With traditional integrals, our "path" was straight and linear (most of the time, we traversed the x-axis). Now we can explore taking integrals over any line or curve (called line integrals).
You've done some work with line integral with scalar functions and you know something about parameterizing position-vector valued functions. In that case, welcome! You are now ready to explore a core tool math and physics: the line integral for vector fields. Need to know the work done as a mass is moved through a gravitational field. No sweat with line integrals.
This 17-minute video lesson looks at the iIntuition behind the Mean Value Theorem. [Calculus playlist: Lesson 55 of 156]
Let's jump out of that boring (okay, it wasn't THAT boring) 2-D world into the exciting 3-D world that we all live and breath in. Instead of functions of x that can be visualized as lines, we can have functions of x and y that can be visualized as surfaces. But does the idea of a derivative still make sense? Of course it does! As long as you specify what direction you're going in. Welcome to the world of partial derivatives!
This 8-minute video lecture demonstrates how to use a position vector valued function to describe a curve or path. [Calculus playlist: Lesson 133 of 156]
In this tutorial, we will learn to approximate differentiable functions with polynomials. Beyond just being super cool, this can be useful for approximating functions so that they are easier to calculate, differentiate or integrate. So whether you will have to write simulations or become a bond trader (bond traders use polynomial approximation to estimate changes in bond prices given interest rate changes and vice versa), this tutorial could be fun. If that isn't motivation enough, we also come up with one of the most epic and powerful conclusions in all of mathematics in this tutorial: Euler's identity.
This series of videos focusing on calculus covers using definite integrals with the shell and disc methods to find volumes of solids of revolution.
This 8-minute video lesson presents an intuition (but not a proof) of the Squeeze Theorem. [Calculus playlist: Lesson 7 of 156]
This series of videos focusing on calculus covers parameterizing a surface, surface integrals, stokes' theorem.
You can parameterize a line with a position vector valued function and understand what a differential means in that context already. This tutorial will take things further by parametrizing surfaces (2 parameters baby!) and have us thinking about partial differentials.
You know what Stokes' theorem is and how to apply it, but are craving for some real proof that it is true. Well, you've found the right tutorial!
Finding line integrals to be a bit boring? Well, this tutorial will add new dimension to your life by explore what surface integrals are and how we can calculate them.
This series of videos focusing on calculus covers calculating derivatives, power rule, product and quotient rules, chain rule, implicit differentiation, derivatives of common functions.
You can take the derivatives of f(x) and g(x), but what about f(g(x)) or g(f(x))? The chain rule gives us this ability. Because most complex and hairy functions can be thought of the composition of several simpler ones (ones that you can find derivatives of), you'll be able to take the derivative of almost any function after this tutorial. Just imagine.
Discover what magic we can derive when we take a derivative, which is the slope of the tangent line at any point on a curve.
The topic that is now known as "calculus" was really called "the calculus of differentials" when first devised by Newton (and Leibniz) roughly four hundred years ago. To Newton, differentials were infinitely small "changes" in numbers that previous mathematics didn't know what to do with. Think this has no relevence to you? Well how would you figure out how fast something is going *right* at this moment (you'd have to figure out the very, very small change in distance over an infinitely small change in time)? This tutorial gives a gentle introduction to the world of Newton and Leibniz.
We told you about the derivatives of many functions, but you might want proof that what we told you is actually true. That's what this tutorial tries to do!
Tijdens de cursus Caleidoscoop worden verschillende aspecten belicht waarmee de eerstejaarsstudenten worden voorzien van basisvaardigheden en basiskennis die noodzakelijk zijn voor het succesvol volgen van een studie in de wiskunde.
This art history video discussion examines Robert Campin's (also called the Master of Flemalle) "Christ and the Virgin," c. 1430-35, oil and gold on panel, 11-1/4 x 17-15/16 inches / 28.6 x 45.6 cm (Philadelphia Museum of Art).
This art history video discussion examines Robert Campin's Merode Altarpiece, tempera and oil on panel, 1425-28 (Metropolitan Museum of Art).