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Installing/Adding new latex packages in ubuntu environment

2010 February 5
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by ivanky

Been using ubuntu for a while, here I made some notes on how to add/install new latex packages..

A. If the package in the sty format

1. create a new directory under tex tree

–> sudo mkdir /usr/share/texmf-texlive/tex/latex/<packagename>

2. copy the package inside the new directory

3, run the following command

–> sudo mktexlsr

B. if the package is not the sty format

1. Download <packagename>.ins and <packagename>.dtx (you need both)

2. Run the following command

–> latex  <packagename>.ins

3. You will get the package in the sty format and you can follow instructions in A.

I hope this helps. Thanks to this page.

from → Uncategorized

Merry Christmas

2009 December 23
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by ivanky

Wishing you a very merry Christmas and a wonderful new year ahead.
Hoping you get your new year’s resolutions, a healthy life and many more.

Happy christmas..

ivanky

1. This Christmas, your brother Jack will be 2 years from being twice as old as your sister Jen. The sum of Jack’s age and three times Jen’s age is 66. How old is Jen?

2. One of your friends is heading north for the Christmas holiday and the other friend is heading south. If their destinies are 1029 miles apart and one car is traveling at 45 miles per hour and the other car is traveling at 53 miles per hour. How many hours before the two cars pass each other?

3. This Christmas we decided to buy some sweets and give those sweets to the children in the orphanage. If we gave each child 8 sweets then we would have 30 sweets left. If we gave the child 12 sweets each then we would have needed to boy 30 sweets more. Find the number of children in the orphanage?

4. This Christmas, my parents gave us a lot of candy canes. They gave all of those candy canes to my elder sister to distribute it. She then took some and gave me 2/3 of all candy canes. I kept 1/3 of the candy canes I had and gave the rest to my little brother. My brother ate 1/4 of the candy canes he had and gave the last 12 to my parents. How many candy canes did my little brother eat?

from → Justincase

Quiz result for Calculus Ia

2009 October 5
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by ivanky

For all my students in T-21, Bu Mul and I have finished marking your workings.

You can go to this page to view your results.

Comments are welcome.

This week is a mid-test week. Please study hard and do not hesitate to ask either Bu Mul or me if you have any questions.

from → Teachings

Result of mid semester examination of real analysis

2009 July 19
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by ivanky

After a day without interuption, I finally finished marking the real analysis exam.

Let see what you got over here.

Comments are welcome.

Good luck for all of you who finally get off your ass to the next chapter.

You could get to the next level if you get more than or equal to 57.

from → Teachings

Numerical analysis final score

2009 June 9
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by ivanky

The following link will bring you to the numerical analysis teaching page, in which you can access your final score and your indexes, whether you are in class B or class C. I am sorry to announce that the score is final. Congratulations to all of you for finally getting your ass off this lecture (you finally made it).

http://ivanky.wordpress.com/teaching/numerical-analysis/

It was my pleasure to have known you all. I am very sorry if I made some mistakes. I am also very sorry to give you a lot of assignments so that you spent your precious time doing the homework. The intention was no other but to make you understand this lecture.

I hope we can meet again some time. Also, if you bump out of some mathematical problems, you can surely contact me as I will be very happy to help you out.

from → Teachings

Result of final exam of Numerical Analysis

2009 June 2
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by ivanky

Hi all, the result of your final exam has now been available. Get yourself to this page, and you will see the link.

I am so sorry as I have not marked your assignments yet. I am pretty sure I will post your final mark next week.

Thank you.

from → Teachings

Final Mark of Calculus IIa – Class 19

2009 June 2
9 Comments
by ivanky

Hi all,

I have finally marked your final exam. You can find your score in my calculus teaching page as usual. Along with your final exam result, there is also the index of how you’re doing in Calculus during this semester.

I am very surprised to see the overall indeks. No one gets an E, which means you are doing good this semester. Also, there are 15 of your friends who get As.

Congratulations to all of you. It has been a pleasure to have known you. I hope you will do better next semester. Remember that final score is not the end of everything, it is just the beginning. I also hope that all of knowledge you have got will be useful later on.

Final words, I am very sorry if I made some terrible mistakes during my lectures.

Very best regards to you all, mate.

ivanky

from → Teachings

A geometric proof of trigonometric derivatives

2009 May 19
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by ivanky

As we already know, the first derivatives of \sin(x) and \cos(x) are \cos(x) and -\sin(x) respectively. The question is how do we prove it?

Since high school, the only proof that I knew is to use two of the trigonometric identities which are:

  • \sin \alpha - \sin \beta = 2 \sin (\frac{\alpha-\beta}{2}) \cos (\frac{\alpha+\beta}{2}), and
  • \cos \alpha - \cos \beta = -2 \sin (\frac{\alpha-\beta}{2}) \cos (\frac{\alpha+\beta}{2}).

