Vectors and Analytical GeometryLaajuus (3 ECTS)

Objective

The student is able to interpret vectors expressing either state, position, change, or direction.

The student is able to carry out elementary algebraic operation of vectors. In addition he or she can visualize those operations in two dimensional space.

The student is able to apply 2D ja 3D vectors in chemical, environmental or physical problems.

The student recognizes, and can list typical examples of higher dimensional vectors in analytical chemistry and in environmental engineering.

The student is able express dependencies using tools of analytical geometry and linear (empirical) models.

The student can explain what is meant by a function and can apply functions in basic engineering problems.

The student can graph typical functions appearing in engineering problems.

Content

1. Vector algebra

2. Scalar, vector and triple products, and projections

3. Straight lines, planes and hyper-planes

4. Linear and quadratic empirical models

5. Functions

6. Computer aided mathematics

Qualifications

Equations and Matrices

Assessment criteria, satisfactory (1)

1. The student is able to perform simple algebraic operations on vectors, such as addition, subtraction, multiplying by a scalar, and calculating norms. The student can also visualize the aforementioned operations in 2D.

2. The student is able to apply scalar and vector products in calculating angles between vectors, and calculating areas and volumes of simple geometrical objects. The student is able to calculate scalar and vector projection in any dimension.

3. The student is able calculate equidistant points along a given straight line, and the student is able to define the equation of a plane passing given 3 points.

5. The student can graph typical basic functions appearing in environmental engineering.

6. The student attends the mandatory computer labs.

Assessment criteria, good (3)

1. The student can apply vectors in physical 2D or 3D problems of movement or force balances.

2. The student can apply scalar and vector products in calculating properties of real geometrical objects.

3. The student is able apply straight lines either in environmental processes.

4. The student can apply the concept of a plane in linear empirical modeling.

5. The student can determine inverse and composite functions.

6. The student shows that he or she is apply mathematical software in visualizing vectors or geometrical objects.

Assessment criteria, excellent (5)

1. The student can explain the difference between positional (state) and change (directional) vector in a given practical application.

3. The student is able apply straight lines defining new states of a process both distance based or variable change based.

4. The student is able to interpret linear empirical models appearing in environmental research articles.