Calculus
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31:22
The Trillion Dollar Equation
/ 20 viewsThe most famous equation in finance, the Black-Scholes/Merton equation, came from physics. It launched an industry worth trillions of dollars and led to the worlds best investments. Go to https://www.eightsleep.com/veritasium and use the code Veritasium f
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All About Topology
/ 101 viewsPlastic version: http://shpws.me/HEtjThis is joint work with Keenan Crane.I never said it was a good joke.
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14:48
The Fourier Series and Fourier Transform Demystified
/ 119 viewsWatch over 2,400 documentaries for free for 30 days AND get a free Nebula account by signing up at https://curiositystream.com/upandatom and using the code "upandatom". Once you sign up you'll get an email about Nebula. If you don't get one, contact the c
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00:38
Let's Play With Matches #shorts
/ 137 viewsWith just 8 matches (or pens or q-tips or anything straight), you can tie up your mind for hours, days, or WEEKS. The idea is to develop a basic understanding of graph theory, which focuses on the relationships between things -- and you can express those
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20:57
But what is the Fourier Transform? A visual introduction.
/ 125 viewsAn animated introduction to the Fourier Transform. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/fourier-thanks
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26:33
The Algorithm That Transformed The World
/ 129 viewsThe Fast Fourier Transform is used everywhere but it has a fascinating origin story that could have ended the nuclear arms race. This video is sponsored by 80,000 Hours. Head to http://80000hours.org/veritasium to sign up for their newsletter and get sent
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00:59
Are There Infinite Infinities? #shorts
/ 188 viewsBitdefender Total Security (Extended Free Trial) - https://www.bitdefender.com/media/html/consumer/new/WI-S-Bitdefender/?cid=inf&7Cc%7Cig7CVS2Q4Thanks to Bitdefender for supporting Vsauce2.We know what infinity is... it's something that never ends. It's r
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23:29
How Imaginary Numbers Were Invented
/ 266 viewsA general solution to the cubic equation was long considered impossible, until we gave up the requirement that math reflect reality. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a y
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24:26
The Beauty of Bzier Curves
/ 175 viewsBézier curves - how do they do? They're used for animation, text rendering, and all sorts of curved shapes! But how do they actually work? well, like, that's what the video is about, so, watch it to find out etc!! • Lots of love to Jazz "queen
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34:00
There's a Hole at the Bottom of Math
/ 388 viewsNot everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium ge
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1:04:56
Optimization Problems - Calculus
/ 414 viewsThis calculus video explains how to solve optimization problems. It explains how to solve the fence along the river problem, how to calculate the minimum distance between a point and a line, and how to maximize area while minimizing perimeter as in the ca
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48:59 Popular
Area Between Two Curves
/ 962 viewsThis calculus video tutorial provides a basic introduction in finding the area between two curves with respect to y and with respect to x. It explains how to set up the definite integral to calculate the area of the shaded region bounded by the two curves
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21:35 Popular
How To Integrate Using U-Substitution
/ 978 viewsThis calculus video tutorial provides a basic introduction into u-substitution. It explains how to integrate using u-substitution. You need to determine which part of the function to set equal to the u variable and you to find the derivative of u to get d
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16:24
The most important unsolved problem in all of math. The Riemann Hypothesis.
/ 290 viewsThe Riemann hypothesis is the most notorious unsolved problem in all of mathematics. Ever since it was first proposed by Bernhard Riemann in 1859, the conjecture has maintained the status of the "Holy Grail" of mathematics. In fact, the person who solves
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14:44
Newton's quarantine notes that changed math forever
/ 316 viewsDocuments shown:October 1666 Tract on Fluxions (Original) [Starts page 93/190. Demonstration on page 100]: https://cudl.lib.cam.ac.uk/view/MS-ADD-03958/93October 1666 Tract on Fluxions (Translated): http://www.newtonproject.ox.ac.uk/view/texts/normalized/
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13:50
Newton and Leibniz: Crash Course History of Science #17
/ 368 viewsThe standard story of the Scientific Revolution culminates with the long life of one man: Sir Isaac Newtona humble servant of the Royal Mint, two-time parliamentarian, and a scientific titan whose name, along with Einsteins, is synonymous with physics tod
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06:45
How to Read Math
/ 475 viewsBaffled by equations, well no more! Continue learning at this video's sponsor https://brilliant.org/dosLots of people find mathematical equations intimidating because they don't make sense. But they are not hard to understand if you follow a few steps, an
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07:43
Calculus, what is it good for?
