SF1625 Calculus in One Variable 7.5 credits

• Educational level

  First cycle

• Academic level (A-D)

  A

• Subject area

  Mathematics
  Techonology
  

• Grade scale

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

• Link to homepage

• Course page on KTH Social

Learning outcomes

After completing this course with a passing grade the student should be able to

• Use, explain and apply the fundamental concepts and problem solving methods of one variable Calculus, especially:
  - Use the derivative to investigate functions, e.g. sketch graphs and solve extremal value problems
   - Use Taylor’s formula to approximate functions with polynomials to a desired degree of accuracy
   - Explain the definition of the Riemann integral and account for some of its applications, compute integrals using anti-derivatives, partial integration and change of variables
  - Solve certain linear ordinary differential equations with constant coefficients and explain how they are used in applications
  - Compute some elementary limits and use these to study the behavior of a function locally or asymptotically
• Propose mathematical models for applications that can be described by functions of one variable, discuss relevance and accuracy of such models, and be aware of how mathematical software can be used, for example to plot graphs and solve equations
• Read and understand mathematical text about functions of one variable and their applications, communicate mathematical reasoning and computations within this field orally as well as in writing in such a way that it is easy to follow

For the higher grades the student should also be able to:

• Deduce some particularly important theorems and formulas
• Generalize and adapt the methods to fit in new situations
• Solve problem that require complex computations in several steps
• Explain the mathematical theory behind the concepts limit, continuity, series

Course main content

Function, graph of a function. Transcendental function, the unit circle, trigonometric formlulas and equations, exponential function, logarithms, laws of the logarithm, powers. Limits, standard limits, continuity. The derivative, laws of derivation and applications: extremal value problems, curve sketching, inequalities. Taylor’s formula with estimations of the error. Linear ordinary differential equations with constant coefficients and their applications. The Riemann integral, anti-derivatives, change of variables, partial integration, geometric and other applications of the integral, generalized integrals. Series.

Eligibility

Basic and specific requirements for engineering program.
Mandatory for first year, can not be read by other students

Literature

Persson&Böiers/Analys i en variabel.
LTH/Övningar i analys i en variabel.
Kompletterande kompendium om serier som kan laddas ner från kurshemsidan

Examination

• TEN1 - Examination, 7.5 credits, 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

Examiner

Bengt Ek

Version

Course plan valid from: Autumn 10.
Examination information valid from: Autumn 07.