SF1625 Calculus in One Variable 7.5 credits
Envariabelanalys
Educational level
First cycle
Academic level (AD)
A Subject area
Mathematics
Technology
Grade scale
A, B, C, D, E, FX, F
Course offerings
Autumn 17 CELTE1 m.fl. for programme students

Periods
Autumn 17 P1 (7.5 credits)

Application code
50572
Start date
2017 week: 35
End date
2017 week: 43
Language of instruction
Swedish
Campus
KTH Campus
Number of lectures
21 (preliminary)
Number of exercises
14 (preliminary)
Tutoring time
Daytime
Form of study
Normal

Number of places
No limitation
Schedule
Course responsible
Douglas Lundholm <dogge@kth.se>
Teacher
Douglas Lundholm <dogge@kth.se>
Tommy Ekola <ekola@kth.se>
Part of programme
Autumn 17 CMETE1 m.fl. for programme students

Periods
Autumn 17 P1 (7.5 credits)

Application code
50579
Start date
2017 week: 35
End date
2017 week: 43
Language of instruction
Swedish
Campus
KTH Campus
Number of lectures
21 (preliminary)
Number of exercises
14 (preliminary)
Tutoring time
Daytime
Form of study
Normal

Number of places
No limitation
Schedule
Course responsible
Erik Lindgren <eriklin@kth.se>
Teacher
Erik Lindgren <eriklin@kth.se>
Part of programme
Autumn 17 CMATD1 m.fl. for programme students

Periods
Autumn 17 P1 (7.5 credits)

Application code
50580
Start date
2017 week: 35
End date
2017 week: 43
Language of instruction
Swedish
Campus
KTH Campus
Number of lectures
21 (preliminary)
Number of exercises
14 (preliminary)
Tutoring time
Daytime
Form of study
Normal

Number of places
No limitation
Schedule
Course responsible
Lars Filipsson <lfn@kth.se>
Teacher
Lars Filipsson <lfn@kth.se>
Part of programme
Autumn 17 CDEPR1 m.fl. for programme students

Periods
Autumn 17 P2 (7.5 credits)

Application code
50581
Start date
2017 week: 44
End date
2018 week: 3
Language of instruction
Swedish
Campus
KTH Campus
Number of lectures
21 (preliminary)
Number of exercises
14 (preliminary)
Tutoring time
Daytime
Form of study
Normal

Number of places
No limitation
Schedule
Course responsible
David Rydh <dary@kth.se>
Teacher
David Rydh <dary@kth.se>
Part of programme
Autumn 17 CBIOT1 m.fl. for programme students

Periods
Autumn 17 P2 (7.5 credits)

Application code
50582
Start date
2017 week: 44
End date
2018 week: 3
Language of instruction
Swedish
Campus
KTH Campus
Number of lectures
21 (preliminary)
Number of exercises
14 (preliminary)
Tutoring time
Daytime
Form of study
Normal

Number of places
No limitation
Schedule
Course responsible
Kristian Bjerklöv <bjerklov@kth.se>
Teacher
Kristian Bjerklöv <bjerklov@kth.se>
Part of programme
Autumn 17 CMEDT1 for programme students

Periods
Autumn 17 P1 (7.5 credits)

Application code
50583
Start date
2017 week: 35
End date
2017 week: 43
Language of instruction
Swedish
Campus
KTH Flemingsberg
Number of lectures
21 (preliminary)
Number of exercises
14 (preliminary)
Tutoring time
Daytime
Form of study
Normal

Number of places
No limitation
Schedule
Course responsible
Armin Halilovic <armin.halilovic@sth.kth.se>
Teacher
Armin Halilovic <armin.halilovic@sth.kth.se>
Part of programme
Autumn 17 CMAST ITSY1 for programme students

Periods
Autumn 17 P2 (7.5 credits)

Application code
50584
Start date
2017 week: 44
End date
2018 week: 3
Language of instruction
Swedish
Campus
KTH Södertälje
Number of lectures
21 (preliminary)
Number of exercises
14 (preliminary)
Tutoring time
Daytime
Form of study
Normal

Number of places
No limitation
Schedule
Course responsible
Albin Eriksson Östman <albin01@kth.se>
Teacher
Albin Eriksson Östman <albin01@kth.se>
Lars Johansson <larsjo@kth.se>
Part of programme
Spring 18 CDATE1 m.fl. for programme students

