Mathematics lectures and examples. I am an Associate Teaching Professor of Mathematics. On this channel are videos for Multivariable Calculus, Single Variables Calculus II, Mathematical Modeling (intended primarily for high school math teachers), and others. I am currently recording some lectures on Real Analysis II (Advanced Calculus II), and hope next to make a series on proof writing and introductory Real Analysis.

I am pretty skilled with MATLAB--if you are wondering how I made a graphic or animation, it was probably in MATLAB. (I will eventually put some MATLAB videos up here too...)

The material located on this site is not endorsed, sponsored or provided by or on behalf of North Carolina State University.

Examples of optimizing with the Hessian eigenvalues, Real Analysis II
30:00
Examples of optimizing with the Hessian eigenvalues, Real Analysis II
The Second Derivative Test eigenvalues of the Hessian, Real Analysis II
43:29
The Second Derivative Test eigenvalues of the Hessian, Real Analysis II
Taylor series (with remainder) for f(x,y) example, Real Analysis II
31:00
Taylor series (with remainder) for f(x,y) example, Real Analysis II
Taylor polynomial example for f(x,y), Real Analysis II
10:13
Taylor polynomial example for f(x,y), Real Analysis II
Taylor Series and Taylor's Theorem for Multivariable Functions, Real Analysis II
35:45
Taylor Series and Taylor's Theorem for Multivariable Functions, Real Analysis II
Taylor's Theorem with four proofs (Peano, Integral form, Cauchy, Lagrange), Real Analysis
52:54
Taylor's Theorem with four proofs (Peano, Integral form, Cauchy, Lagrange), Real Analysis
Differentiation recap and look ahead, Real Analysis II
9:21
Differentiation recap and look ahead, Real Analysis II
Mean Value Theorem for Multivariable Functions, Real Analysis II
23:00
Mean Value Theorem for Multivariable Functions, Real Analysis II
Linearize a solution to the heat equation, Multivariable Calculus
7:09
Linearize a solution to the heat equation, Multivariable Calculus
The Hessian Matrix: Derivation, Interpretation, and Example, Real Analysis II
51:05
The Hessian Matrix: Derivation, Interpretation, and Example, Real Analysis II
Proof of Clairaut's Theorem, Real Analysis II
43:02
Proof of Clairaut's Theorem, Real Analysis II
Gradients, Directional Derivatives, and Gradient Descent, Real Analysis II
42:14
Gradients, Directional Derivatives, and Gradient Descent, Real Analysis II
The Gradient is perpendicular to level sets, Real Analysis II
49:21
The Gradient is perpendicular to level sets, Real Analysis II
How to compose trig functions with inverse trig functions, many examples
29:53
How to compose trig functions with inverse trig functions, many examples
Surface Area cut out by two cylinders, Multivariable Calculus
16:45
Surface Area cut out by two cylinders, Multivariable Calculus
Is (x^2+y^2)sin(1/(x^2+y^2)) differentiable? Real Analysis II
21:20
Is (x^2+y^2)sin(1/(x^2+y^2)) differentiable? Real Analysis II
Continuous partials imply differentiability proof, Real Analysis II
36:06
Continuous partials imply differentiability proof, Real Analysis II
Example: double integral over a disk in polar coordinates, Multivariable Calculus
12:47
Example: double integral over a disk in polar coordinates, Multivariable Calculus
Proof of the Chain Rule for vector valued multivariable functions, Real Analysis II
17:52
Proof of the Chain Rule for vector valued multivariable functions, Real Analysis II
Multivariable Chain Rule, Real Analysis II
31:12
Multivariable Chain Rule, Real Analysis II
Compute all directional derivatives and determine if f is differentiable, Real Analysis II
8:33
Compute all directional derivatives and determine if f is differentiable, Real Analysis II
An example checking differentiability of f(x,y), Real Analysis II
20:54
An example checking differentiability of f(x,y), Real Analysis II
Linearization of scalar valued functions, Real Analysis II
14:00
Linearization of scalar valued functions, Real Analysis II
Example of a scalar surface integral (spherical and cylindrical coordinates), Multivariable Calculus
13:37
Example of a scalar surface integral (spherical and cylindrical coordinates), Multivariable Calculus
f : [0,1] to [0,1] has a fixed point (Brouwer Fixed Point theorem, dimension 1)
18:48
f : [0,1] to [0,1] has a fixed point (Brouwer Fixed Point theorem, dimension 1)
The Jacobian Matrix, Real Analysis II
33:59
The Jacobian Matrix, Real Analysis II
If f is differentiable, then f is continuous and a little more, Real Analysis II
11:40
If f is differentiable, then f is continuous and a little more, Real Analysis II
The Definition of Differentiability (Introduction and Example), Real Analysis II
36:25
The Definition of Differentiability (Introduction and Example), Real Analysis II
Review of Linear Transformations T: R^n to R^m
33:48
Review of Linear Transformations T: R^n to R^m
Proofs of the Extreme and Intermediate Value Theorems, Real Analysis II
15:20
Proofs of the Extreme and Intermediate Value Theorems, Real Analysis II