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.
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 - Ex 2.In this video, I do a follow up example where we find dz/dy.
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.
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.