Real Analysis 49 | Riemann Integral for Step Functions

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This is my video series about Real Analysis. We talk about sequences, series, continuous functions, differentiable functions, and integral. I hope that it will help everyone who wants to learn about it.

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#RealAnalysis
#Mathematics
#Calculus
#LearnMath
#Integrals
#Derivatives

I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[NesrineSaadene]

I didn't understand this course in French or Arabic my first language! & Now i understand it from you in English 😂 i'm so happy ❤

[kingofdimensions]

This is extremely helpful for me to teach my students about the Riemann integral.

[EstheraJoannaTietchakTiago]

You are amazing sir, a real life sever thank you very much I now have a hope for my CA😊

[mathmalak]

Good Job
I mean... maths is my life
Now English language could be my life too because I understand math with this language and with your explanation.
I am from North of Africa.

[weinihao]

In the second case (8:00) partition P1 and P2 create equal sums, because both of them contain the set of points where the step function is discontinuous. Couldn't P3 then also be chosen to be the intersection of P1 and P2 to lead to the same conclusion?
Edit: Oh, I just watched the next episode. Now I see the benefit of using the union.

[sinanakhostin]

In the last part of explaining "Case 2" we have that Sigma_p1 = Sigma_p3 and Sigma_p2 = Sigma_p3. It is visible that no matter how many elements do P1 and P2 have and what are the lengths of each segment, all partitions P1, P2 and P3 cover the whole x-axis. However the c_j values (for P1) and d_j values (for P2) are not the same. This is therefore a bit unclear to me to see how the total sum of area under the two partitions turn out to be the same (the same as the total area under P3) !

[nayjer]

For Case 1: if in P2 for example x2 tilde is involved, left from x3 tilde and therefore left from x1 in P1, then the area of P2 is greater then P1, isn't it? And the condition P1 is a subset of P2 still holds.Edit: nevernimd, x0 = a is allways included, in both sets.

[ffar]

For the second case: P1 and P2 must still contain the jumps, right? How do you denote that?

[awesomecraftstudio]

Why is the area under the graph the same for a finer partition? If we have no partition at all for example, and took the value of the rectangle with the first constant value, then we added ik more partitions at the jump points where it jumps to lower values, wouldn't the area get smaller? Doesn't this only work if the jump points are always included?

[pinklady]

What is that symbol really called? I mean that circle with a verticle stroke in it.
Is it a step function?

[gauravnainwal]

Shouldn't the union of the two partitions cover both the cases?

[angelmendez-rivera]

I think it may have been more helpful to define the integral in terms of Riemann sums first. Then it would have been clear why exactly the integral is well-defined in these cases.

[NesrineSaadene]

I didn't understand this course in French or Arabic my first language! & Now i understand it from you in English 😂 i'm so happy ❤