Course syllabus for Linear algebra and calculus

The course syllabus contains changes
See changes

Course syllabus adopted 2024-02-08 by Head of Programme (or corresponding).

Overview

  • Swedish nameLinjär algebra och analys fortsättning
  • CodeMVE466
  • Credits6 Credits
  • OwnerTKKMT
  • Education cycleFirst-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 53135
  • Maximum participants270
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0124 Examination 6 c
Grading: TH		 6 c
  • 16 Jan 2025 am J
  • 14 Apr 2025 am J
  • 25 Aug 2025 pm J

In programmes

Examiner

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Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Knowledge equivalent to the content in the course Single variable calculus and analytical geometry.

Aim

The purpose of the course is to provide a general knowledge in one variable analysis and linear algebra required in further studies as well as in the future professional career.

Learning outcomes (after completion of the course the student should be able to)

  • define the concept integral and account for its relation to differentiation
  • apply and explain analytical methods for calculating integrals
  • explain the meaning of an ordinary differential equation and its directional field
  • apply and explain analytical methods for solving ordinary differential equations
  • account for the concepts of linear algebra given in this course.
  • account for the connections between the different concepts and use these connections in problem solving

Content

  • Linear transformations, matrix representation
  • Matrix algebra, matrix inverse and systems of linear equations
  • The Euclidean vector space Rn, linear independence, subspaces of Rn, null space (kernel), column space (range), bases, change of basis, dimension, rank
  • Eigenvalues, real and complex, eigenvectors, diagonalization
  • Orthogonal projection, orthonormal basis, method of least squares, the spectral theorem
  • Determinants
  • Antiderivatives
  • Riemann sums and the definite integral, techniques of integration, integrals of rational functions and some other functions
  • Improper integrals
  • Application of integration: volumes by slicing, solids by revolution, arclengt and surface area
  • Complex numbers, the fundamental theorem of algebra
  • Ordinary differential equations: First-order equation in general, analytical solution of separable and linear equations. Second-order linear equations with constant coefficients, the equations of simple and damped harmonic motion
  • Systems of first order linear differential equations with constant coefficients
  • Numerical methods for solving integrals and systems of ordinary differential equations

Organisation

Instruction is given in lectures and classes. More detailed information will be given on the course web page before start of the course.

Literature

Literature will be announced on the course web page before start of the course.

Examination including compulsory elements

The exam moment is examined with a written exam at the end of the course and has the grading scale U,3,4,5.

During the course there may be tests that generate bonus credits on the exam. Examples of such tests include intermediate tests and hand-in assignments. Information pertaining to the actual course round is provided on the course homepage.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.

The course syllabus contains changes

  • Changes to course rounds:
    • 2024-06-20: Examinator Examinator changed from Stefan Lemurell (sj) to Anna Karlsson (karann) by Viceprefekt/adm
      [Course round 1]