Deciding if Lines Coincide, Are Skew, Are Parallel or Intersect in 3D. Here I describe two lines in 3space using parametric equations. We have to decide if they coincide, are parallel, are skew or if they intersect in exactly one point.
In this video, I give the formula for the cross product of two vectors, discuss geometrically what the cross product is, and do an example of finding the cross product.
Finding the Scalar Equation of a Plane - In this video, I discuss the formula to find the scalar equation of a plane, how to derive it, and a simple example using it!
Torque - When you tighten a bolt on the tire of your car, you are using torque! An application of the cross product involving torque is shown. In this video, I calculate the magnitude of the torque vector.
Finding the Point Where a Line Intersects a Plane - Multivariable Calculus Stuff!In this video, I find the point at which a line would intersect a plane.
Finding the Domain of a Vector Function - In this video I find the domain of one vector function. Nothing too heavy here!
Finding the Limit of a Vector Function - In this video I do one example of finding the limit of a vector function.
The Arc Length of a Vector Function - In this video I give the formula to find the arc length of a 3-dimensional vector function and do one concrete example of finding the length of a vector function.
Multivariable Calculus: Showing a Limit Does NOT Exist - In this video, I spend a bit of time talking about what it means for a limit not to exist and do one example showing that the limit does not exist.
Multivariable Calculus: Finding and Sketching the Domain of a function z = f(x,y).I discuss the basic idea and do examples.
Finding Partial Derviatives - 3 examples are shown of finding partial derivatives of a multivariable function.
Calculus: Higher Order Partial Derivatives. In this video, I briefly discuss the notation for higher order partial derivatives and do an example of finding a 3rd partial derivative.
In this video, I give the formula and use it to find a tangent plane approximation. Both the tangent plane and the actual numerical estimate are shown.
General Chain Rule - Part 1 - In this video, I discuss the general version of the chain rule for a multivariable function. There will be a follow up video doing a few other examples as well!
General Chain Rule - Part 2. In this video I finish off two examples of the general chain rule from Part 1.
Multivariable Calculus - Implicit Function Theorem.In this video, I show how to find partial derivatives of an implicitly defined multivariable function using the Implicit Function Theorem.
MultiVariable Calculus - Implicit Differentiation.In this video, I point out a few things to remember about implicit differentiation and then find one partial derivative.
MultiVariable Calculus - Implicit Differentiation - Ex 2.In this video, I do a follow up example where we find dz/dy.
Finding the Directional Derivative - In this video, I give the formula and do an example of finding the directional derivative that corresponds to a given angle.
The Gradient Vector - Notation and Definition. In this video, I talk about the directional derivative, and the corresponding definition of the gradient vector. Nothing deep here!! Just a small observation and some notation!
Local Maximum and Minimum Values/ Function of Two Variables.An outline of the procedure, along with a complete example are shown.
Local Maximum and Minimum Values/ Function of Two Variables.Another example is shown!
Vector Functions: Position, Velocity, Acceleration Word Problem, Ex . In this video, we are given the velocity vector of a car as well as its initial displacement. We have to find the position of the car after 1 second.
Smooth Vector Functions, Ex 1. In this video, I show how to determine if a given curve is smooth or not.
Smooth Vector Functions, Ex 2. Another example where we have to decide if a given vector function is smooth or not.
Finding a Unit Tangent Vector at a Given Point. In this video, I find a unit tangent vector to a space curve at a given value of t.
Derivative of a Vector Function - Another Ex 1. In this video, I show an example of finding the derivative of a vector function. It is pretty simple: just take the derivative of each part!
Finding the Limit of a Vector Function - Another Ex 1. In this video, I find the limit of a vector valued function.
Finding the Limit of a Vector Function - Another Ex 2. In this video, I find the limit of another vector valued function. In this example I have to use both the Squeeze Theorem and also L'Hospital's rule.
Deciding if Lines Coincide, Are Skew, Are Parallel or Intersect in 3D. Here I describe two lines in 3space using parametric equations. We have to decide if they coincide, are parallel, are skew or if they intersect in exactly one point.
Parametric Equations of Line Passing Through a Point. In this video, I show how to find the parametric equations of a line that passes through a given point with a given direction vector.
Orthogonal Projections - Scalar and Vector Projections. In this video, we look at the idea of a scalar and vector projection of one vector onto another.
Triple Integrals, Changing the Order of Integration, Part 1 of 3. In this video, I start discussing how a particular order of integration for a given region and integral ' makes sense '! Then I go about changing the order of integration. In this part, we integrate with respect to z first.
Triple Integrals, Changing the Order of Integration, Part 2 of 3. In this video, I show how to integrate the region by integrating with respect to x first.
Triple Integrals, Changing the Order of Integration, Part 2 of 3. In this video, I show how to integrate the region by integrating with respect to y first.