# ING1020 Analysis and linear algebra

## Course description for academic year 2018/2019

### 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/Riemannsum
• Ordinary differential equations

Linear algebra:

• Vector and matrix representation
• Solving linear equation systems
• Vector space and linear mapping
• Eigen values 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

• Knowledge:
• The student is able to explain and exemplify the concepts of function, continuity, derivation, integration and differential equations.
• The student 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.
• The student is able to explain and exemplify the concepts of complex numbers and numerical algorithm.
• Skills:
• The student is able to use derivation, integration, methods for solving differential equations, linear algebra, and numerical algorithms to solve mathematically formulated problems.
• The student is able to use mathematical notation to define and manipulate functions, integral, differential equations, complex numbers, vectors, and matrixes.
• General Qualifications:
• 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.
• The student knows how to use mathematics to communicate a problem with a mathematical content.
• The student knows how to design, read, and communicate the contents of an algorithm designed to perform calculations on or find solutions to mathematical problems.

None.

### Recommended previous knowledge

Mathematics R1+R2 from upper secondary school, or similar.

### Teaching methods

Lectures, workshop and/or work in the computer lab.

### Compulsory learning activities

Work 1 (will be specified in the course plan by semester start). Valid for the semester that Compulsory assignments are completed and the next semester.

Work 2: Programming

### 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.)