Periods
Spring 18 P3 (7.5 credits)

Application code
60443
Start date
2018 week: 3
End date
2018 week: 11
Language of instruction
Swedish
Campus
KTH Campus
Number of lectures
21 (preliminary)
Number of exercises
14 (preliminary)
Tutoring time
Daytime
Form of study
Normal

Number of places
No limitation
Course responsible
Hans Thunberg <thunberg@kth.se>
Teacher
Hans Thunberg <thunberg@kth.se>
Part of programme
Spring 18 CINTE1 for programme students

Periods
Spring 18 P3 (7.5 credits)

Application code
60445
Start date
2018 week: 3
End date
2018 week: 11
Language of instruction
Swedish
Campus
KTH Kista
Number of lectures
21 (preliminary)
Number of exercises
14 (preliminary)
Tutoring time
Daytime
Form of study
Normal

Number of places
No limitation
Course responsible
Bengt Y L Ek <bek@kth.se>
Teacher
Bengt Y L Ek <bek@kth.se>
Part of programme
Intended learning outcomes
After completing the course the student a passing grade to:
 Use, explain and apply fundamental concepts and problem solving methods of one variable calculus, especially:
 Describe the fundamental characteristics of elementary functions, such as power laws, logarithm lawss and trigonometric formulas and use them in problem solving and calculations
 Calculating derivatives using, among other things, the product, quotient and the chain rule
 Using derivatives to investigate the properties of a function, for example, decide questions of increasing and decreasing behavior, sketch function graphs, determine the tangent, prove inequalities and find extreme values
 Using Taylor's formula to approximate functions with polynomials to desired degree of accuracy
 Account for the definition of the Riemann Integral and its applications, as well as approximate integrals with Riemann sums
 Calculate integrals using primitive functions, integration by parts, variable substitution and partial fractions
 Account for the fundamental theorem of calculus about the relationship between the derivative and integral, and use it in problem solving and calculations
 Solve some linear ordinary differential equations with constant coefficients and explain how they arise in applications
 Calculate limits and use these to study the behavior of functions locally or asymptotically
 Determine whether a given function is invertible and if possible calculate the inverse function
 Determine if certain series converges or diverges and if possible calculate them  Set up simple mathematical models for applications that can be described with the help of functions of one variable, and discuss such models relevance, plausibility and accuracy.
 Read and understand mathematical text about functions of one variable and their applications, communicate mathematical reasoning and computations within this filed orally as well as in writing in such a way that they are easy to follow.
For higher grades, the student should be able to:
 Account for the theory of one variable calculus, with definitions, theorems and proofs
 Generalize and adapt methods to fit in new situations
 Solve problems requiring a combination of methods, or more extensive calculations in several steps
 Solve more advanced problems in, for example, limits, series, integrals and applications
Course main content
Function, function graph, domain, range. Increasing and decreasing functions, odd and even functions. Inverse functions. The class of elementary functions. Unit circle, trigonometric formulas and equations, exponential and logarithmic functions, power laws, logarithms. Limits, rules for calculating limits, standard limits. Continuity, theorems on continuous functions. Derivative, rules of differentiation and applications: rate of change, linear approximation, tangent, extreme value problems, sketching the graph of a function, inequalities etc. Taylor's formula with error estimates. Linear differential equations with constant coefficients and their applications. Riemann integral, primitive functions, variable substitution, integration by parts, partial fractions. Riemann sums, geometric and other applications of integrals, improper integrals. Something about sequences and series. Something about numerical methods (eg Newton's method).
Eligibility
Basic and specific requirements for engineering program.
Mandatory for first year, can not be read by other students
Literature
Robert A. Adams, Christopher Essex, Calculus  A Complete Course, 8th edition. ISBN 9780321781079.
Examination
 TEN1  Examination, 7.5, grade scale: A, B, C, D, E, FX, F
Requirements for final grade
Written exam, possibly with the possibility of continuous examination.
Offered by
SCI/Mathematics
Contact
Roy M Skjelnes (skjelnes@kth.se)
Examiner
Lars Filipsson <lfn@kth.se>
Roy M Skjelnes <skjelnes@kth.se>
Version
Course syllabus valid from: Autumn 2015.
Examination information valid from: Autumn 2007.