| TATA90 |
Multivariable Calculus and Differential Equations, 4 ECTS credits.
/Flervariabelanalys och differentialekvationer/
For:
U
|
| |
Prel. scheduled
hours: 46
Rec. self-study hours: 61
|
| |
Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
|
| |
Advancement level
(G1, G2, A): G1
|
|
Aim:
Gain familiarity with mathematical concepts, reasoning and relationships in multivariable calculus and linear differential equations in one variable, and gain the calculation and problem solving skills needed for further studies. After completing this course you should be able to
- cite and explain the definitions of the course's key concepts, such as topological fundamental concepts, functions, limits, continuity, partial derivatives, multiple integrals, functional determinants etc..
- handle differential equations (first order linear, separable and higher order linear equations with constant coefficients).
- quote, explain and use the course central theorems, such as the chain rule, change of variables in multiple integrals, the relationship between gradients and directional derivatives, theorems concerning multiple integral properties etc..
- solving some partial differential equations using the chain rule.
- verify that results are correct or reasonable.
- calculate the directional derivatives and tangent-, normal- and tangent plane equations and explain and use the concepts geometrical significance in problem solving.
- compute multiple integrals using repeated integration, change of variables (e.g. polar, spherical and linear).
|
|
Prerequisites: (valid for students admitted to programmes within which the course is offered)
Calculus in one variable 1, Linear Algebra
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
|
|
Organisation:
The course consists of lectures and classes.
|
|
Course contents:
The space R ^ n. Basic topological concepts. Functions from R ^ n to R ^ p. Function surfaces, level surfaces and level curves. Limits. Partial derivatives. The chain rule. Gradient, normal, tangent and tangent plane. Directional derivative. Multiple integrals. Repeated integration. Variable Substitution. Functional determinants. Ordinary Differential Equations. First order linear and separable equations. Linear equations of higher order with constant coefficients.
|
|
Course literature:
|
|
Examination: |
|
Written examination
|
4 ECTS
|
| |
|
|
Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Göran Forsling
Link to the course homepage at the department
Course Syllabus in Swedish
|
|