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Multiple Integrals 1: Definition of the Double Integral
Posted by: donylee

Video duration: 654 seconds

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

Related: calculus, double, integral, integration, limit, math, multivariable

	Vector Integral Calculus - Gradient Vector Field p1 Posted by: donylee Video duration: 392 seconds 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! Related: calculus, donny, gaussian, math, vector

$Line Integral - Green\$	Line Integral - Green's Theorem Posted by: donylee Video duration: 647 seconds A short introduction to Green's Theorem which concerns turning a closed loop integral into a double integral given certain conditions. Check out www.gaussianmath.com for an indepth study and more calculus related lessons. Related: calculus, donny, gaussian, math, vector

QM0.1: Postulates of Quantum Mechanics
Posted by: donylee

Video duration: 631 seconds

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.
For an in-depth study, check out www.gaussianmath.com

Related: density, mechanics, physics, postulates, probability, quantum, schrodinger, spin, state

	Kinematics - deriving equations of constant acceleration Posted by: donylee Video duration: 538 seconds A short lesson on basic Kinematics, how to derive the equations of motion under constant acceleration. Check out www.gaussianmath.com for more mechanics and calculus related topics. Related: donny, gaussian, kinematics, math

	Mathematical Wormhole pt1 Posted by: donylee Video duration: 547 seconds Time travel is possible in mathematics! Hope you enjoy the 2-part video. Check out www.gaussianmath.com for a more indepth explanation and other interesting topics in mathematics. Related: donny, gaussian, math, time, travel

Adv Diff Calc 4: The Total Differential
Posted by: donylee

Video duration: 491 seconds

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.

Related: advanced, calculus, derivatives, differential, differentiation, dz, limit, multivariable, partial, total, z

	Arithmetic Progression Posted by: donylee Video duration: 638 seconds A short video on arithmetic progression. Check out my webpage www.gaussianmath.com for more interesting math topics. Related: ap, gaussian, gp, math, physics, sequences, series

	Functions - How to sketch a complicated function Posted by: donylee Video duration: 442 seconds 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. Check out www.gaussianmath.com for a better experience and more problems on the AMC. Related: donny, functions, gaussian, math, olympiad

$Line Integral - proof of Green\$	Line Integral - proof of Green's Theorem pt1 Posted by: donylee Video duration: 601 seconds A proof of a special case of Green's Theorem where the graph can be described in two ways. Check out www.gaussianmath.com for an indepth study and more calculus related lessons. Related: calculus, donny, gaussian, math, vector

	Vector Integral Calculus - Gradient Vector Field p2 Posted by: donylee Video duration: 286 seconds 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! Related: calculus, donny, gaussian, math, vector

Multiple Integrals 12: Double Integrals in Polar Coordinates
Posted by: donylee

Video duration: 582 seconds

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

Related: calculus, double, integral, integration, math, multivariable, polar

Hyperbolic Functions - Definitions and graph of cosh x
Posted by: donylee

Video duration: 618 seconds

A short introduction to hyperbolic functions. Don't get mislead by their 'unpopularity' compared to trigonometric functions. Hyperbolic functions do have their uses.
Check out www.gaussianmath.com for an indepth study and for more calculus related topics.

Related: catenary, donny, gaussian, hyperbolic, math

Fluid Mechanics - Pressure Field Compressible Fluid
Posted by: donylee

Video duration: 454 seconds

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.
Check out www.gaussianmath.com for an indepth study with downloadable notes or for more math related content.

Related: fluid, gaussian, math, mechanics, physics, pressure

	Multiple Integrals 9: Finding Volume Problems (Cylinder) Posted by: donylee Video duration: 342 seconds 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 Related: calculus, double, integral, integration, limit, math, multivariable

Multiple Integrals 9: Finding Volume Problems (Tetrahedron)
Posted by: donylee

Video duration: 360 seconds

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

Related: calculus, double, integral, integration, limit, math, multivariable

Difficult Functions Question from 1996 AHSME #25
Posted by: donylee

Video duration: 640 seconds

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
Check out www.gaussianmath.com for more amc problems and calculus related content.

Related: donny, functions, gaussian, math, olympiad

Fluid Mechanics - Syphoning Water
Posted by: donylee

Video duration: 508 seconds

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.

Related: bernoulli, fluid, gaussian, math, mechanics, physics

Multiple Integrals 15: Volume of Sphere in Polar Coordinate
Posted by: donylee

Video duration: 547 seconds

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

Related: calculus, double, integral, math, multivariable, polar, sphere

The Fundamental Theorem of Arithmetic
Posted by: donylee

Video duration: 644 seconds

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.
Check out www.gaussianmath.com for an indepth look at the proof or for calculus related content.

Related: arithmetic, donny, fundamental, gaussian, math