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Content and Exercises
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How to type mathematics in the course?
The following mathematical operators can be used to create expressions:
| Operator | Example | Result |
|---|---|---|
| Addition | 2+3 | |
| Subtraction | 2-3 | |
| Multiplication | 2*3 | |
| Division | 2/3x+1, 2/(3x+1) | , |
| Powers | 2^3, 2^(-3), (2^3)^4 | , , |
| Roots | sqrt(4), cbrt(9) | , |
| Functions | exp(3x), e^(3x) | , |
| log(2), ln(e), log_5(25) | , , | |
| sin(2*pi), cos(2*pi), tan(2*pi) | , , | |
| arcsin(pi), arccos(pi), arctan(pi) | , , | |
| Infinity | -infty, infinity, +unendlich | , , |
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If you have any questions regarding the course, need help solving a particular problem or would like more information regarding certain mathematical concepts, then we (the tutors) are happy to help.
Work on the course regularly for one long, continuous period of time . For example, four hours a day, from Monday to Friday, over the course of three weeks.
Try not using a calculator. This way you will benefit more from the course. For the goals of this course try only using them only in exceptional cases, for example for calculating or .
Even though the course can be worked on from a mobile device, to work on it comfortably we recommend to use a laptop or desktop computer
We recommend that you work through the course in the following fashion:
Begin with Chapter I "Elementary Calculus" and work through the chapters in the given order (I, II, … ,X), as subsequent chapters may require knowledge from previous chapters.
Working on a chapter
A chapter consists of multiple sections and each section contains- an article,
- practise exercises,
- traning exercises and
- a quiz.
For each section, you start working through the article so that you become familiar with all terms and concepts corresponding to the topic. Articles will come with visualizations, videos and quick-checks in order to help you understand the content better.
Once you are comfortable with all the terms and concepts from the article, you can do the practise exercises, strengthen your knowledge with the training exercises and finally test your knowledge in the quiz.
After successfully completing the quiz you continue to the next section.
When you are stuck at finding the solution of a problem
- First, try solving the solution yourself.
If you succeed in this, the learning effect will be greater. To try this, first formulate the problem in your own words and then ask the following questions:
- "Have I seen a similar problem before?"
- "Can I solve a simpler version of the problem, or is there a special case that I can solve?"
- "Can I break down the problem into smaller parts and solve those parts?"
- "Have I thought about everything and used all the information given to me in the problem statement?"
- "What could the solution look like?"
- If these questions still have not helped, you can contact our call center. Our tutors are happy to help you out.
You should only do the final exam of a chapter when you have understood the corresponding content. After successfully completing the final exam you can go to the next chapter.
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