/ 423 viewsCalculus is an incredibly useful tool for deriving new physics. Check out this video's sponsor https://brilliant.org/dosHere is a brief description of calculus, integration and differentiation and one example of where it is useful: deriving new physics. I
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15:16
So why do colliding blocks compute pi?
/ 492 viewsPart 1: https://youtu.be/HEfHFsfGXjs Part 3: https://youtu.be/brU5yLm9DZM Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/clacks-thanks Many of you shared solutions, attempts, and simulations with me this last week. I loved it
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09:31
Infinite Series - Numberphile
/ 457 viewsFields Medallist Charlie Fefferman talks about some classic infinite series. More links & stuff in full description below ↓↓↓ Charles Fefferman at Princeton: https://www.math.princeton.edu/people/charles-fefferman Numberphile is supported by the Mathemati
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09:02
How To Think About Imaginary Numbers
/ 499 viewsSign up to brilliant.org with this link to receive a 20% discount! https://brilliant.org/upandatom/ For more info on imaginary numbers read these articles! https://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/ http://acko.net
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08:25
What is a Fourier Series? (Explained by drawing circles) - Smarter Every Day 205
/ 698 viewsGet a free crate for a kid you love (Awesome Chrsitmas gifts) at: https://www.kiwico.com/smarter Click here if you're interested in subscribing: http://bit.ly/Subscribe2SED ⇊ Click below for more links! ⇊ Doga's a super smart dude who writes a Turkish blo
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07:15
Product Rule for derivatives: Visualized with 3D animations
/ 531 viewsVisual representation of the product rule for derivatives in Calculus.
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08:23
Polynomial derivatives: 3D visualization
/ 438 viewsHow to visualize the derivatives of polynomials.
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19:04
Calculus -- The foundation of modern science
/ 451 viewsEasy to understand explanation of integrals and derivatives using 3D animations.
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03:51
Drawing the 4th, 5th, 6th, and 7th dimension
/ 582 viewsHow to draw 4, 5, 6, and 7 dimensional objects.
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19:56
Laplace Transform Explained and Visualized Intuitively
/ 623 viewsLaplace Transform explained and visualized with 3D animations, giving an intuitive understanding of the equations. My Patreon page is at https://www.patreon.com/EugeneK
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24:49
Stability Analysis, State Space - 3D visualization
/ 412 viewsIntroduction to Stability and to State Space. Visualization of why real components of all eigenvalues must be negative for a system to be stable. My Patreon page is at https://www.patreon.com/EugeneK
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12:42
Eigenvalues and Eigenvectors, Imaginary and Real
/ 475 views3D visualization of eigenvectors and eigenvalues. Includes imaginary and real components. My Patreon page is at https://www.patreon.com/EugeneK
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22:56
Quantum Spin - Visualizing the physics and mathematics
/ 502 viewsQuantum spin states explained with 3D animations. My Patreon page is at https://www.patreon.com/EugeneK
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08:58
Schrodinger's Equation
/ 476 viewsSchrodinger's Equation for wave functions in Quantum Physics. My Patreon Page is at https://www.patreon.com/EugeneK
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16:02
Double integrals and Polar integrals: Explained with 3D visualizations
/ 454 viewsDouble integrals in rectangular and polar coordinates. Explained with easy to understand 3D animations. My Patreon page is at https://www.patreon.com/EugeneK
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05:24
Gradients and Partial Derivatives
/ 497 views3D visualization of partial derivatives and gradient vectors. My Patreon account is at https://www.patreon.com/EugeneK
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25:33
Divergence and Curl
/ 449 viewsVisualization of the Divergence and Curl of a vector field. My Patreon Page: https://www.patreon.com/EugeneK
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14:33
Imaginary Numbers, Functions of Complex Variables: 3D animations.
/ 531 viewsVisualization explaining imaginary numbers and functions of complex variables. Includes exponentials (Euler’s Formula) and the sine and cosine of complex numbers.
