We begin our study on the work of Joseph Fourier (1768-1830) with the definition of the Fourier Series - a way of expressing functions as infinite sums or integrals or trigonometry functions.
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Our first official lesson on multivariable calculus. We start by examining the double integral, how we use the limiting process and apply it to two variables.
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A proof of a special case of Green's Theorem where the graph can be described in two ways.
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A short video explaining the Gradient Vector Field, a difficult part in understing vector Calculus. Hope you enjoy it.
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Suppose that x^2+y^2=14x+6y+6. What is the maximum value of 3x+4y?
It took me a while to solve it.
A written solution can be read from http://www.gaussianm ath.com/functions/19 96AHSME25/1996AHSME2 5.html
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Time travel is possible in mathematics! Hope you enjoy the 2-part video.
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Before we head to evaluating double integrals, we need to be familiar with a somewhat new technique of integrating, how we integrate a function in two variable with respect to one variable only.
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A long 3-part video on the 'Fundamental Theorem of Space Curves', a theorem in Vector Differential Caculus.
I suggest you view this only if you are taking a course in vector calculus. If not, it could just be a waste of your time.
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Let's look at the graphs of various Fourier Series. To illustrate the series, we will be taking the Nth partial sum. It is also here where we notice some interesting behaviour of some Fourier Series.
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A short introduction to hyperbolic functions. Don't get mislead by their 'unpopularity' compared to trigonometric functions. Hyperbolic functions do have their uses.
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Following up with my previous video on the directional derivative, here is a short example. Situable for those taking vector calculus or enginnering math in general.
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A short lesson on basic Kinematics, how to derive the equations of motion under constant acceleration.
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We derive the magnitude and direction of a hydrostatic force on a plane surface.
Gaussian Math Fluid Mechanics module, situable for those studying it as an undergraduate module.
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A mathematical rigorious approach to derive Archimedes' principle. We find the magnitude of the Buoyancy force here.
Gaussian Math Fluid Mechanics module, situable for those studying it as an undergraduate module.
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In this 3-part video we follow Leibniz in his pursuit to find the area of a quater circle of unit radius via integration, trigonometry and series expansion. Simply amazing!
Hope you like it. Check out www.gaussianmath.com for a more indepth explanation.
Using partial integration, we can now go in the proper methods of evaluating double integrals.
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We start our tour into Bernoulli's Equation by resolving forces.
Gaussian Math Fluid Mechanics module, situable for those studying it as an undergraduate module.
Check out www.gaussianmath.com for an indepth study with downloadable notes or for more math related content.
Here is a basic example of implementing the line integral. You must substitute the parametric equations into both the vector field and position vector and then integrate.
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![Line Integral - proof of Green\](http://img.youtube.com/vi/8ozE7hyOMz4/2.jpg "Line Integral - proof of Green\")
![Complex Numbers de Moivre\](http://img.youtube.com/vi/PFJ7J8tvrQo/2.jpg "Complex Numbers de Moivre\")
![Fluid Mechanics - Archimedes\](http://img.youtube.com/vi/ZdfLnxTQnqQ/2.jpg "Fluid Mechanics - Archimedes\")
![Bernoulli\](http://img.youtube.com/vi/qSb0D61qfQE/2.jpg "Bernoulli\")
