Autumn. The course is also offered in the spring semester with limited number of lectures and excercise groups. In the spring semester, the course is mostly based on self-study.
Objectives and Content
The course aims at giving an introduction to the most important notions
and techniques in mathematical calculus, especially continuity,
differentiation and integration, which are needed later in most studies
in mathematics and natural sciences. At the same time, the course shall
convey how the subject is logically build up and why one needs strict
proofs and give insight into how one uses mathematics to depict (models
of) the real world.
The subject gives an introduction to the concept of limits,
continuity, differentiation and integration of real functions of one
real variable, as well as theory of real and complex numbers, with
applications to theoretical and practical problems. Central themes are
inverse functions, logarithmic and exponential functions, trigonometric
functions, Taylor polynomials and Taylor's formula with remainder.
Moreover, topics such as implicit differentiation, fixed point iteration
and Newton's method, computations of areas in the plane and volumes of
solids of revolution, numerical integration and separable and first
order linear differential equations are included.
On completion of the course the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:
* is able to compute with and use complex numbers to find real and
complex solutions to simple equations
* is able to prove statements using mathematical induction
* is able to state and apply the mathematical definitions of limits,
continuity and derivative, also in theoretical problems.
* is able to state and apply both the formal definition and other
techinques such as the limit theorems, squeeze theorem and l'Hôpital's
rule to compute limits
* is able to state and apply the Intermediate Value Theorem, the
Extremal Value Theorem and the Mean Value Theorem, also in theoretical
* is able to use rules to find derivatives and antiderivatives
* is able to study functions and sketch their graphs
* is able to apply Taylor's formula
* is able to use integration techniques such as substitution, partial
integration, as well as polynomial division, method of partial fractions
and completing the square, to find antiderivatives.
* is able to apply the Fundamental theorem of Calculus
* is able to solve simple separable and first order linear differential
* is able to model simple problems with the help of differential
equations and use implicit differentiation and functions to solve simple
* is able to use numerical methods to find approximative values for
roots of equations and definite integrals.
* masters fundamental techniques within calculus and how to use these in
both theoretical and applied problems
* is able to argue mathematically and present simple proofs and
* is able to recognize structure and formulate simple problems
* is able to work individually and in groups
* is able to formulate in a precise and scientific way on an elementary
* is able to decide whether simple mathematical arguments are correct
Recommended Previous Knowledge
R2 (Highest level of mathematics from Norwegian high school)
Forms of Assessment
Written examination: 5 hours
Examination support materials: Non- programmable calculator, according to model listed in faculty regulations and Textbook
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.
For written exams, please note that the start time may change from 09:00 to 15:00 or vice versa until 14 days prior to the exam. The exam location will be published 14 days prior to the exam. Candidates must check their room allocation on Studentweb 3 days prior to the exam.
Type of assessment: Written examination (New exam)
- 01.10.2019, 09:00
- 5 hours
- Withdrawal deadline
Type of assessment: Written examination
- 13.12.2019, 09:00
- 5 hours
- Withdrawal deadline