• Svenska

SF1685 Calculus in One Variable 7.5 credits

For course offering

Spring 2025 Start 14 Jan 2025 programme students

Target group

No information inserted

P3 (7.5 hp)

14 Jan 2025
16 Mar 2025

50%

Normal Daytime

English

KTH Campus

Number of places

Places are not limited

Application

For course offering

Spring 2025 Start 14 Jan 2025 programme students

60129

Contact

For course offering

Spring 2025 Start 14 Jan 2025 programme students

Examiner

No information inserted

Course coordinator

No information inserted

Teachers

No information inserted
Headings with content from the Course syllabus SF1685 (Autumn 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Function, function graph, domain, range. Increasing and decreasing functions, odd and even functions. Inverse functions. The class of elementary functions. Trigonometric functions, exponential and logarithmic functions. Power laws, logarithms. Limits, rules for calculating limits, standard limits. Continuity, theorems on continuous functions. Derivative, rules of differentiation, the mean value theorem,  implicit differentiation, applications: rate of change, linear approximation, tangent, extreme value problems, sketching the graph of a function, l'Hôpital's rule. Taylor's formula with error estimates. Linear differential equations with constant coefficients and their applications. The Riemann integral, primitive functions, the fundamental theorem integral calcolus, variable substitution, integration by parts, partial fractions. Riemann sums, geometric and other applications of integrals, improper integrals, estimates and convergence. Paramterization of curves and arc length. Sequences and series, convergence criteria, the Cauchy integral test. Taylor series.

Intended learning outcomes

After the course the student should be able to

• use concepts. theorems and methods to solve and present solutions to problems within the parts of one variable caclulus described by the course content,
• read and comprehend mathematical text.

Literature and preparations

Specific prerequisites

Basic requirements.

Recommended prerequisites

SF1624/SF1684 Algebra and Geometry, SF1675 Applied Linear Algebra or similar.

Equipment

No information inserted

Literature

Announced no later than 4 weeks before the start of the course on the course web page.

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

Examination

• TEN1 - Examination, 7.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability.

Written exam, possibly with the possibility of continuous examination.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Technology

First cycle