Multivariable Calculus 1

The course is taken during the second semester of the Mathematics program, but can also be taken as a stand-alone course. The course can be included in the following programs: Mathematics program (N1MAT).

General entry requirements and the equivalent of Single Variable Calculus 2 MMG240 and Linear Algebra MMG250.

Limits. Continuity. Cauchy sequences. Open and closed sets. Compactness. Pointwise and uniform continuity. Partial derivatives. Differentiability. Gradient. Directional derivatives. The chain rule. Level curves and surfaces. Curves and surfaces in parametric form. Tangent plane. Taylor's formula. Local and global extreme values. Lagrange's multiplier method. Inverse and implicit function theorems (without proof). Differentiation under the integral sign. Completeness of R^n. The supremum axiom. Bolzano-Weierstrass' theorem. Cauchy's convergence principle. The extreme value theorem and the intermediate value theorem.

After passing the course, the student should be able to:

• calculate and use limits ​​and derivatives of various kinds for functions of several variables and interpret them geometrically,
• sketch level curves and find tangent planes of surfaces in three dimensions, as well as sketch simple parameterized curves and surfaces,
• transform a partial differential equation using given variable substitution and in simple cases also determine the solution,
• determine local and global extreme values ​​of functions in R^n in simpler cases,
• know fundamental topological properties of sets in R^n,
• formulate and use important definitions and theorems in the course and be able to prove some of them.

The examination consists of a written exam at the end of the course. During the course, there may be optional assignments that give bonus points on the exam. Examples of such assignments are small written tests, labs, and oral or written presentations. Information about this is found on the course home page.

If a student who has been failed twice for the same examination element wishes to change examiner before the next examination session, such a request is to be granted unless there are specific reasons to the contrary (Chapter 6 Section 22 HF).

If a student has received a certificate of disability study support from the University of Gothenburg with a recommendation of adapted examination and/or adapted forms of assessment, an examiner may decide, if this is consistent with the course’s intended learning outcomes and provided that no unreasonable resources would be needed, to grant the student adapted examination and/or adapted forms of assessment.

If a course has been discontinued or undergone major changes, the student must be offered at least two examination sessions in addition to ordinary examination sessions. These sessions are to be spread over a period of at least one year but no more than two years after the course has been discontinued/changed. The same applies to placement and internship (VFU) except that this is restricted to only one further examination session.

If a student has been notified that they fulfil the requirements for being a student at Riksidrottsuniversitetet (RIU student), to combine elite sports activities with studies, the examiner is entitled to decide on adaptation of examinations if this is done in accordance with the Local rules regarding RIU students at the University of Gothenburg.

The grading scale comprises: Pass with Distinction (VG), Pass (G) and Fail (U).

The course is evaluated with an anonymous questionnaire and/or a discussion with the student representatives. The results of and possible changes to the course will be shared with students who participated in the evaluation and students who are starting the course.

An earlier version of this course was previously included as a sub-course in Multivariable Analysis MMG300. It is not permitted to take both this course and the sub-course Multivariable Analysis 1 in MMG300.