CTS Advanced Calculus batch 101

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PCH

Summary

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(sqrt(cos(x))*cos(200x)+sqrt(abs(x))-0.7)*(4-x*x)^0.01, sqrt(9-x^2), -sqrt(9-x^2) from -4.5 to 4.5

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[Final Exam] Tutorial 6-Tutorial 9. You need also Tutorial 2 -Tutorial 5.
2 1/2 Hour, 6 questions.

Pythagorean trigonometric identity

[Development of Series]... The Kerala school made use of the rectification (computation of length) of the arc of a circle to give a proof of these results...

Kerala school of astronomy and mathematics - Wikipedia, the free encyclopedia The Kerala school of astronomy and mathematics was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. The ...

Another example in presentation form

http://www2.latech.edu/~schroder/slides/DE_slides/method_of_Frobenius.pdf

More example for Frobenius method

[Frobenius_method] Solving second-order ordinary differential equation using Power series.

Frobenius method - Wikipedia, the free encyclopedia In mathematics, the Frobenius method, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a second-order ordinary differential equation of the form

[Power Series]
A function f defined on some open subset U of R or C is called analytic if it is locally given by a convergent power series.

Power series - Wikipedia, the free encyclopedia where an represents the coefficient of the nth term, c is a constant, and x varies around c (for this reason one sometimes speaks of the series as being centered at c). This series usually arises as the Taylor series of some known function; the Taylor series article contains many examples.

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http://staff.iium.edu.my/pahchinhee/sms%202307-101-result.pdf