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15:45
Fourier Transform, Fourier Series, and frequency spectrum
/ 601 viewsFourier Series and Fourier Transform with easy to understand 3D animations.
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02:29 Popular
Division with Zero - Maths Tricks #4
/ 1,506 viewsIn this video Bawa first explains what is division and then goes on to talk about division by zero. You will understand exactly why anything divided by zero is not defined, zero divided by anything is zero and zero divided by itself is indeterminate. This
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04:01 Popular
Product rule - Calculus derivatives tutorial
/ 974 viewsLearn how to take the derivative of a function using the product rule. This complete calculus derivatives tutorial explains why and how to use the product rule. To see all my calculus videos check out my website http://MathMeeting.com My name is Chris and
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07:16
Derivative as a concept
/ 594 viewsIntroduction to the idea of a derivative as instantaneous rate of change or the slope of the tangent line.
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19:53 Popular
Calculus at a Fifth Grade Level
/ 1,193 viewsThe foreign concepts of calculus often make it hard to jump right into learning it. If you ever wanted to dive into the world of mathematics - or if you are just having difficulty in your calculus class - and are having a hard time grasping the ideas, you
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04:22 Popular
Calculus Limits - Factoring Example
/ 1,407 viewsLearning Calculus limits is a breeze with this tutorial and video example.. This example teaches you how to solve limits by factoring. Check out my Calculus limits playlist if you want some harder examples. I also offer live tutoring if you need any extra
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04:30 Popular
Calculus Limits - Easy Problem and Introduction
/ 1,232 viewsLearning Calculus limits is a breeze with this problem and introduction. This example is an easy problem. Check out my Calculus limits playlist if you want some harder examples. I also offer live tutoring if you need any extra help. Check out my website i
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05:47 Popular
Imaginary Numbers Are Real [Part 1: Introduction]
/ 1,531 viewsMore information and resources: http://www.welchlabs.com Imaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimen
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10:42
e - Famed Euler's Number.
/ 548 viewsFree trial at The Great Courses Plus: http://ow.ly/tKWt306Gg7a Dr James Grime discusses "e" - the famed Euler's Number. A bit extra from this video: https://youtu.be/uawO3-tjP1c More James Grime videos from Numberphile: http://bit.ly/grimevideos NUMBERPHI
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10:09
Integrals: Crash Course Physics #3
/ 618 viewsContinuing with last week's introduction of calculus, Shini leads us through the ways that integrals can help us figure out things like distance when we have several other key bits of information. Say, for instance, you wanted to know how far your window
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10:02 Popular
Derivatives: Crash Course Physics #2
/ 1,099 viewsCALCULUS! Today we take our first steps into the language of Physics; mathematics. Every branch of science has its own way to describe the things that it investigates. And, with Physics, that's math. In this episode, Shini talks us through derivatives and
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09:07
Newton Leibniz And Usain Bolt
/ 604 viewsWhy we study differential calculus More free lessons at: http://www.khanacademy.org/video?v=EKvHQc3QEow
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02:55
Example Comparing X Components Of Vectors
/ 591 viewsExample comparing x components of vectors
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07:15
Deriving Formula For Sum Of Finite Geometric Series
/ 642 viewsDeriving formula for sum of finite geometric series
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05:21 Popular
Finding Sum From Recursive Definition Of Sequence
/ 809 viewsFinding sum from recursive definition of sequence
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02:28 Popular
Linear And Exponential Growth — Basic Example | Math | New SAT | Khan Academy
/ 1,122 viewsWatch Sal work through a basic Linear and exponential growth problem. Watch the next lesson: https://www.khanacademy.org/test-prep/new-sat/new-sat-math/new-sat-problem-solving-data-analysis/v/sat-math-q6-harder?utm_source=YT&utm_medium=Desc&utm_campaign=N
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05:18 Popular
Linear And Exponential Growth — Harder Example | Math | New SAT | Khan Academy
/ 847 viewsWatch Sal work through a harder Linear and exponential growth problem. Watch the next lesson: https://www.khanacademy.org/test-prep/new-sat/new-sat-math/new-sat-problem-solving-data-analysis/v/sat-math-q8-easier?utm_source=YT&utm_medium=Desc&utm_campaign=
