# SF1609 Mathematics II 9.0 credits

#### Matematik II

Basic course in differential calculus of several variables and introductory linear algebra.

### Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

## Course information

### Content and learning outcomes

#### Course contents *

Systems of linear equations and matrices; determinants, Cramerís rule, geometric interpretation of determinants. Vectors and geometry in two and three dimensions, dot product, cross product. Matrices as linear transformations from Rn to Rm. The least-squares method. Quadratic forms and diagonalization. Functions of several variables; partial derivatives, gradient, chain rule. Differentials. Curves and their parametrization in R2 and R3. Extreme value problems, the method of Lagrangeís multipliers. Implicit functions. Taylor approximation.

#### Intended learning outcomes *

After finished course a student should be able to

• recognize and use the basic concepts of linear algebra: vectors and their operations, straight lines and planes, linear dependence and independence, base vectors, linear transformations, matrices and determinants, eigenvalues and eigenvectors, quadratic forms.
• recognize and use the basic concepts of differential multivariable calculus: partial derivative, differentiability, differential, gradient, directional derivative, functional matrix and functional determinant.
• understand and explain the interaction between linear algebra and differential calculus, e.g. in connection with linearization of functions or analysis of the stationary points of multivariable functions.
• More precisely, after finished course the student should be able to:
• solve geometric problems involving points, lines and planes by means of dot and cross product.
• apply chain rules on partial derivations and decide whether a function satisfies a certain partial differential equation.

#### Course Disposition

No information inserted

### Literature and preparations

#### Specific prerequisites *

Mathematics I (SF1608) or equivalent.

#### Recommended prerequisites

No information inserted

#### Equipment

No information inserted

#### Literature

Andersson Lennart m.fl./Linjär algebra med geometri.

Persson&Böiers/Analys i flera variabler.

LTH/Övningar i analys i flera variabler.

### Examination and completion

#### Grading scale *

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

#### Examination *

• TEN1 - Examination, 9.0 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.

#### Other requirements for final grade *

One written exam (TEN1; 9 hp).

#### Opportunity to complete the requirements via supplementary examination

No information inserted

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

No information inserted

#### Examiner

No information inserted

### Further information

#### Course web

No information inserted

SCI/Mathematics

#### Main field of study *

Mathematics, Technology

First cycle