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. Free e-books and e-lectures on Algorithms, Math, and Cryptography. Electrical Engineering and Computer Science. Math21b, Fall 2003, Linear Algebra and Differential Equations. Calculus - Exampleproblems. Math Help - SolveMyMath. The momentum representation. 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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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: ∑ f(n)(x0) * (x - x0)n / n! Where the sum goes from n=0 to n=infinity and f(n)(x0) means the n-th derivative of f(x) evaluated at x0. Also, note that f(0)(x) is just f(x). 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?) With an interest rate of 100% per year, growing continuously. 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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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) 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. 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. First, we draw a sketch of the problem in Figure 3.6.4. Algebra Help Math Sheet. Arithmetic OperationsReturn to Top The basic arithmetic operations are addition, subtraction, multiplication, and division. Pascal's Triangle. Patterns Within the Triangle Using Pascal's Triangle Heads and Tails. Calculus and Differential Equations. A Gentle Introduction To Learning Calculus.

I have a love/hate relationship with calculus: it demonstrates the beauty of math and the agony of math education. Calculus relates topics in an elegant, brain-bending manner. My closest analogy is Darwin’s Theory of Evolution: once understood, you start seeing Nature in terms of survival. Reflections on Relativity. Mathematics Department - Mathematics Web Sites. Maths Online Courses. Ask Dr. Math - College Level Archive. English names of the first 10000 powers of 10 - American System without dashes. Mathematics Department : Mathematics Courses. The Math Guy. Visualizing Basic Algebra. Last weekend, I shared some interesting properties of numbers with my kids. The great thing about explaining something to a non-expert is that you have to actually understand the topic. (This is why making teaching universities and research universities the same actually makes sense.)

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