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05:43 Popular
Modeling Situations With Arithmetic And Geometric Sequences
/ 806 viewsModeling situations with arithmetic and geometric sequences
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05:38 Popular
Defining Geometric Sequence Explicitly And Recursively
/ 840 viewsDefining geometric sequence explicitly and recursively
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06:08 Popular
Converting Between Explicit And Recursive Function Definitions For Arithmetic Sequence
/ 965 viewsConverting between explicit and recursive function definitions for arithmetic sequence
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06:17 Popular
Explicitly Defining Function For Arithmetic Sequence
/ 708 viewsExplicitly defining function for arithmetic sequence
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09:07 Popular
Recursive Functions To Define Sequences
/ 704 viewsRecursive functions to define sequences
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11:39
Optimization - Maximum Profit
/ 560 viewsOptimization is explained completely in this calculus video. In this example we maximize profit using optimization. I also provided the links for my other optimization videos as well. Optimization - "minimum fence required" example https://www.youtube.com
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18:57
Optimization - Minimum Time To Cross River
/ 677 viewsOptimization is explained completely in this calculus video. In this example we maximize profit using optimization. I also provided the links for my other optimization videos as well. Optimization - "minimum fence required" example https://www.youtube.com
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04:51
Integration By Parts - With Natural Log
/ 652 viewsIntegration by parts example with a natural log. Check out all of my videos on my channel page http://youtube.com/MathMeeting. For Free homework help check out my website http://MathMeeting.com
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10:45
Optimization - Minimum Sum Of Two Numbers
/ 574 viewsOptimization is explained completely in this calculus video. I also provided the links for my other optimization videos as well. Optimization - "minimum fence required" example https://www.youtube.com/watch?v=kV3K4Ppz6fw Optimization - "Maximum volume of
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11:51 Popular
Optimization - Calculus
/ 720 viewsOptimization is explained completely in this calculus video. I also provided the links for my other optimization videos as well. Optimization - "minimum sum of two numbers" example https://www.youtube.com/watch?v=WJy3EEJPV3g Optimization - "Maximum volume
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04:05
(3/4) Analysis: Explaining Fourier Analysis With A Machine
/ 690 views► Learn more at: http://www.engineerguy.com/fourier ► Buy the book on Amazon: http://www.amazon.com/gp/product/0983966176/ ► Buy the posters on Zazzle: http://www.zazzle.com/engineerguy ► Main videos in the series: (1/4) Introduction: https://www.youtube.
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15:22
Optimization - Maximum Volume Of Box
/ 617 viewsOptimization is explained completely in this calculus video. I also provided the links for my other optimization videos as well. Optimization - "minimum fence required" example https://www.youtube.com/watch?v=kV3K4Ppz6fw Optimization - "Minimum sum of two
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02:44 Popular
Domain And Range For Piecewise Constant Function
/ 1,003 viewsDomain and Range for piecewise constant function
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07:25 Popular
Domain And Range For Piecewise Linear Function
/ 819 viewsDomain and range for piecewise linear function
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03:04
Identifying Relative And Global Maxima And Minima
/ 601 viewsExamples identifying relative maximum points, relative minimum points, global maximum points and global minimum points.
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05:56
Intervals When Function Is Increasing, Decreasing, Postive Or Negative
/ 665 viewsIntervals when function is increasing, decreasing, postive or negative
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03:55 Popular
Interpreting Function Graphs Word Problems
/ 915 viewsInterpreting function graphs word problems
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03:40 Popular
Average Rate Of Change For Function From Table
/ 847 viewsAverage rate of change for function from table
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04:33 Popular
Average Rate Of Change With Function Notation
/ 4,454 viewsAverage rate of change with function notation
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1:27:26 Popular
Calculus 1 Lecture 1.1: An Introduction to Limits
/ 845 viewsCalculus 1 Lecture 1.1: An Introduction to Limits. Great intro video on Calculus.
