TATA69 · 6 credits · Basic level (G1F) · Matematik, Tillämpad matematik
Calculus in Several Variables
Active · next start VT 2027
86%
passed the latest ordinary exam
TEN1 · 4 Jun 2026 · 258 students
56%
passed the ordinary exams, all sittings over the last 5 years
TEN1 · 2,716 students
Unusually easy in 2025/26
86% passed the ordinary exam in 2025/26 (258 students), against 53% on average in earlier years (2,458 students).
Part of 1 programme
Exam
TEN1 Written examination
- 5
- 4
- 3
- U
Ordinary exams
56% passed · 2,716 students
- 86%258
- 35%260
- 51%352
- 79%229
- 67%336
- 60%345
- 27%300
- 79%300
- 29%336
Re-exams
28% passed · 1,411 students
- 56%72
- 10%88
- 19%115
- 42%178
- 61%128
- 7%98
- 47%96
- 13%151
- 14%170
- 22%128
- 24%187
- Pass the re-exam: 28% (1,411 students), compared with 56% (2,716 students) on the ordinary exam
- Get 4 or 5: 17% (4,127 students)
Show small sittings (1)
Sittings with fewer than 5 students, often credit transfers or special sittings. They are not part of any figure on this page.
- 100%1
About the course
Aim
After completing the course, the student should be able to
- choose and apply methods to problems within all parts of the course, as they are described in the course content
- present and justify solutions to tasks within the course content using relevant concepts and clear reasoning
Content
Part I: Basic properties of subsets of R^n and functions of several variables, derivatives.
The room R^n. Basic topological concepts. Real- and vector-valued functions of several variables. Functional surfaces and level sets. Limit value and continuity. Partial derivatives. Differentiability and differential. The chain rule.
Part II: Gradients with applications, local extrema and inverse and implicitly given functions
Gradient, normal, tangent and tangent plane. Directional derivatives. Taylor's formula. Local maxima and minima. Inverse the function theorem and the implicit function theorem. Implicit derivation.
Part III: Multiple Integrals
Repeated integration (Fubini's theorem). Variable changes. Area, volume, mass and center of mass. Generalized multiple integrals.
- Examiner
- David Rule
- Scheduled hours
- 64 h
- Main field of study
- Matematik, Tillämpad matematik