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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 |
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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 |
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QM0.3: Time-Independent Schrödinger Equation Posted by: donylee
Video duration: 643 seconds Assuming that potentials don't change with time, we deal with the time-independent Schrödinger Equation, which is more manageable. This lesson involves writing its most general solutions. For an in-depth study, check out www.gaussianmath.com Related: density, mechanics, physics, postulates, probability, quantum, schrodinger, spin, state |
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Multiple Integrals 5: Limits of Region R (Type I) Posted by: donylee
Video duration: 594 seconds We see how, through a simple procedure, we define the limits of a type I region R. 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 |
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Multiple Integrals 7: Reversing the order of integration Posted by: donylee
Video duration: 534 seconds Up to now, we should have realized that we can either integrate dx dy or integrate dy dx. This lesson looks at reversing the order. 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 |
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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 |
![QM0.4: \"Square\" Potentials](http://img.youtube.com/vi/R08_h1IZJTM/2.jpg "QM0.4: \\"Square\\" Potentials") |
QM0.4: "Square" Potentials Posted by: donylee
Video duration: 660 seconds In order to display quantum effects, we are going to consider potentials which varied considerably over small distances. Quantitatively, this is represented by a 'Square' potential. For an in-depth study, check out www.gaussianmath.com Related: density, mechanics, physics, postulates, probability, quantum, schrodinger, spin, state |
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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 |
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QM0.7: Solutions to the 2nd-order Differential Equation Posted by: donylee
Video duration: 584 seconds Knowing that we need to solve a 2nd-order differential equation in the time-independent Schrödinger Equation, we shall write the solutions here, based on which form the equation takes. For an in-depth study, check out www.gaussianmath.com Related: density, mechanics, physics, postulates, probability, quantum, schrodinger, spin, state |
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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 |
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QM0.2: Time Evolution of a system Posted by: donylee
Video duration: 239 seconds The 5th postulate of quantum mechanics. It says that the dynamics of a system is regulated by the Time-dependent Schrödinger equation. Not easy to solve. For an in-depth study, check out www.gaussianmath.com Related: density, mechanics, physics, postulates, probability, quantum, schrodinger, spin, state |
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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 |
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Multiple Integrals 4: Nonrectangular regions Posted by: donylee
Video duration: 575 seconds We learn how to calculate the double integral over nonrectangular regions. 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 |
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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 |
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Multiple Integrals 13: Evaluation of Polar Double Integrals Posted by: donylee
Video duration: 554 seconds Still sticking in the polar coordinates systems, this lessons focuses on evaluating the double integral. 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 |
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Multiple Integrals 6: Limits of Region R (Type II) Posted by: donylee
Video duration: 587 seconds We see how, through a simple procedure, we define the limits of a type II region R. 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 |
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Adv Diff Calc 6: Theorem of the Total Differential Posted by: donylee
Video duration: 537 seconds Advanced Differential Calculus - Theorem of the Total Differential In fact, there is a quick way in calculating the total differential of a function IF it exist. Here, we see how we get to the result: a = ?z / ?x, b = ?z / ?y Gassianmath.com - using numbers to solve the greatest mysteries. Related: advanced, calculus, derivatives, differential, differentiation, dz, limit, multivariable, partial, total, z, z |
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QM0.5: Bound States - Properties of one-dimensional motion Posted by: donylee
Video duration: 527 seconds To study the dynamic properties of a single particle, we consider a potential V(x) general enough to allow for the illustration of all the required features. First, we deal with bound states which occur whenever the particle cannot move to infinity such as the infinite square well potential and the harmonic oscillator. Related: density, mechanics, physics, postulates, probability, quantum, schrodinger, spin, state |
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QM0.8: General Approach in solving problems Posted by: donylee
Video duration: 516 seconds Before setting out to solve physical problems, we discuss a general method, relating solutions with bound and unbound states, that we will undertake when dealing with these problems. For an in-depth study, check out www.gaussianmath.com Related: density, mechanics, physics, postulates, probability, quantum, schrodinger, spin, state |
![Bernoulli\](http://img.youtube.com/vi/rXl0oYtCDZg/2.jpg "Bernoulli\") |
Bernoulli's Equation (after integration) Posted by: donylee
Video duration: 647 seconds Getting Bernoulli's Equation by CAREFULLY considering each term. 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 |