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An Interactive Guide To The Fourier Transform

An Interactive Guide To The Fourier Transform
The Fourier Transform is one of deepest insights ever made. Unfortunately, the meaning is buried within dense equations: Yikes. What does the Fourier Transform do? Here's the "math English" version of the above: The Fourier Transform takes a time-based pattern, measures every possible cycle, and returns the overall "cycle recipe" (the strength, offset, & rotation speed for every cycle that was found). Time for the equations? If all goes well, we'll have an aha! This isn't a force-march through the equations, it's the casual stroll I wish I had. From Smoothie to Recipe A math transformation is a change of perspective. The Fourier Transform changes our perspective from consumer to producer, turning What did I see? In other words: given a smoothie, let's find the recipe. Why? So... given a smoothie, how do we find the recipe? Well, imagine you had a few filters lying around: We can reverse-engineer the recipe by filtering each ingredient. Filters must be independent. See The World As Cycles Oh!

How to Disappear Online Immersive Linear Algebra immersivemath immersive linear algebra by J. Ström, K. The world's first linear algebra book with fully interactive figures. Learn More Check us out on Twitter and Facebook Table of Contents Preface A few words about this book. Chapter 1: Introduction How to navigate, notation, and a recap of some math that we think you already know. Chapter 2: Vectors The concept of a vector is introduced, and we learn how to add and subtract vectors, and more. Chapter 3: The Dot Product A powerful tool that takes two vectors and produces a scalar. Chapter 4: The Vector Product In three-dimensional spaces you can produce a vector from two other vectors using this tool. Chapter 5: Gaussian Elimination A way to solve systems of linear equations. Chapter 6: The Matrix Enter the matrix. Chapter 7: Determinants A fundamental property of square matrices. Chapter 8: Rank Discover the behaviour of matrices. Chapter 9: Linear Mappings Learn to harness the power of linearity... Chapter 10: Eigenvalues and Eigenvectors

Optical illusion cut-out and fold characters Math ∩ Programming Lateral Thinking Puzzles - Preconceptions Lateral thinking puzzles that challenge your preconceptions. 1. You are driving down the road in your car on a wild, stormy night, when you pass by a bus stop and you see three people waiting for the bus: 1. An old lady who looks as if she is about to die. 2. An old friend who once saved your life. 3. Knowing that there can only be one passenger in your car, whom would you choose? Hint: You can make everyone happy. Solution: The old lady of course! 2. Hint: The police only know two things, that the criminal's name is John and that he is in a particular house. Solution: The fireman is the only man in the room. 3. Hint: He is very proud, so refuses to ever ask for help. Solution: The man is a dwarf. 4. Hint: It does not matter what the baby lands on, and it has nothing to do with luck. Solution: The baby fell out of a ground floor window. 5. Hint: His mother was an odd woman. Solution: When Bad Boy Bubby opened the cellar door he saw the living room and, through its windows, the garden. 6. 7.

Differential Equations Explained $\cos$PLAY You're probably used to equations like $$(t-.5)(t-1)= 0,$$ where 'solving' means finding an unknown number. A differential equation (DE), by contrast, is a fact about the derivative of an unknown function, and 'solving' one means finding a function that fits. To visualize derivatives, we can draw a right triangle whose hypoteneuse is tangent to a function. If the triangle's width is $1$, then its height is the derivative. With that one weird trick, the plots to the right show how the derivative of $\sin(t)$ is $\cos(t)$. That's a pretty basic DE, though. Consider a cart rolling to a stop. The solution is a function $v(t)$ giving velocity at time $t$. It turns out the exponential function, $e^{-kt}$, has the properties $$ \begin{align} \frac{d}{dt}e^{-kt}=-ke^{-kt} && e^{-k\cdot 0}=1. To make the solution more intuitive, here you'll solve the cart's DE manually by picking a series of $\left( t, v \right)$ points. The first cart below obeys the $v(t)$ function you designed.

techinterview Bayesian Methods for Hackers An intro to Bayesian methods and probabilistic programming from a computation/understanding-first, mathematics-second point of view. Prologue The Bayesian method is the natural approach to inference, yet it is hidden from readers behind chapters of slow, mathematical analysis. The typical text on Bayesian inference involves two to three chapters on probability theory, then enters what Bayesian inference is. Unfortunately, due to mathematical intractability of most Bayesian models, the reader is only shown simple, artificial examples. After some recent success of Bayesian methods in machine-learning competitions, I decided to investigate the subject again. If Bayesian inference is the destination, then mathematical analysis is a particular path towards it. Bayesian Methods for Hackers is designed as a introduction to Bayesian inference from a computational/understanding-first, and mathematics-second, point of view. The choice of PyMC as the probabilistic programming language is two-fold.

Brainteaser Quizzes Read you CAN!Weakest Link Brainteaser TestBrainteaser Quiz 1 Brainteaser Quiz 2 Brainteaser Quiz 3 Brainteaser Quiz 4 Back to Brainteasers & Riddles Index The phaonmneel pweor of the hmuan mnid: I cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdgnieg. The rset can be a taotl mses and you can sitll raed it wouthit a porbelm. Weakest Link Brainteaser Test Brainteaser Quiz #2! Great Brainteaser Quiz #3! How did you do? Brainteaser Quiz #4 Quiz for people who know everything: Back to Quizzes Back to Riddles & Brainteasers