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04:24 Popular
Examples Evaluating Piecewise Functions
/ 752 viewsExamples evaluating piecewise functions
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07:14 Popular
Examples Of Finding The Domain Of A Function
/ 766 viewsExamples of finding the domain of a function
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02:34 Popular
Domain Of Function Modeling Candy Bars
/ 761 viewsDomain of function modeling candy bars
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09:48 Popular
Equation For Parabola From Focus And Directrix
/ 725 viewsEquation for parabola from focus and directrix
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06:25
Change In Continuous Function Approaches 0
/ 670 viewsChange in continuous function approaches 0
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04:48 Popular
Infinite Series As Limit Of Partial Sums
/ 838 viewsInfinite series as limit of partial sums
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08:08 Popular
Restricting Domain Of Function To Make Invertible
/ 753 viewsRestricting domain of function to make invertible
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12:59
Simple Differential Equation Example
/ 619 views2010 IIT JEE Paper 1 Problem 56 Differential Equation More free lessons at: http://www.khanacademy.org/video?v=fqnPabGV6A4
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14:18 Popular
Series Sum Example
/ 771 views2010 IIT JEE Paper 1 Problem 54 Series Sum More free lessons at: http://www.khanacademy.org/video?v=A6fbDssPeac
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12:58 Popular
Complex Determinant Example
/ 822 views2010 IIT JEE Paper 1 Problem 53 Complex Determinant More free lessons at: http://www.khanacademy.org/video?v=E7OkUomRq1Q
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09:58
Normal vector from plane equation
/ 665 viewsFiguring out a normal vector to a plane from its equation More free lessons at: http://www.khanacademy.org/video?v=gw-4wltP5tY
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10:04 Popular
Tangent Line Hyperbola Relationship (very optional)
/ 1,194 viewsHow a tangent line relates to a hyperbola. Might be useful for some competitive exams where there isn't time to derive (like we are doing in this video) More free lessons at: http://www.khanacademy.org/video?v=c_8QQbVQKU0
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11:30 Popular
IIT JEE Lagrange's Formula
/ 803 views2010 IIT JEE Paper 1 Problem 49 Lagrange's Formula More free lessons at: http://www.khanacademy.org/video?v=rndex9FCIdo
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14:25 Popular
Vector Triple Product Expansion (very optional)
/ 874 viewsA shortcut for having to evaluate the cross product of three vectors More free lessons at: http://www.khanacademy.org/video?v=b7JTVLc_aMk
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09:55 Popular
IIT JEE Trigonometric Maximum
/ 757 views2010 IIT JEE Paper 1 Problem 48 Trigonometric Maximum More free lessons at: http://www.khanacademy.org/video?v=tzR9jUCSniQ
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12:49 Popular
IIT JEE Trigonometric Constraints
/ 809 views2010 IIT JEE Paper 1 Problem 47 Trigonometric Constraints More free lessons at: http://www.khanacademy.org/video?v=EjtjdJZ2x8w
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12:17 Popular
IIT JEE Circle Hyperbola Common Tangent Part 5
/ 853 views2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent Part 5 More free lessons at: http://www.khanacademy.org/video?v=rPoqpQcgNv4
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10:36
IIT JEE Circle Hyperbola Common Tangent Part 4
/ 686 views2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent Part 4 More free lessons at: http://www.khanacademy.org/video?v=eGo8C2Jshzs
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08:55
IIT JEE Circle Hyperbola Common Tangent Part 3
/ 692 views2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent Part 3 More free lessons at: http://www.khanacademy.org/video?v=RomnHMWSLoE
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10:45 Popular
IIT JEE Circle Hyperbola Common Tangent Part 2
/ 712 views2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent Part 2 More free lessons at: http://www.khanacademy.org/video?v=0imeUgSxR10
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06:16 Popular
IIT JEE Circle Hyperbola Common Tangent Part 1
/ 750 views2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tan More free lessons at: http://www.khanacademy.org/video?v=MhLfun2Vask
