ING1102 Analysis and linear algebra

Contents and structure

The course contains the following subjects:

 

Functions of one real variable:

• The function concept and covariation of unknowns in applications
• Derivation and rate of change
• Integration as an antiderivative and as an area/Riemann sum
• Ordinary differential equations

 

Linear algebra:

• Vector and matrix representation
• Solving linear equation systems
• Vector space and linear mapping
• Eigenvalues and eigenvectors, diagonalization
• Bases and change of bases

 

Complex numbers

 

Basic programming:

• Constants, variables
• Numbers, strings
• Loops
• Conditional branching

 

Achieving a basic understanding is the goal of the course. Central items include the use of functions in modelling practical problems, and algorithms for numerical solutions as an alternative to analytical methods of solutions.

 

The items above are further illustrated with appropriate examples.

Learning Outcome

The student:

• is able to explain and exemplify the concepts of function, continuity, derivation, integration and differential equations
• is able to explain and exemplify the central concepts within linear algebra, such as matrixes, linear equation systems, conditions for inverting matrixes, bases, and eigenvectors
• is able to explain and exemplify the concepts of complex numbers and numerical algorithm

 

The student:

• is able to use derivation, integration, methods for solving differential equations, linear algebra, and numerical algorithms to solve mathematically formulated problems
• is able to use mathematical notation to define and manipulate functions, integrals, differential equations, complex numbers, vectors, and matrixes

 

The student:

• is able to use the fact that change and change pr. unit of time may be measured, calculated, added, and used in equations
• knows how to use mathematics to communicate a problem with a mathematical content
• knows how to design, read, and communicate the contents of an algorithm designed to perform calculations on or find solutions to mathematical problems

Entry requirements

None

Recommended previous knowledge

Mathematics R1 + R2 from upper secondary school or equivalent.

Teaching methods

Lectures, workshops, and work in the computer lab.

Regular lectures, exercises, laboratory work, and similar activities will be given every third week. During the two weeks where there is no regular teaching, the students are expected to work on the subject by themselves or in teams and to follow course material that is made available online.

In special cases instruction will be given by an English speaking lecturer/guest lecturer. The exam will still be given in Norwegian.

Parts of the course might be given in Haugesund.

Compulsory learning activities

Preliminary Examination 1: Will be specified in the course plan by semester start. Valid for the semester that the Preliminary Examination is completed and the next semester. 

Preliminary Examination 2: Programming. Will be specified in the course plan by semester start.

Assessment

Written exam, 5 hours.

Graded scale: A - E / F (failed).

Examination support material

Simple calculator: Allowed calculator is Casio fx-82 (all varieties: ES, ES Plus, EX, Solar etc.)

More about examination support material