Math and Science Basics 2 (5 ECTS)

Objective

Functions and vectors
On completion of the course the student can:
- use elementary functions in applications
- recognise scalar and vector quantities
- perform operations with vectors.
Fluids and Thermal Physics
On completion of the course the student can:
- perform unit conversion
- present and apply the definitions of density and pressure
- describe the effects of pressure in fluids
- present the principle of hydraulic press
- apply the depth dependence of fluid pressure
- apply the Archimedes principle to the dynamics of a body
- define the basic flow quantities and use them
- study changes in flow velocity using the equation of continuity
- work with common temperature scales
- model and apply laws of thermal expansion
- present the ideal gas law and use it to model gas
- model heat storage and changes of state.

Content

Functions and vectors:
1. Main elementary functions and graphs of them.
2. Scalars and vectors.
3. Perform operations with vectors.
Fluids and Thermal Physics:
1. Unit conversions
2. Density and pressure
3. Pressure in fluid and gas
4. The hydraulic press principle
5. The depth dependence of fluid and gas pressure
6. Archimedes principle
7. Basic quantities related to fluid flow
8. Continuum equation
9. Temperature scales
10. Thermal expansion
11. Ideal gas
12. Heat storage capacity
13. Changes of state.

Evaluation scale

0-5

Assessment criteria, satisfactory (1)

Functions and vectors
The student
- knows the meaning of the value of a function at a certain point as well as the meaning of the zero point of a function
- is able to form a graph of a simple function with the expression given
- knows what the graph of a linear polynomial function is like and how it changes as the coefficient values change
- knows what the graph of a quadratic polynomial function is like and how it changes as coefficient values change
- can interpret the form of graphs
- knows the meaning of direct and inverse proportionality
- recognises power functions and exponential functions
- knows the definition of a logarithm
- can use trigonometric functions in plane geometry calculations
- recognises the graphs of trigonometric functions and knows the periodicity of trigonometric functions
- is able to use vectors to represent quantities with direction.
Fluids and Thermal Physics
On completion of the course the student can:
- perform simple unit conversions
- apply the definitions of density and pressure
- apply the model equation of the hydraulic press
- find the fluid pressure at a given depth
- find the buoyancy exerted on a body
- find the volume flow rate and the mass flow rate of a fluid, and model simple fluid flows
- work with common temperature scales
- find the relative changes of lengths and volumes of substances due to temperature variations
- work with the ideal gas equation
- compare the heat capacities of simple systems
- estimate the energy related to changes of state.

Assessment criteria, good (3)

Functions and vectors
In addition to the requirements above, the student
- is able to employ functions and equations in describing simple phenomena
- is able to solve trigonometric functions, logarithms and other equations with common functions
- is able to solve problems with vector quantities.
Fluids and Thermal physics
The student can:
- perform unit conversions
- apply the definitions of density and pressure
- describe the effects of pressure on fluids
- present the principle of the hydraulic press
- apply the depth dependence of fluid pressure
- apply the Archimedes principle in the case of a static equilibrium
- model simple fluid flow
- work with temperature scales
- model the simultaneous thermal expansion of several materials
- model the changes of state of a gas
- model processes including heat storage and changes of state.

Assessment criteria, excellent (5)

Functions and vectors
In addition to the requirements above, the student
- is able to employ functions and equations diversely in describing various types of phenomena
- is able to solve problems which require synthesizing the knowledge acquired during the course.
Fluids and Thermal physics
The student can:
- perform unit conversions
- apply the definitions of density and pressure
- describe the effects of pressure in fluids and present the basics of hydraulics
- present the principle of the hydraulic press
- apply the depth dependence of fluid pressure
- apply the Archimedes principle to the dynamics of a body
- model fluid flow
- work with temperature scales
- model the simultaneous thermal expansion of several materials
- model in detail the changes of state of a gas
- model complicated processes including heat storage and
changes of state.

Assessment criteria, approved/failed

Functions and vectors
The student
- knows the meaning of the value of a function at a certain point as well as the meaning of the zero point of a function
- is able to form a graph of a simple function with the expression given
- knows what the graph of a linear polynomial function is like and how it changes as the coefficient values change
- knows what the graph of a quadratic polynomial function is like and how it changes as coefficient values change
- can interpret the form of graphs
- knows the meaning of direct and inverse proportionality
- recognises power functions and exponential functions
- knows the definition of a logarithm
- can use trigonometric functions in plane geometry calculations
- recognises the graphs of trigonometric functions and knows the periodicity of trigonometric functions
- is able to use vectors to represent quantities with direction.
Fluids and Thermal Physics
On completion of the course the student can:
- perform simple unit conversions
- apply the definitions of density and pressure
- apply the model equation of the hydraulic press
- find the fluid pressure at a given depth
- find the buoyancy exerted on a body
- find the volume flow rate and the mass flow rate of a fluid, and model simple fluid flows
- work with common temperature scales
- find the relative changes of lengths and volumes of substances due to temperature variations
- work with the ideal gas equation
- compare the heat capacities of simple systems
- estimate the energy related to changes of state.

Qualifications

Math and Science Basics 1