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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Definition of the viscosity of a liquid.
Gaussian Math Fluid Mechanics module, situable for those studying it as an undergraduate module.
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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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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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Analyzing the forces on a water particle, we now derive the basic equation of the pressure field - a highly important equation when dealing with change in pressure.
Gaussian Math Fluid Mechanics module, situable for those studying it as an undergraduate module.
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Using our previous definitions, here is an example of how you write a Fourier Series from a graph of a function, a 'broken' function in this case.
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Welcome to GussianMath's module on Quantum Mechanics.
We start by briefly discussing the postulates of quantum mechanics - the minimum set of assumptions from which we'll build the theory upon.
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A short introduction to Green's Theorem which concerns turning a closed loop integral into a double integral given certain conditions.
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We'll study a flow of a fluid with a complex velocity function and see how Bernoulli's equation gives us the velocity and pressure relationship.
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.
Time travel is possible in mathematics! Hope you enjoy the 2-part video.
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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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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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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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A short lesson on basic Kinematics, how to derive the equations of motion under constant acceleration.
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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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We see how, through a simple procedure, we define the limits of a type I region R.
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Following our previous lesson, we now derive the location of a hydrostatic force on a plane surface. It turns out that the centre of pressure and centroid is NOT the same.
Gaussian Math Fluid Mechanics module, situable for those studying it as an undergraduate module.
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![Line Integral - proof of Green\](http://img.youtube.com/vi/8ozE7hyOMz4/2.jpg "Line Integral - proof of Green\")
![Fourier Analysis 2: Fourier Series of a \](http://img.youtube.com/vi/CK9NaHBe2CE/2.jpg "Fourier Analysis 2: Fourier Series of a \")
![Line Integral - Green\](http://img.youtube.com/vi/P5LCSatuIvo/2.jpg "Line Integral - Green\")
![Complex Numbers de Moivre\](http://img.youtube.com/vi/PFJ7J8tvrQo/2.jpg "Complex Numbers de Moivre\")
