# HF1904 Linear Algebra 5.0 credits

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Headings with content from the Course syllabus HF1904 (Autumn 2021–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

• Euler´s and de Moivre´s theorems. Binomial equations. Algebraic equations.
• Systems of linear equations.  Gauss elimination method.
• Vectors. Linear independent vectors.
• Dot product, vector cross product, scalar triple product.
• Equations of lines in 3D. Equations of planes in 3D.
• Determinant.
• Matrices, matrix operations. Matrix equations.
• Eigenvalues, eigenvectors.
• The method of least squares.
• Complex numbers: The complex plane. Modulus and argument. Polar, rectangular and exponential form.

### Intended learning outcomes

After completing the course, students should for a passing grade be able to:

• Define and interpret the fundamental concepts of linear algebra and calculus: vector,
dot product, cross product, triple product, line, plane, matrix, determinant, limit, continuity, derivative, integral.
• Do calculations with complex numbers  in polar, rectangular and exponential form
• Solve and geometrically interpret systems of linear equations.
• Use vector algebra to evaluate projections, distance, areas and volumes.
• Find eigenvalues and eigenvectors.
• Apply the method of least squares in data fitting.
• Set up simple mathematical models where the fundamental concepts in linear algebra are used.
• Use suitable software (Maple or Matlab) for symbolic as well as numerical solving mathematical   problems and applications.

• Derive important relations in linear algebra.
• Generalize and adapt the methods to use in somewhat new contexts.
• Solve problems that require synthesis of material and ideas from all over the course.

### Course disposition

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## Literature and preparations

### Specific prerequisites

Basic and specific requirements for bachelor's program in engineering.

### Recommended prerequisites

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### Equipment

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### Literature

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## Examination and completion

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

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

### Examination

• TEN1 - Examination, 5.0 credits, grading scale: A, B, C, D, E, FX, 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.

### Opportunity to complete the requirements via supplementary examination

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### Opportunity to raise an approved grade via renewed examination

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### 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 web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web HF1904

### Offered by

ABE/Constructional Engineering and Design

Technology

First cycle