Objectives:
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.
Contents:
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:
Knowledge
The student
Skills:
The students
General competence
The student
Written examination on campus: 5 hours
Examination support materials: Non- programmable calculator, according to model listed in faculty regulations and Textbook
The following changes is made to assessment spring semester 2021:
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.
Due to the measures taken to avoid the spread of Covid-19, UiB is closed for on-campus assessment. As a consequence, the following changes is made to assessment autumn semester 2020: