Problems with parameters
Problems with parameters, Analytical, graphical and functional methods of solving problems with parameter.
This course will challenge your knowledge in high-school mathematics. You will learn new ways of solving problems with parameter and comparing ways of solving these problems and choosing the best one.
This course is first of all made for school and university teachers and technical university students, but anyone who wants to put their knowledge of basic mathematics in systematic order can take it.
The course covers three main ways of solving problems with parameter:
- Analytical method.
You will learn about:
- linear equations and inequalities with parameter
- systems of linear equations and inequalities with parameter
- rational equations and inequalities with parameter
- quadratic equations and inequalities with parameter
- theorems about positions of the roots of quadratic equations and inequalities with parameter
- problems reducible to quadratic equations and inequalities with parameter
- Graphical method.
You will learn about:
- graphs of linear, quadratic, rational, modular, irrational, exponential, logarithmic and trigonometric functions
- transformations of graphs of functions
- graphs of equations and inequalities
- using graphs as a visualisation tool to solve problems with parameter
- Functional method.
You will learn about:- monotonous functions
- limited functions
- even\odd functions
- using properties of functions to solve problems with parameter
In conclusion you will face some problems solvable in every mentioned way and learn to compare different ideas and choose the one that fits the best for every unique situation.
