Calculus I, 6 credits

Main field of study

Course level

Advancement level

Course offered for

• Electronics Design Engineering, M Sc in Engineering
• Communications, Transport and Infrastructure, M Sc in Engineering
• Media Technology and Engineering, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Foundation course in mathematics

Intended learning outcomes

To give basic proficiency in mathematical concepts, reasoning and relations contained in single-variable calculus. To provide the skills in calculus and problem solving required for subsequent studies. After a completed course, the student should be able to

• read and interpret mathematical text
• quote and explain definitions of concepts like local extremum, limit, continuity, derivative, antiderivative and integral
• quote, explain and use central theorems such as the first and second fundamental theorem of calculus, the mean value theorems, the intermediate value theorem, the extreme value theorem
• use rules for limits, derivatives, antiderivatives and integrals
• carry out examinations of functions, e.g., using derivatives, limits and the properties of the elementary functions, and by that means draw conclusions concerning the properties of functions
• use standard techniques in order to determine antiderivatives and definite integrals
• investigate improper integrals with antiderivatives
• compare sums and integrals
• perform routine calculations with confidence
• carry out inspections of results and partial results, in order to verify that these are correct or reasonable

Course content

Functions of a real variable. Limits and continuity. Derivatives. Rules of differentiation. Properties of differentiable functions. Derivative and monotonicity. Graph sketching, tangents and normals, asymptotes. Local and global extrema. Derivatives of higher order. Convex and concave functions. How to find primitive functions. The Riemann integral. Definition and properties. Connection between the definite integral and primitive function. Methods of integration. Improper integrals. Sums and integrals.

Teaching and working methods

Lectures and problem classes or classes alone.

Examination

Grades

Department

Director of Studies or equivalent

Examiner

Course website and other links

Education components

Course literature