Course unit, curriculum year 2023–2024
MATH.APP.220
Multivariable Calculus, 5 cr
Tampere University
- Description
- Completion options
Teaching periods
Active in period 1 (1.8.2023–22.10.2023)
Active in period 2 (23.10.2023–31.12.2023)
Active in period 3 (1.1.2024–3.3.2024)
Active in period 4 (4.3.2024–31.5.2024)
Course code
MATH.APP.220Language of instruction
English, FinnishAcademic years
2021–2022, 2022–2023, 2023–2024Level of study
Basic studiesGrading scale
General scale, 0-5Persons responsible
Responsible teacher:
Merja Laaksonen, Contact person for the Finnish language implementationResponsible teacher:
Jani Hirvonen, Contact person for the English language implementationResponsible organisation
Faculty of Information Technology and Communication Sciences 100 %
Coordinating organisation
Computing Sciences Studies 100 %
Core content
- Real valued functions of several variables: Graphs and contour plots of functions of two variables. Limits and continuity, first and higher order partial derivatives, directed derivative and gradient.
- Vector-valued functions of several variables: Derivative matrix and the chain rule.
- Extreme values of a function: Local and global maxima and minima.
- Integrals of functions of two and three variables: Computing in vertically and horizontally simple domains, computing using polar, cylinder and spherical coordinates.
Complementary knowledge
- Linear approximation and differentiability
- Hessian matrix, Taylor's formula
- Constrained extremal values and Lagrange's method.
- Center of mass, improper integrals.
- Using Matlab as a tool in solving the exercise problems.
Specialist knowledge
- A ball, open and closed sets
- General change of variables, mean value theorem and average of a function
Learning outcomes
Prerequisites
Compulsory prerequisites
Further information
Equivalences
Studies that include this course
Completion option 1
This is only in Finnish
Completion of all options is required.
Participation in teaching
29.08.2023 – 15.10.2023
Active in period 1 (1.8.2023–22.10.2023)
Completion option 2
This is in english.
Completion of all options is required.
Participation in teaching
08.01.2024 – 25.02.2024
Active in period 3 (1.1.2024–3.3.2024)