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12:44 Popular
IIT JEE Circle Hyperbola Intersection
/ 781 views2010 IIT JEE Paper 1 Problem 46 Circle Hyperbola Intersection More free lessons at: http://www.khanacademy.org/video?v=6g3DPg2HqGw
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13:44 Popular
IIT JEE Integral with Binomial Expansion
/ 780 views2010 IIT JEE Paper 1 Problem 41 Integral with Binomial Expansion and Algebraic Long Division More free lessons at: http://www.khanacademy.org/video?v=1-5sTDLrcp4
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14:00 Popular
IIT JEE Differentiability and Boundedness
/ 723 views2010 IIT JEE Paper 1 Problem 40 Differentiability and Boundedness More free lessons at: http://www.khanacademy.org/video?v=FIt1RNiCO6U
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03:09 Popular
IIT JEE Complex Numbers (part 3)
/ 707 views2010 IIT JEE Paper 1 Problem 39 Complex Numbers (part 3) More free lessons at: http://www.khanacademy.org/video?v=FwA_UZkI-JM
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07:26 Popular
IIT JEE Complex Numbers (part 2)
/ 733 views2010 IIT JEE Paper 1 Problem 39 Complex Numbers (part 2) More free lessons at: http://www.khanacademy.org/video?v=pQwoBOpVoWw
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07:21 Popular
IIT JEE Complex Numbers (part 1)
/ 792 views2010 IIT JEE Paper 1 Problem 39 Complex Numbers (part 1) More free lessons at: http://www.khanacademy.org/video?v=_5ei_I02huY
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07:48 Popular
IIT JEE Diameter Slope
/ 747 views2010 IIT JEE Paper 1 problem 37 Diameter Slope More free lessons at: http://www.khanacademy.org/video?v=pdXcf5ZWHf0
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09:29 Popular
IIT JEE Function Maxima
/ 737 views2010 IIT JEE Paper 1 problem 36 Function Maxima More free lessons at: http://www.khanacademy.org/video?v=2E_DB5VuAoo
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13:11 Popular
IIT JEE Algebraic Manipulation
/ 724 views2010 Paper 1 problem 35 Algebraic Manipulation More free lessons at: http://www.khanacademy.org/video?v=zs5LM7dxyTo
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07:05 Popular
IIT JEE Integral Limit
/ 749 views2010 IIT JEE Paper 1 #34 Integral Limit More free lessons at: http://www.khanacademy.org/video?v=pnwrNnZGVEw
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06:43 Popular
IIT JEE Position Vectors
/ 784 views2010 IIT JEE Paper 1 problem 32 Position Vectors More free lessons at: http://www.khanacademy.org/video?v=GDXyGy5TjnI
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08:24 Popular
IIT JEE Complex Root Probability (part 2)
/ 766 views2010 Paper 1 problem 31 Math (part 2).avi More free lessons at: http://www.khanacademy.org/video?v=S3KMyYYGuPE
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13:43
IIT JEE Complex Root Probability (part 1)
/ 693 views2010 Paper 1 problem 31 Math (part 1) More free lessons at: http://www.khanacademy.org/video?v=bV_HSZ_W0nk
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10:26 Popular
IIT JEE Perpendicular Planes (Part 1)
/ 822 views2010 IIT JEE Paper 1 #30 normal vector and planes (Part 1) More free lessons at: http://www.khanacademy.org/video?v=2u535-HVJ_o
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09:32
2003 AIME II Problem 15 (part 3)
/ 639 viewsFinding the sum of the absolute value of the imaginary parts of the square of the roots of a crazy polynomial More free lessons at: http://www.khanacademy.org/video?v=JTpXK2mENH4
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05:20
Introduction to i and Imaginary Numbers
/ 651 viewsIntroduction to i and imaginary numbers More free lessons at: http://www.khanacademy.org/video?v=ysVcAYo7UPI
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15:43 Popular
Calculus: Derivatives 1 (new HD version)
/ 880 viewsCalculus-Derivative: Understanding that the derivative is just the slope of a curve at a point (or the slope of the tangent line) More free lessons at: http://www.khanacademy.org/video?v=ANyVpMS3HL4
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09:12
Koch Snowflake Fractal
/ 689 viewsA shape that has an infinite perimeter but finite area More free lessons at: http://www.khanacademy.org/video?v=azBNsPa1WC4
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06:01
Visualizing Taylor Series Approximations
/ 698 viewsUsing Wolfram Alpha to approximate sin(x) More free lessons at: http://www.khanacademy.org/video?v=8dMLK2Wueaw