Lagrange multipliers.Tutorial and homework problems.
- 22.5. lecture: Metric spaces.Lecture notes.