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HF1000 Mathematics 2 7.5 credits

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Information per course offering

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Course syllabus as PDF

Please note: all information from the Course syllabus is available on this page in an accessible format.

Course syllabus HF1000 (Autumn 2007–)
Headings with content from the Course syllabus HF1000 (Autumn 2007–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

  • Complex numbers: The complex plane. Modulus and argument. Polar, rectangular and exponential form. Euler´s and de Moivre´s theorems. Binomial equations. Algebraic equations.

  • Taylor’s formula

  • Differential equations: Separable differential equations. First order differential equations.

  • Linear differential equations with constant coefficients. Applications.

  • Transforms:

  • Heaviside function. Dirac function.

  • Laplace transforms.

  • Z-transform.

  • Fourier transforms.

  • Fourier series.

  • Applications on continuous and discrete dynamical systems. Stability.

Intended learning outcomes

  • After completing this course, students should be able to:
    Solve problems which involve complex numbers
  • Solve first order differential equation.
  • Solve second order linear differential equation with constant coefficient.
  • Apply differential equations to different technical fields 
    Use Laplace an Fourier transforms to solve differential and integral equations  
  • Use  the Z-transform  to solve difference equations
  • Use suitable software for symbolic as well as numerical solving mathematical   problems and applications mentioned above.

Literature and preparations

Specific prerequisites

No information inserted

Literature

Part 1:   Modern Engineering Mathematics, 4th Edition, Glyn James
Alternatives for part 1: Matematik för ingenjörer, S Rodhe, H Sollervall
Part 2: Transformteori för ingenjörer; författare: H. Sollervall, B Styf

Examination and completion

Grading scale

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

Examination

  • TEN2 - Transforms, 3.0 credits, grading scale: A, B, C, D, E, FX, F
  • TEN1 - Defferential Equations, 3.0 credits, grading scale: A, B, C, D, E, FX, F
  • LAB1 - Assignments, 1.5 credits, grading scale: P, 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.

If the course is discontinued, students may request to be examined during the following two academic years.

Other requirements for final grade

  • LAB1 - Assignments, 1.5 credits, grade scale: P, F
  • TEN1 - Defferential Equations, 3.0 credits, grade scale: A, B, C, D, E, FX, F
  • TEN2 - Transforms, 3.0 credits, grade scale: A, B, C, D, E, FX, F

Examiner

No information inserted

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

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

STH/Basic Science

Main field of study

Mathematics, Technology

Education cycle

First cycle