Course: Mathematical Analysis 4

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Course title Mathematical Analysis 4
Course code KMA/MMAN4
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Pastor Karel, doc. Mgr. Ph.D.
  • Vodák Rostislav, RNDr. Ph.D.
  • Kouřilová Pavla, Mgr. Ph.D.
Course content
1. Differential calculus in R^n: Partial derivatives and directional derivatives in R^n. Partial derivatives of higher order, interchanging the order of differentiation, total differential of a function and its application in approximate computing. Partial derivatives of compound functions. Differentials of higher order. The Taylor formula. Local extrema of functions, global extrema. 2. Implicit functions: Implicit functions of a single variable, its existence, uniqueness and differentiability. Extrema of implicit functions. Implicit functions of several variables. Constraint extrema, method of the Lagrange multipliers. 3. Integral calculus in R^n: The Jordan measure of a set in R^n. Properties of the measure. Definition and fundamental properties of the Riemann integral in R^n, its geometric interpretation. Multiple integration over intervals and normal domains. Substitution in integrals, especially polar, cylindrical and spherical coordinates. Practical aplications.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 52 hours per semester
  • Preparation for the Course Credit - 20 hours per semester
  • Preparation for the Exam - 50 hours per semester
Learning outcomes
Understand differential and integral calculus of functions of several variables.
Comprehension Understand differential and integral calculus of functions of several variables.
Prerequisites
Understanding the basic properties of functions of several variables.
KMA/MMAN3 and KAG/MA2
----- or -----
KMA/MA2M

Assessment methods and criteria
Oral exam, Written exam

Credit: the student has to pass two written tests (i.e. to obtain at least half of the possible points in each test). Attendance at seminars: absence is tolerated at most three times. Exam: the student has to understand the subject and be able to prove the principal results.
Recommended literature
  • B. Budínský, J. Charvát. (1990). Matematika II. SNTL Praha.
  • Brabec J., Hrůza B. (1989). Matematická analýza II. SNTL, Praha.
  • V. Jarník. (1976). Diferenciální počet I a II. SPN, Praha.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Mathematics (1) Mathematics courses 2 Summer
Faculty of Science Discrete Mathematics (2016) Mathematics courses 2 Summer