Calculus. Since 2008, Academic Earth has worked diligently to compile an ever-growing collection of online college courses, made available free of charge, from some of the most respected universities.

We proudly build on the precedent set forth by MIT OpenCourseware, believing that everyone deserves access to a world-class education. To facilitate this goal, we have curated links to over 750 online courses and 8,500 individual online lectures, giving students of all ages unparalleled access to college courses they may otherwise never experience. Whether supplementing existing coursework, or learning for the sake of learning, anyone with an internet connection has the freedom to learn at their own pace from world-renowned experts, without the burden of rising tuition costs.

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You may also find this book at Google Books. Math Help - SolveMyMath. The momentum representation. Next: The uncertainty principle Up: Fundamentals of quantum mechanics Previous: Operators Contents Fourier's theorerm (see Sect. 3.9), applied to wave-functions, yields where represents wave-number.

However, How to Calculate a Square Root by Hand: 21 steps (with pictures) Edit Article CalculatorUsing Prime FactorizationFinding Square Roots Manually Edited by NatK, Maluniu, Luís Miguel Armendáriz, Webster and 44 others In the days before calculators, students and professors alike had to calculate square roots by hand. Several different methods have evolved for tackling this daunting process, some giving a rough approximation, others giving an exact value.

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Below are links to some of these problems and topics. Mathematics Applied to Physics and Engineering Applications and Use of the Inverse Functions. Examples on how to apply and use inverse functions in real life situations and solve problems in mathematics. Maximize Volume of a Box. Why Does e^(pi i) + 1 = 0? This page is just a collection of a couple of answers on the LiveJournal Mathematics Community in a thread about eπi + 1 = 0.

Soon, I will whip them into a more coherent form. In collegiate calculus, you probably learned about something called Taylor series. You can use Taylor series to make polynomial approximations of infinitely-differentiable functions. If you take the Taylor series out infinitely, you actually have the function. The general form for a Taylor series is this: Graduate Program in Mathematics, Study guides for Comp Exams, University of Illinois at Urbana-Champaign. Demystifying the Natural Logarithm (ln)

After understanding the exponential function, our next target is the natural logarithm.

Given how the natural log is described in math books, there’s little “natural” about it: it’s defined as the inverse of e^x, a strange enough exponent already. But there’s a fresh, intuitive explanation: The natural log gives you the time needed to reach a certain level of growth. Suppose you have an investment in gummy bears (who doesn’t?) Main Page - Exampleproblems. Untitled. Two by Two. Essentially the technique converts the first factor into binary, multiplies each of its constituents by the second factor, and sums the results.

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Geometry was extremely important to ancient societies and was used for surveying, astronomy, navigation, and building. Geometry, as we know it is actually known as Euclidean geometry which was written well over 2000 years ago in Ancient Greece by Euclid, Pythagoras, Thales, Plato and Aristotle just to mention a few. The most fascinating and accurate geometry text was written by Euclid, and was called Elements. Euclid's text has been used for over 2000 years! Calculus Derivatives Cheat Sheet. What are the best rules, formulas and tricks in math? - math formulas rules. GEM1518K - Mathematics in Art & Architecture - Project Submission. “For me it remains an open question whether [this work] pertains to the realm of mathematics or to that of art.” - M.C.

Escher Contents Page 1 Introduction The Art of Alhambra Our Area of Focus Our Aim Page 2 The Principals behind Tessellations - Translation - Rotation - Reflection - Glide Reflection. Learning Calculus: Overcoming Our Artificial Need for Precision. Accepting that numbers can do strange, new things is one of the toughest parts of math: There’s numbers between the numbers we count with?

(Yes — decimals)There’s a number for nothing at all? (Sure — zero)The number line is two dimensional? (You bet — imaginary numbers) Calculus is a beautiful subject, but challenges some long-held assumptions: Geometry Help. Looking for some Geometry Help? Our materials here review the basic terms and concepts in geometry and provide further lessons to help you develop your understanding of geometry and its applications to solving problems in real life. Geometry is about the shape and size of things. It is the study of points, lines, angles, shapes, their relationships, and their properties. Videos have been included in almost all the following topics to help reinforce your understanding.

Angles Triangles Polygons Circles. No, really, pi is wrong: The Tau Manifesto by Michael Hartl. Elementary Calculus: Example 3: Inscribing a Cylinder Into a Sphere. Find the shape of the cylinder of maximum volume which can be inscribed in a given sphere. The shape of a right circular cylinder can be described by the ratio of the radius of its base to its height. This ratio for the inscribed cylinder of maximum volume should be a number which does not depend on the radius of thesphere. For example, we should get the same shape whether the radius of the sphere is given in inches or centimeters. Let r be the radius of the given sphere, x the radius of the base of the cylinder, h its height, and V its volume.

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