The post Limit of Sequence appeared first on Bigsigma Math Tutorials.

]]>Let’s see some examples:

The post Limit of Sequence appeared first on Bigsigma Math Tutorials.

]]>The post Power Set (powerset) appeared first on Bigsigma Math Tutorials.

]]>Let’s see some examples:

Click here to view the video on YouTube.

The post Power Set (powerset) appeared first on Bigsigma Math Tutorials.

]]>The post What is a function appeared first on Bigsigma Math Tutorials.

]]>Click here to view the video on YouTube.

The post What is a function appeared first on Bigsigma Math Tutorials.

]]>The post Mapping, Full Mapping and Unique Mapping appeared first on Bigsigma Math Tutorials.

]]>Let’s see the tutorial:

Click here to view the video on YouTube.

The post Mapping, Full Mapping and Unique Mapping appeared first on Bigsigma Math Tutorials.

]]>The post Equality of Sets appeared first on Bigsigma Math Tutorials.

]]>Set A is equal to set B if and only if

- A is subset of B
- B is subset of A

In other words, set A is equal to B if

- Each item of A belong to B
- Each item of B belong to A

Let’s see some techniques to prove that 2 sets are equals

Click here to view the video on YouTube.

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]]>The post Empty Set appeared first on Bigsigma Math Tutorials.

]]>In the following example we see how to prove that a set is the emptyset.

Click here to view the video on YouTube.

The post Empty Set appeared first on Bigsigma Math Tutorials.

]]>The post Venn Diagrams – How to use them to find the relation of sets appeared first on Bigsigma Math Tutorials.

]]>Let’s see how can we use Venn diagram to find the relation of sets.

For example, Suppose we have 2 sets A and B, With Venn diagram we can find:

- Whether the A is equal to B
- Whether the A is superset of B
- Whether the A is subset of B
- None of the above

Let’s see some examples:

Click here to view the video on YouTube.

The post Venn Diagrams – How to use them to find the relation of sets appeared first on Bigsigma Math Tutorials.

]]>The post Complex Functions – Visualize appeared first on Bigsigma Math Tutorials.

]]>While it is easy to visualize real functions — functions whose domain and codomain are subsets of the set of complex numbers C R, It is more difficult to visualize Complex functions. In the following movies we see nice method to visualize Complex functions.

My idea behind the visualization of Complex functions is displaying the graph of the domain and codomain as graph where the x axis display is real number and the y axis is the imaginary part. Yes, this a simple task to do. But you may ask how can we see the mapping between the complex number in the domain maps to the complex number in the codomain? We add a moving red dot that will display this mapping – In other words, the when the dot is displayed in complex number in the domain graph it will also displayed in complex number in the codomain graph.

By doing this, We add another time to visualization.

Let’s see some examples:

The following demo shows how can we narrow complex domain by k by applying complex function. The domains in the movie are a hexagon and a circle. They are being narrowed by 2,3,4.

Click here to view the video on YouTube.

The following demo shows how can we expand complex domain by k by applying complex function. The domains in the movie are a hexagon and a circle. They are being expanded by 2,3,4.

Click here to view the video on YouTube.

The following demos shows how can we rotate complex domain by angle k by applying complex function.

In the first demo, the domain is a arc(0°,270°) of circle with radius 3. It is being rotated by 60° steps (60°, 120°, 180°, 240°, 300°, 0°).

Click here to view the video on YouTube.

In the first demo, The domain is the rectangle (0,4,4+4i,4i,0) and it is being rotated by 45° steps (45°, 90°, 135°, 180°, 225°, 270°, 315° and 0°).

Click here to view the video on YouTube.

The following demo show how can we move complex domain by c by applying complex function. The domains in the movie are a helmensicata and a circle. They are being moved by ( 5, 5+5i, 5i, -5+5i, -5. -5-5i, -5i . -5i+5)

Click here to view the video on YouTube.

Absolute value and argument are basic complex numbers operators. Let’s see them in action, we see squares,hexagons and circles.

Click here to view the video on YouTube.

What do you think about this method visualization of Complex functions? Do you have more complex function you want to visualize?

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