TATA43 · 8 credits · Basic level (G1F) · Matematik, Tillämpad matematik
Calculus in Several Variables
Active · next start VT 2027
72%
passed the latest ordinary exam
TEN1 · 4 Jun 2026 · 112 students
59%
passed the ordinary exams, all sittings over the last 5 years
TEN1 · 635 students
Unusually easy in 2025/26
72% passed the ordinary exam in 2025/26 (112 students), against 55% on average in earlier years (523 students).
Exam
TEN1 Written examination
- 5
- 4
- 3
- U
Ordinary exams
59% passed · 635 students
- 72%112
- 66%149
- 33%108
- 54%145
- 65%121
Re-exams
47% passed · 510 students
- 56%59
- 52%23
- 66%58
- 59%41
- 36%75
- 13%15
- 67%48
- 30%54
- 63%16
- 30%23
- 33%40
- 45%20
- 50%38
- Pass the re-exam: 47% (510 students), compared with 59% (635 students) on the ordinary exam
- Get 4 or 5: 26% (1,145 students)
Show small sittings (4)
Sittings with fewer than 5 students, often credit transfers or special sittings. They are not part of any figure on this page.
- 100%1
- 100%1
- 100%1
- 100%1
Who takes the course?
About the course
Aim
After completing the course, the student should be able to:
- choose and apply methods to problems involving real- and vector-valued functions of several variables and multiple integrals.
- account for and justify solutions to assignments within the course content using relevant concepts and clear reasoning
Content
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.
Gradients with applications, local and global extremes, implicitly given functions and optimization with constraints
- Gradient, normal, tangent and tangent plane. Directional derivative. Taylor's formula.Local and global extrema. Inverse and implicit function theorems. Implicit derivation. Extremal problems with constraints by means of linearly dependent gradients.
Multiple Integrals
- Multiple integrals. Repeated integration (Fubini's theorem). Change of variables. Area, volume, mass and center of mass. Improper multiple integrals.
- Examiner
- Vladimir Tkatjev
- Scheduled hours
- 76 h
- Main field of study
- Matematik, Tillämpad matematik