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.
For a more in depth look at multiple integrals or other calculus related topices, please visit www.gaussianmath.com
A short video explaining the Gradient Vector Field, a difficult part in understing vector Calculus. Hope you enjoy it.
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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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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 lesson on basic Kinematics, how to derive the equations of motion under constant acceleration.
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Time travel is possible in mathematics! Hope you enjoy the 2-part video.
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Advanced Differential Calculus - The Total Differential
Previously for partial derivatives, ?x and ?y were considered separately. Now we look at the effect of changing x and y together. We discover a new term called the total differential which is
dz = a?x + b?y
Gassianmath.com - using numbers to solve the greatest mysteries.
A video on how to sketch a complicated function namely f(x)=1+(x^2/(x+2)(3- x))^(1/2). Hope you learn something from it.
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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.
Check out www.gaussianmath.com for more vector calculus. Thanks!
We now move on to another coordinate system, Polar Coordinates and see how the double integral is defined here.
For a more in depth look at multiple integrals or other calculus related topices, please visit www.gaussianmath.com
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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Using the basic equation, we find the pressure field of an compressible fluid assuming density constant, slightly more work need compared to the incompressible fluid.
Gaussian Math Fluid Mechanics module, situable for those studying it as an undergraduate module.
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Using the Double integral to find the volume of a cylinder with a flat bottom and slanted top.
For a more in depth look at multiple integrals or other calculus related topices, please visit www.gaussianmath.com
Using the Double integral to find the volume of a tetrahedron bounded by a plane and the coordinate planes.
For a more in depth look at multiple integrals or other calculus related topices, please visit www.gaussianmath.com
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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We visit an age-old problem of finding the volume of a sphere but this time curiously using polar double integrals.
For a more in depth look at multiple integrals or other calculus related topices, please visit www.gaussianmath.com
Bernoulli's equation used to explain a common phenomena in syphoning water.
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.
Hey guys, my best attempt in proving this theorem. I am not too good with mathematical reasoning but hope I did a decent job in the proof.
Any comments will be greatly appreciated.
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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.
Check out www.gaussianmath.com for an indepth study with downloadable notes or for more math related content.
![Line Integral - Green\](http://img.youtube.com/vi/P5LCSatuIvo/2.jpg "Line Integral - Green\")
![Line Integral - proof of Green\](http://img.youtube.com/vi/8ozE7hyOMz4/2.jpg "Line Integral - proof of Green\")
