Course - Multivariate analysis and vector calculus - MA1103
Multivariate analysis and vector calculus
Assessments and mandatory activities may be changed until September 20th.
About
About the course
Course content
Vector-valued functions of one variable. Differentiability. Differentiation rules. Curves given by vector-valued functions. Unit tangent and normal vectors. Arc length. Curvature.
Functions of two or more variables (scalar fields). Limit. Continuity. Partial differentiation. The chain rule. Automated differentiation. Linear approximation. Differentiability. Gradient. Directional derivative. Level curves and level surfaces. Implicit function theorem. Inverse function theorem.
Optimization of functions of two or more variables (identifying maxima and minima). The extreme value theorem. The second derivative test. Lagrange multipliers.
Multiple integrals. Riemann sums. Iterated integrals. Change of order of integration. Change of variables. Jacobi determinant. Polar, cylindrical and spherical coordinates.
Vector-valued functions of two or more variables. Vector field. Conservative vector field. Line integrals for functions and vector fields.
Surface integrals. Parametrized surfaces. Orientable surfaces. Surface integral of vector fields on an oriented surface.
Vector calculus. Divergence. Curl. Vector potential. Green's theorem. The divergence theorem. Stokes' theorem. Conservation laws on integral form.
Examples of mathematical modelling and applications in science and technology.
Learning outcome
The student understands and can apply basic concepts, results and methods from multivariate calculus concerning limits, continuity, differentiation, multiple integration, line and surface integrals. The student understands and can apply basic concepts and methods from vector calculus.
The student can apply multivariate calculus and vector calculus to formulate, modell and solve simple technological problems, if necessary with the additional aid of mathematical software.
The course will primarily contribute to competence area K1; show specialist knowledge and a professionally grounded perspective. It will also contribute to competence area K2; analysing engineering problems, in collaboration with the various study programmes that the subject serves.
Learning methods and activities
Lectures and compulsory exercises. The number of exercises that must be approved will be stated at the start of the semester on the course's website. The course will be taught in Norwegian.
Compulsory assignments
- Exercises
Further on evaluation
The grade will be based on final written exam. In the event of a re-sit exam, the written exam may be changed to an oral exam. The re-sit exam will be held in August.
Recommended previous knowledge
MA1101 Foundational calculus 1 and MA1201 Linear algebra and geometry; or TMA4401 Calculus and TMA4413 Linear algebra and differential equations; or equivalent.
Course materials
To be announced at the start of the semester.
Credit reductions
Course code | Reduction | From |
---|---|---|
MNFMA109 | 7.5 sp | |
TMA4105 | 7.5 sp | |
SIF5005 | 7.5 sp | Autumn 2025 |
TMA4111 | 4 sp | Autumn 2025 |
TMA4121 | 3.5 sp | Autumn 2025 |
TMA4411 | 3.5 sp | Autumn 2025 |
IMAA2012 | 3.5 sp | Autumn 2025 |
IMAA2022 | 3.5 sp | Autumn 2025 |
IMAA2100 | 5 sp | Autumn 2025 |
IMAA3012 | 5 sp | Autumn 2025 |
IMAG2012 | 3.5 sp | Autumn 2025 |
IMAG2022 | 3.5 sp | Autumn 2025 |
IMAG2100 | 5 sp | Autumn 2025 |
IMAG3012 | 5 sp | Autumn 2025 |
IMAT2012 | 3.5 sp | Autumn 2025 |
IMAT2022 | 3.5 sp | Autumn 2025 |
IMAT2100 | 5 sp | Autumn 2025 |
IMAT3012 | 5 sp | Autumn 2025 |
Subject areas
- Mathematics