Introduction to natural sciences: mathematics

The course is given as preliminary education and cannot be included in a degree at university level. The course is studied within the Natural Sciences Foundation Year (Z1BAN), but can also be studied as a stand-alone course. Passing the course gives eligibility equivalent to the upper secondary school course Mathematics 4 or Mathematics continuation level 2 according to GY25. The course can be included in the following programs: 1) Natural Sciences Foundation Year (Z1BAN).

The course aims to provide the knowledge in mathematics required for admission to university studies in the natural sciences. The course is divided into two equal sub-courses and its content includes, but is slightly larger than, the upper secondary school course Mathematics 4 or Mathematics continuation level 2.

Mathematics part 1, 7.5 pre-education credits

Grading scale: Pass with distinction (VG), Pass (G) and Fail (U)

Repetition and practice of algebraic calculations, including powers and roots. Sets and logic. Equations and systems of equations. Basic concepts in plane geometry. Trigonometry and triangle solving. Polynomials, polynomial division and the factor theorem. Inequalities. Absolute value. Analytic geometry of lines and circles. The concept of function. Exponential and logarithmic functions. Trigonometric functions and simple trigonometric equations. Complex numbers, including de Moivre's formula.

Mathematics part 2, 7.5 pre-education credits

Grading scale: Pass with distinction (VG), Pass (G) and Fail (U)

Limits. Derivatives and rules for differentiation. Derivatives of elementary functions. Tangents and normals to curves. Finding maximums and minimums of functions. Asymptotes. Curve constructions. Primitive functions. Definite integrals. Area calculation. A little of differential equations.

In parallel with the two sub-courses, a module on programming as a tool for problem solving, data processing or application of numerical methods is also included.

After passing the course, the student should be able to:

•  define and use central concepts in the course,
• perform simple mathematical reasoning and proofs,
• assess whether the result of a calculation is reasonable,
• use and account for algebraic calculation rules and the laws of power and logarithms,
• complete squares, perform polynomial division, apply the factor theorem and solve algebraic equations and inequalities,
• define trigonometric functions using the unit circle, perform triangle solving, and solve simple trigonometric equations,
• interpret the equations of circles and straight lines in the plane and calculate the coordinates of the points of intersection between them,
• calculate simple limits for rational expressions of elementary functions,
• calculate derivatives of functions composed of elementary functions,
• determine equations for tangents and normals to curves given in the form y=f(x),
• carry out curve constructions,
• solve simple maximum and minimum problems,
• determine simple primitive functions and calculate simple definite integrals and apply this when calculating areas,
• represent complex numbers in different ways, apply the four arithmetic operations to complex numbers and solve quadratic equations with complex roots, 
• at a basic level use programming as a tool in problem solving, data processing or application of numerical methods.

The language of instruction is Swedish.

The course is examined through web-based tests during the course and through exams at the end of each module. Students who do not pass the regular exam are offered additional exam opportunities.

The course is awarded one of the grades Pass with Distinction (VG), Pass (G) and Fail (U). For the grade Pass for the entire course, it is required that both sub-courses and the module on programming are passed. For the grade Pass with Distinction for the entire course, it is also required that the total score for part 1 and part 2 is at least the sum of the score requirement for VG for each sub-course.

The course is evaluated with an anonymous questionnaire and/or a discussion with the student representatives. The results of and possible changes to the course will be shared with students who participated in the evaluation and students who are starting the course.

The course NBAM01 replaces NBAM00 in the Natural Sciences Foundation Year (Z1BAN) starting in the fall semester 2020.