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.
SF1685 Calculus in One Variable 7.5 credits
Information per course offering
Information for Spring 2025 Start 14 Jan 2025 programme students
- Course location
KTH Campus
- Duration
- 14 Jan 2025 - 16 Mar 2025
- Periods
- P3 (7.5 hp)
- Pace of study
50%
- Application code
60129
- Form of study
Normal Daytime
- Language of instruction
English
- Course memo
- Course memo is not published
- Number of places
Places are not limited
- Target group
- No information inserted
- Planned modular schedule
- [object Object]
- Schedule
- Schedule is not published
Contact
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus SF1685 (Autumn 2019–)Content and learning outcomes
Course contents
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
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.
Grading scale
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
Opportunity to raise an approved grade via renewed examination
Examiner
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
Offered by
Main field of study
Education cycle
Add-on studies
Supplementary information
Language: English
Mandatory for first year, can not be read by other students.