## Multivariable Calculus Resources

This is a hard question whaich found in UKMT question test online Evaluate the following integral using any Vector Calculus method

Evaluate the following integral using any Vector Calculus method The integral with bounds C; [(4+eyz)i+(xzeyz+2yz)j+(6z2+xyeyz+y2)k] dot dr, where C is the part of...

The vector from the point (1,2, -3) to the centre of the sphere x2+y2+z2-kx+3y-lz=1  is given by < 3, h, -2 > . Then the value of hkl is? Area of a parallelogram using 4 points

I need some help using vectors to find the area of this parallelogram. I use three points to create two vectors with the same initial points and use a 2x2 determinant to compute the cross... Suppose S_1={u_1,u_2} and S_2={v_1,v_2} are each independent sets of vectors in an n-dimensional vector space V.

Let us assume that every vector in S_2 is a linear combination of vectors in S_1. Question: Does that mean that S_1 and S_2 are bases for the same subspace of V? I know that the... Moment of inertia question

The boundary of a thin plate is an ellipse with semiaxes a and b. Let L denote a line in the plane of the plate passing through the center of the ellipse and making an angle k with the axis... The surface z = (x^2 - y^2)/(x^2 + y^2) has the simple equation z (r, t) = Cos (2 t) in cylindrical coordinates. The surface is therefore obtained by wrapping the graph of the curve z = Cos (2 t) on a circular cylinder and then expanding this... Document 5.29MB

In this lesson plan I explain the idea of delta-epsilon proofs and develop some notions of limits in the setting of several variables.... Document 104k

This is a more thorough study of the general n by n determinant. I use it as optional lecture in my Multivariate Calculus course. Document 4.47MB

This is a 3rd lecture on Multivariate Calculus, where I give an intuitive development of the determinant. Document 15.39MB

This lesson plan introduces vectors and vector operations. It is my first lesson on Multivariate Calculus. Can The Following Double Integral Be Evaluated or Can It Only Be Approximated Numerically

∫∫ √(4v2 + 4u2 + 1) dvdu, with limits of integration 0≤v≤1 & 0≤u≤2 *Note: the entire expression is supposed to be under the square root symbol   I have tried... Containment and Equality If A and B are sets, then A is said to be contained in B iff (if and only if) every element of A is contained in B. So A⊆B means that A is a subset of B. Example: All squares ⊆ all rectangles All right triangles ⊆ all triangles Important! This implies the idea of forwards and backwards logic: If Joe has three million dollars, he is a millionaire... read more Sets and Other Elementary Subjects Sets are a collection of things called objects. Objects are all unambiguously defined. In other words, objects have unmistakably clear definitions with one meaning and one interpretation that leads to one conclusion. This may seem convoluted because we are so used to words and phrases having different meanings and whatnot, but not in this case. Look... read more  