Hence,

\frac{d}{dx}\sin x = \displaystyle{\lim_{\Delta x \rightarrow 0} \frac{\sin(x+\Delta x)-\sin(x)}{\Delta x} = \lim_{\Delta x \rightarrow 0} 2 \sin(\frac{\Delta x}{2})\cos(\frac{2x+\Delta x}{2})=\cos x}.

The derivative of \cos x can also be derived using the second identity.

However, there is another proof, which is (I think) more elegant. It is using a geometric interpretation of \sin x and \cos x. Let us draw a unit circle in \mathbb{R}^2.

geo_proof1

Thus we have y=\sin \theta and x=\cos \theta. We are looking for \frac{dy}{d \theta} and\frac{dx}{d \theta}, however we are not going to discuss the first derivative of \cos \theta as it can be done in the same way as \sin \theta.

\displaystyle{\frac{d \sin \theta}{d \theta}=\lim_{\Delta \theta \rightarrow 0} \frac{\sin(\theta + \Delta \theta)-\sin(\theta)}{\Delta \theta}=\lim_{\Delta \theta \rightarrow 0} \frac{y+\Delta y - y}{\Delta \theta}=\lim_{\Delta \theta \rightarrow 0} \frac{\Delta y}{\Delta \theta}}.

We are now going to estimate \Delta y, see the second figure.  geo_proof2The following relationship applies:

\sin \phi = \frac{\Delta y}{r} . or \Delta y = r \sin \phi.

Thus,

\displaystyle{\frac{d \sin \theta}{d \theta}=\lim_{\Delta \theta \rightarrow 0} \frac{\Delta y}{\Delta \theta}=\lim_{\Delta \theta \rightarrow 0} \sin \phi \frac{r}{\Delta \theta}},

where r is the chord PQ and \Delta \theta is the arc PQ. As \Delta \theta goes to zero, the ratio of the arc PQ and the chord PQ tends to 1 and the chord PQ tends to become a tangent line of the unit circle at (x,y), therefore \sin \phi = \sin (\theta + \pi/2). Assuming that the limit of multiplication is the same as the multiplication of limit, we have the following:

\frac{d \sin \theta}{d \theta}=\sin(\theta + \pi/2) = \cos(\theta).

As mentioned before, the first derivative of \cos \theta can be done the same way.

Also, I should thank Pak Yudi Soeharyadi as I got the idea of this geometric proof from him.

from → Justincase

Fundamental Theorem of Calculus is fundamental !

2009 May 11
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by ivanky

Most of my students do not seem to understand the two concepts of integrals. I have been there as well, so I did not blame them for not understanding the concept of integrals.  Even I sometimes forget. From that reason I try to post what the fundamental theorem of calculus means exactly.

It is all started with the definition first definition of integrals, which is formulated by the famous mathematician Bernhard Riemann. This is called the definite integral, or \int_a^b f(x) dx .

We can think that \int_a^b f(x) dx as the area below the curve f(x), see the picture below.

kalkulusThus,\int_a^b f(x) dx is the area S. As a first approximation, we shall divide the interval (a,b) into an equal number of segments, say \Delta x. Then we can approximate the area of S as follows:

\int_a^b f(x) dx \approx \sum_{i=0}^n f(x_i) \Delta x.

The right hand side of the equation above is called the Riemann sum. Our final step to find the value of definite integral is to take limit the Riemann sum as \Delta x \rightarrow 0,

\int_a^b f(x) dx = \lim_{\Delta x \rightarrow 0} \sum_{i=0}^n f(x_i) \Delta x.

Now, the second concept about integrals will be explained. This concept is called the indefinite integral or is also usually called the anti-derivative. Suppose F,f are functions of x such that F'(x)=f(x) (or we can say that the derivative of F(x) is f(x) or, the anti-derivative of f(x) is F(x)), then

\int f(x) dx = F(x) + C,

where C is a constant real number.

Hence, these two are two different concepts that are not related one to another. However, there is a great theorem that relates those two. The theorem perfectly and comfortably links the limit of Riemann sum and the anti-derivative. Actually there are two great theorems.

First Fundamental Theorem of Calculus Suppose f is a continuous function defined on closed interval [a,b] and define F as

F(x) = \int_a^x f(t) dt,

then F is continuous and differentiable, moreover, F'(x) = f(x).

Second Fundamental Theorem of Calculus Supposef is a function defined on closed interval [a,b] and F is the anti-derivative of f. If f is integrable on [a,b], then

\int_a^b f(x) dx = F(b) - F(a).

Therefore, if we want to compute, for examples, \int_0^1 x^2 dx, we don’t have to find the limit of Riemann sum of \sum_{i=0}^n x_i^2 \Delta x as \Delta x goes to zero.

from → Justincase, Teachings

Result of mid semester exam 2 of Calculus II (UTS 2)

2009 May 7
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by ivanky

As I promised yesterday, you can now see the result of mid semester exam 2 of calculus II.

Please go to this page.

Next wednesday is gonna be our last tutorial. I hope you can do well in the final examination.

from → Teachings

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