# NABP1002 Mathematics

## Course description for academic year 2022/2023

### Contents and structure

This course provides the students with an understandig of mathemathics as tools to be used in further nautical science studies.

### Learning Outcome

Knowledge: The student has knowledge of:

• Arithmetic and algebra. Fractions, parenthesis rules, factorization, reduction of rational fractions, laws of exponents, roots.
• Equations and inequalities. Formulas. Equations, equation systems and inequalities of first and second degree. Factorization of polynomials. Irrational equations.
• Functions. The meaning of functions, linear functions, equations for straight lines, polynomial functions, rational functions, limits, asymptotes, coordinate system, polar coordinates, discussion.
• Differentiation. Rules of differentiation. How to solve problems of monotony, max/min, slope, and point of inflection. Function analysis.
• Integration. Indefinite and definite integrals, different methods of integration. Area computations. Volume of solid of revolution. Numerical integration.
• Exponential- and logarithmic functions. Briggs and natural logarithms. Rules for logarithms and exponentials. Functional analysis including graphical drawing.
• Trigonometry. Definition of trigonometric functions. Triangle calculations, area and volume, sinus law, cosine law. Angles, degrees, and radians. Trigonometric equations. Functional analysis including graphical drawing.
• Vector calculus. Vectors in two and three dimensions, vector coordinates, scalar product, vector product, scalar triple product. Use vector calculus to find angles, lengths, area, and volume.
• Parameterised motion in two dimensions. Spherical coordinates and great-circle navigation. Compass course and conversion between three dimensional coordinates to longitude and latitude.

Skills - The student:

• Is able to understand and use mathematical rules and techniques within the topics of the course.
• Is able to analyse 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 completed pre course in mathematics/physics

### 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: 3 out of 5 tests must be passed.
• Assignments: 2 out of 2 assignments must be passed.
• Peer assessments: 2 assignments done by 2 other fellow students must be graded.

### Assessment

Written exam 5 hours.

### Examination support material

Allowed calculator is: Casio fx-991EX. "Standard, non-programmable calculator" as specified in Examination support material is also allowed.

Technical table of formulas: "Teknisk formelsamling" (Pedersen, Gustavsen, Kaasa and Olsen).