Preliminary MathematicsLaajuus (5 ECTS)

Objective

After completing this course the student will be able to perform numerical computations and symbolic calculations using real numbers. The student will understand the concepts of constant and variable. The student will be able to solve first-order equations and quadratic equations, simple radical equations, inequalities and systems of linear equations. The student will be familiar with common real functions and their graphs. The student will understand the basics of geometry and plane analytic geometry. The student will be able to solve triangle problems with the aid of trigonometric functions. The student will have a command of simple vector calculations.

Content

1) Real numbers and algebraic expressions
Real numbers, rational expressions, power expressions, applications of algebraic rules, square root and cube root.
2) Equations and systems of equations
Rules for equations, linear and quadratic equations, inequalities. Pairs of linear equations, three-equation linear systems, 2-by-2 and 3-by-3 determinants, existence and uniqueness of a solution to a linear system of equations.
3) Geometry and vectors
Similarity, radian as the standard unit of angular measure, triangle, areas and volumes. Equations of lines and circles. Basic concepts of vectors, adding and subtracting vectors, multiplication of a vector by a scalar, expressing vectors in coordinates, scalar product.

Assessment criteria, satisfactory (1)

1) Real numbers and algebraic expressions
The student is able to simplify straightforward expressions.
2) Equations and systems of equations
The student is able to solve linear and quadratic equations. The student is able to solve pairs of linear equations. The student is able to solve simple inequalities. The student is able to apply equations to elementary problems appearing in real world.
3) Geometry and vectors
The student is familiar with the basic concepts in geometry, analytic geometry and vector algebra. The student is able to perform simple calculations. The student is able to apply geometry and vectors to elementary real-world problems.

Assessment criteria, good (3)

1) Real numbers and algebraic expressions
The student is able to simplify expressions.
2) Equations and systems of equations
The student is able to solve linear and quadratic equations. The student is able to solve pairs of linear equations and three-equation linear systems. The student is able to solve inequalities. The student is able to apply equations to problems appearing in real world.
3) Geometry and vectors
The student is familiar with the concepts in geometry, analytic geometry and vector algebra. The student is able to perform calculations. The student is able to apply geometry and vectors to real-world problems.

Assessment criteria, excellent (5)

1) Real numbers and algebraic expressions
The student is able to simplify challenging expressions.
2) Equations and systems of equations
The student is able to solve linear and quadratic equations. The student is able to solve pairs of linear equations and three-equation linear systems and he/she understands the nature of the solution when the system fails to have a unique solution. The student is able to solve inequalities. The student is able to apply equations to challenging real-world problems.
3) Geometry and vectors
The student has a profound knowledge of the concepts in geometry, analytic geometry and vector algebra and he/she is an ingenious problem solver. The student is able to perform challenging calculations. The student is able to apply geometry and vectors to real-world problems in a proficient manner.

Assessment criteria, approved/failed

1) Real numbers and algebraic expressions
The student is able to simplify straightforward expressions.
2) Equations and systems of equations
The student is able to solve linear and quadratic equations. The student is able to solve pairs of linear equations. The student is able to solve simple inequalities. The student is able to apply equations to elementary problems appearing in real world.
3) Geometry and vectors
The student is familiar with the basic concepts in geometry, analytic geometry and vector algebra. The student is able to perform simple calculations. The student is able to apply geometry and vectors to elementary real-world problems.

Further information

Computer exercises will be included.