# NAB1030 Basic Mathematics

## Course description for academic year 2021/2022

### Contents and structure

This course provides the students with an understandig of basic and fundamental mathemathicsas tools to be used in further nautical science studies.

### Learning Outcome

Knowledge:

The student has knowledge of:

• Aritmetic and algebra
• Fractions, parenthesis rules, factorization, reduce rational fractions, laws of exponents, integer and rational exponents, roots.
• Equations and inequalities
• Formulars. Equations, equation systems and inequalities of first, second and higher degree. Factorization of polynomials, divisjon of polynomials and sign schemes.Irrational equations.
• Differentiation and integration
• Rules of differentiation, simple and more complicated functions. Indefinite and definite integrals, different methods of integration. How to solve problems of monotony, max/min, slope and point of inflection, divided -, inverse- and symmetrical functions. Area and volum calculus of a motion of a body about an axis.
• Functions
• The meaning of functions, linear functions, equations for straight lines, polynomial functions, rational functions, limits, asymptotes, coordinate system, polar coordinates, discussion.
• Exponential- and logarithmic functions, Briggs and natural logarithms. Rules and 1st and 2nd degree equation for logarithms and exponentials. Graphical drawing and discussion.
• Trigonometry
• Definition of trigonometric functions. Triangel calculations, area and volum, sinuslaw, cosinelaw, angles, degrees and radians. Trigonometric equations, 1st an 2nd degree. Graphs of trigonometric functions. Differentiation, integration and dicuss graphical solutions.
• Vector calculus
• Vectors in two and three dimensions, vector coordinates, scalar product, vector product, triple scalarproduct, in geometry to use vectorcalculus to find angles, length, area and  volum.
• Sequences and series
• Sequences, series, arithmetic ¿ and geometric series, finite and infinite series,convergence.

Skills:

The student :

• Are able to understand and use mathematical rules and techniques within the topics of the course.
• Are able to analyze and solve different problems.

General qualifications:

The student:

• Has insight in mathematics as a tool for other courses, and can use logical and analytical methods relevant in further nautical science studies.

### Entry requirements

None.

Nautical Science Y-vei- students must have passed NAB1023 Grunnleggende realfag Y-vei.

### Recommended previous knowledge

Mathematics equal to higher education entrance qualification.

### Teaching methods

Lectures and joint exercise sessions.

### Compulsory learning activities

Tests, Assignments and Peer assessments:

• Tests: 2 out of 3 tests must be passed.
• Assignments nr. 1 or nr. 2 must be passed. Nr. 3 must also be passed. Three assignments in total.
• Peer assessments: 2 assignments of 2 other fellow students must be graded.

### Assessment

Written exam 5 hours.