# ING0009 Elementary Mathematics

## Course description for academic year 2018/2019

### Contents and structure

Arithmetic and algebra, powers and roots, equations and inequalities, graphs and functions, limits and continuity. Differentiation and function analysis.Trigonometry and geometry, trigonometric equations and functions, vectors and integration.

### Learning Outcome

-Knowledge: The students can

• Define mathematical concepts, such as natural numbers, whole numbers, rational and irrational numbers.
• Explain quadratic equations and factorisation, together with  caculation rules for powers and roots.
• Explain the function concept, define the domain and range of a function, and how a coordinate system is constructed.
• Describe continuity and discontinuity graphically.
• Explain the definition of the derivative and differential.
• Explain the definitions of logarithmic functions and exponential functions with different basic numbers.
• Explain definition of sine, cosine and tangent, and other simple trigonometric correlations.
• Describe the unit circle for a fellow student.
• Define a vector.
• Explain the trigonometric definitions and present them graphically.
• Explain graphically the definite integral of a function.

-Skills The students can

• Solve equations of the first and second degree, and inequalities using mathematical operations.
• Run a polynomial division and factoring polynomials.
• Draw different functions in a coordinate system and solve equations, systems of equations and inequalities graphically.
• Set up the equation for a straight line.
• Find limits and asymptotes of functions.
• Use calculation rules of differentiation to find the derivatives of sums, differences, products, quotients of composite functions.
• Use calculation rules for logarithms in exercises and to solve equations.
• Practice calculation rules of volume and area and can solve practical maximums and minimum calculations.
• Apply trigonometric formulas and exact trigonometric values for triangle calculation and solution of equations.
• Use trigonometric formula to solve equations and inequalities, analyze trigonometric, exponential and logarithmic functions .
• Derivate and analyze trigonometric functions.
• Use calculation rules of vector calculation in the plane and in space, in component and coordinate form.
• Find indefinite and definite integrals using integration rules and methods of integration substitution and partial fractions.

-General qualification: The students:

• Can write mathematics correctly with the correct use of mathematical symbols and notation.
• Can explain mathematical problems and solution methods to others, both in writing, verbally and in other ways.
• Has acquired the knowledge necessary for engineering studies.

None.

None.

### Teaching methods

Lecture and workshop

The course is taught intensively in summer. The exam will be held before the regular semester begins. There is the possibility to make a repeat examination, before the registration deadline of the autumn courses.

Because this course is a prerequisite for the engineering programme, the course must be passed in order to participate in the regular courses in the autumn.

### Compulsory learning activities

Yes (will be specified in the course plan at course start).

### Assessment

Written exam, 5 hours.