SF1685 Calculus in One Variable 7.5 credits

Envariabelanalys

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Offering and execution

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Course information

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.

Course Disposition

No information inserted

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

Grading scale *

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.

Other requirements for final grade *

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

Examiner

Lars Filipsson

Kristian Bjerklöv

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF1685

Offered by

SCI/Mathematics

Main field of study *

Technology

Education cycle *

First cycle

Add-on studies

No information inserted

Contact

Roy M Skjelnes (skjelnes@kth.se)

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.

Supplementary information

Language: English

Mandatory for first year, can not be read by other students.