The study demonstrates that graphic instructional representations for functions and their derivatives, and students' concomitant images, have the potential for producing a richer understanding than that achieved by analytic study alone. Stimulated by graphic instructional representations, students form and can...
This study is a comparative case study of what three college calculus teachers did in their classrooms and what their students understood about the concept of derivatives. The teachers were solicited on the basis of peer, supervisor and student recommendations as being good teachers; several volunteer...
Instead of multiplication, the interaction is taking a partial derivative. As before, thei→component of curl is based on the vectors and derivatives in thej→andk→directions. Relation to the Pythagorean Theorem The cross and dot product are like the orthogonal sides of a triangle: For unit ...
usually $x$. For example, $\frac{dF}{dx}$ tells us how much the function $F$ changes for a change in $x$. But if a function takes multiple variables, such as $x$ and $y$, it will have multiple derivatives: the value of the function will change when we “wiggle” $x$ ($\...
, n times, we were able to express f(x) in terms of its n derivatives evaluated at a point a with the last terms being evaluated at some point c, between a and x. The series took the form: Taylor.s Theorem thus states: The important point to realize here is that n stands for ...
Like all things in life, there are varying levels of comprehension of calculus which could be deemed sufficient for differing depths of neural networks understanding. You could, for instance, feel justified in possessing a basic intuition of derivatives and an understanding of how backpropagation work...
Our introductory study of Calculus ends with a short but important study of series. The special type of series known as Taylor series, allow us to express any mathematical function, real or complex, in terms of its n derivatives. The Taylor series can also be called a power series as each...
Ch 3. Vectors in Calculus Ch 4. Geometry and Trigonometry Ch 5. How to Use a Scientific... Ch 6. Limits Using a Graph to Define Limits 5:24 Understanding Limits: Using Notation 3:43 4:33 Next Lesson One-Sided Limits and Continuity Limit of a Function | Definition, Rules & Exa...
I'm reading parts of the paper The Concentration-Compactness Principle in the Calculus of Variations. The Limit Case, Part 1 by P.L. Lions. I'm trying to understand the proof of Lemma 1.1, but I'm having some trouble. The hypotheses of the lemma are the following: Let (un)n(un)...
On smile properties of volatility derivatives and exotic products: understanding the VIX skew We develop a method to study the implied volatility for exotic options and volatility derivatives with European payoffs such as VIX options. Our approach, based on Malliavin calculus techniques, allows us to...