Single Variable Calculus 2

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).

In addition to basic qualifications, knowledge equivalent to Single Variable Analysis 1 MMG230 is required.

Primitive functions. Definite integrals. Partial integration and substitution of variables. The mean value theorem of integral calculus. The fundamental theorem of analysis. Generalized integrals and comparison theorems. Applications of integrals to area, mass, and volume calculations. Linear differential equations of the first order. Separable differential equations. Linear differential equations of the second order. Series and integral criterion. Approximation with polynomials. Taylor's formula with residue term. Quantitative estimation of residue term. Taylor series. Applications of Taylor series to limits and extreme values. Mathematical writing.

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

• calculate integrals and use them in area, mass, and volume calculations,
• solve simple ordinary differential equations,
• calculate and use Taylor expansions,
• formulate and use important definitions and theorems in the course and be able to prove some of them,
• write a short mathematical text.

The examination consists of a written exam at the end of the course, as well as with a mandatory written assignment. 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 website.

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 MMG200 Mathematics 1. It is not permitted to be examined in both this course and the sub-course Single Variable Analysis 2 in MMG200 Mathematics.