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HN1002 Applied Mathematics 7.5 credits

Tillämpad matematik

  • Educational level

    First cycle

  • Academic level (A-D)

    A

  • Subject area

    Mathematics
    Techonology

  • Grade scale

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

At present this course is not scheduled to be offered.

Learning outcomes

The objective of the course is to provide the following abilities:

  • Solving linear differential equations, homogeneous and inhomogeneous, of first and second order.
  • Solving elementary separable differential equations
  • Solving elementary differential equations using integrating factor
  • Transferring complex numbers from rectangular form to polar, and vice versa.
  • Using algebraic rules applicable to complex numbers
  • Representing elementary dynamical problems with differential equations and solving them by hand and by mathematical software
  • Simulating elementary mathematical problems using mathematical software
  • Applying the classical definition of probability on elementary probability problems
  • Selecting applicable probability distribution for well-defined problems
  • Applying the central limit theorem
  • Solving probability problems using information from complementary events
  • Making comparisons between stocastic variables and observed data
  • Calculating confidence intervals based on samples acquired from normally distributed populations
  • Estimating credibility of calculations

Course main content

  • Mathematics: Complex numbers. Differential equations of first and second order. Separable differential equations. Homogenous and inhomogenous differential equations. Mathematical applications.
  • Mechanics: Velocity and acceleration problem. Applications of Newton’s laws.
  • Statistics: Descriptive statistics. Probability theory. Conditional probability. Discrete and continuous random variables. The most common density, probability, and distribution functions. Expectation, variance, and standard deviation for descriptive and random variables.

Eligibility

Have a thorough knowledge of mathematics (by means of course HN1901, Mathematics 1) and basic knowledge of the mathematical part of MATLAB (be means of course HM1002, Computerized Tools in the Design Process).

Literature

Matematik för ingenjörer, Staffan Rodhe, Håkan Sollervall

  • ISBN: 9789144067964
  • Publisher: Studentlitteratur AB
  • Country of publication: Sverige
  • Edition: 6

Ett stycke statistik, Dag Jonsson, Lennart Norell (paperback)

  • ISBN: 9789144029894
  • Publisher: Studentlitteratur AB
  • Country of publication: Sverige
  • Edition: 3

Examination

  • KON1 - Examination, 2.0 credits, grade scale: A, B, C, D, E, FX, F
  • TEN1 - Examination, 3.5 credits, grade scale: A, B, C, D, E, FX, F
  • ÖVN1 - Exercises, 2.0 credits, grade scale: A, B, C, D, E, FX, F

Requirements for final grade

Passed written exam in statistics (TEN1), grades A-F.
Passed written exam in complex numbers and differential equations (KON1), grades A-F.
Passed Exercises in mathematic software (MATLAB) and assignments in statistics (ÖVN1), grades A-F.

Offered by

ITM/Applied Mechanical Engineering

Examiner

Håkan Carlqvist, hakanc@kth.se, 08- 790 95 43

Version

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