Fourier Transform 11 | Sum Formulas for Sine and Cosine [dark version]
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🌙 There is also a dark mode version of this video: • Fourier Transform 11 | Sum Formulas f...
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This is my video series about Fourier Transform where we talk a lot about Fourier Series. So important topics are trigonometric polynomials, integrable functions, inner products for functions, orthogonal projections, and a lot of formulas for Cosine and Sine functions.I hope that it will help everyone who wants to learn about these things.
00:00 Introduction
01:00 Statement for Cosine Formula
01:51 Note about finite sum of Cosine functions
07:10 Lemma about Sine Formula
08:40 Proof of Lemma
17:13 Visualization of Lemma
18:00 Theorem (Cosine Formula)
18:30 Proof of Theorem
22:22 Applying Weierstrass M-Test
23:57 Find integration constant
25:23 Credits
#FourierTransform
#Mathematics
#FourierSeries
#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)
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