Single Variable Calculus 1

The course is read during the first semester in the Mathematical program, but can also be read as a freestanding course.

The course can be part of the following programmes: Bachelor's Programme in Mathematics (N1MAT).

Elementary functions and their properties (polynomials, power functions, exponential functions, logarithmic functions, trigonometric functions and arc functions). Sequences, subsequences, upper and lower bounded sequences. Complex numbers: calculations, polar form, polynomial equations, binomial equation. Limits. Continuous functions. Standard limits. Use of the limit, for example for calculating asymptotes. The number e. The derivative. Derivative rules including the product, quotient and chain rules. Properties of differentiable functions. Higher-order derivatives. Applications of derivatives: curve sketching, extreme values, optimization, inequalities. Convex/concave functions and their properties. Inflection points.

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

• define and use basic concepts within the course, such as sequence, limit, continuity, derivative, convex/concave function,
• prove and use central theorems within the course, such as the chain rule, the intermediate value theorem, and the mean value theorem,
• perform calculations with complex numbers in both rectangular and polar form, visualize numbers in the complex number plane, and solve polynomial equations using complex numbers,
• calculate limit values ​​and use these in problem solving,
• use derivatives in problem solving, for example to sketch curves, optimize, and prove inequalities.

The course is assessed by means 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 assignemnts are tests, written assignments, laboratory sessions or project work. Information for the current course instance is given via the course homepage.

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 on both this course and the sub-course Single Variable Calculus 1 in MMG200 Mathematics 1.

For a list of course literature, see: https://studentportal.gu.se/dina-studier/kursplan-och-litteraturlista?f_nn=1&i_ma=1