Multivariable Calculus, Online teaching

On this course the students learn to study and visualize the behaviour
of a real valued function of two variables using its graphs and contour
plots, compute limits of multivariable functions, compute first
and higher order partial derivatives, gradients and directed
derivatives, and to find local and global maxima of functions. The
students learn to form the derivative matrix of a vector-valued function
and to use the chain rule of differentiation. The students learn how to
compute integrals of real-value functions of two and three variables
using cartesian, polar, cylinder and spherical coordinates. The students
learn how to justify their claims using mathematical methods and to
present their solutions orally as well as in written form.

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

Other learning events

Exercise:

14.01.2022 12:00 - 14:00
17.01.2022 12:00 - 14:00
18.01.2022 14:00 - 16:00
19.01.2022 12:00 - 14:00
21.01.2022 12:00 - 14:00
24.01.2022 12:00 - 14:00
25.01.2022 14:00 - 16:00
26.01.2022 12:00 - 14:00
28.01.2022 12:00 - 14:00
31.01.2022 12:00 - 14:00
01.02.2022 14:00 - 16:00
02.02.2022 12:00 - 14:00
04.02.2022 12:00 - 14:00
07.02.2022 12:00 - 14:00
08.02.2022 14:00 - 16:00
09.02.2022 12:00 - 14:00
11.02.2022 12:00 - 14:00
14.02.2022 12:00 - 14:00
15.02.2022 14:00 - 16:00
16.02.2022 12:00 - 14:00
18.02.2022 12:00 - 14:00
21.02.2022 12:00 - 14:00
22.02.2022 14:00 - 16:00
23.02.2022 12:00 - 14:00
25.02.2022 12:00 - 14:00

Lecture: Info lecture

10.01.2022 12:00 - 13:00

Prerequisites

The compulsory prerequisite knowledge is differential and integral calculus of one variable real functions, and the fundamentals of matrix algebra (Mathematics 1-3 or similar courses).

Compulsory Prerequisites

• Introductory Calculus, MATH.APP.111, 5 cr
• Vectors and Matrices, MATH.MA.140, 5 cr
• Differential and Integral Calculus, MATH.APP.160, 5 cr
• Vectors and Matrices, MATH.MA.140, 5 cr
• Analysis A: Limit and Continuity, MATH.MA.420, 5 cr
• Differential and Integral Calculus, MATH.APP.160, 5 cr
• Calculus, Part 1, MATH.MA.120, 5 cr
• Calculus, Part 2, MATH.MA.160, 5 cr
• Vectors and Matrices, MATH.MA.140, 5 cr

General scale, 0-5

• AYBIODIVO Open University Route, Biotechnology and Biomedical Engineering, MSc
• AYBSEMSCVO Open University Route, Biomedical Sciences and Engineering, MSc
• AYCSMSCVO Open University Route, Computing Sciences, MSc. Tech.
• AYEEMSCVO Open University Route, Electrical Engineering, MSc
• AYITMSCVO Open University Route, Information Technology, MSc
• AYKODIVO Open University Route, Mechanical Engineering, MSc
• AYMADIVO Open University Route, Materials Engineering, MSc
• AYMAMSCVO Open University Route, Materials Science and Engineering, MSc
• AYRAKDIVO Open University Route, Civil Engineering, MSc
• AYSDIVO Open University Route, Electrical  Engineering, MSc