11:00

Multivariable Second Derivative Test

13:27

TOPOLOGY! Global Extrema of Continuous z=f(x,y) over a Closed and Bounded (Compact) Domain

17:21

Gradient Vector in Polar Coordinates ||∇u||^2 = (∂u/∂r)^2 + (∂u/∂θ)^2/r^2 | Geometric Interpretation

04:47

Implicit Differentiation Using Partial Derivatives (Implicit Function Theorem Formula)

36:20

Gradient Vectors, Directional Derivatives, & Chain Rule in Multivariable Calculus

41:06

Multivariable Calculus Problem-Solving Review for Exam 2 (w/ Introduction to Directional Derivative)

39:04

Linear Approximations, Differentiability, Total Differentials, Gradient Vectors, Tangent Planes

39:54

Multi Calc, Lec 15: Partial Derivatives (Notation & Geometric Interpretation)

56:22

Limits and Continuity of Multivariable Functions

37:14

Multi Calc, Lec 13B: Functions of 2 and 3 Variables (Domain, Range, and Graphs)

03:51

Multi Calc, Lec 13A: Curvature of a Helix is CONSTANT! (Use Wolfram Mathematica to Compute It)

08:14

Multi Calc, Lec 12B: Curvature (Definition, Meaning, and Formulas)

29:20

Multi Calc, Lec 12A: Unit Tangent & Normal Vectors, Tangential & Normal Components of Acceleration

21:08

Multivariable Calculus, 20 Minute Review of Topics on Exam 1

03:39

The SURPRISING Derivative of ||r(t)||^4

15:38

Multi Calc, Lec 11A: Arc Length Parameterization Example

41:15

In-Depth Parametric Curve Example with Mathematica (Velocity, Acceleration, Speed, & Distance)

45:12

Multi Calc, Lec 9: Differential Calculus of Vector-Valued Functions (Velocity Vector is Tangent)

10:44

How To Find The Equation of a Plane Given Three Points in ℝ^3

22:22

Multi Calc, Lec 8A: Describing Lines in ℝ^3 (including Symmetric Equations)

44:30

Multi Calc, Lec 7: Vector Cross Product (includes 3x3 Determinant Shortcut)

07:50

Why does v∙w = ||v|| ||w|| cos(θ)? The proof is fun!

16:45

Why Does proj_w(v)=((v∙w)/(v∙w))w??? (Projection Vector Formula Derivation)

14:28

Multi Calc, Lec 6A: The Dot Product and Angle Between Two Vectors

17:49

Multi Calc, Lec 5B: Vector Geometry and Vector Algebra in ℝ^3

27:48

Multi Calc, Lec 5A: 3-Dimensional Space ℝ^3 (including Distance Formula, Spheres, and Hyperboloids)

01:05:51

Multi Calc, Lec 4: Polar Coordinates

13:45

Multi Calc, Lec 3B: Surface Area of Solid of Revolution (from Parametric Curve)

24:16

Multi Calc, Lec 3A: Position & Velocity Vectors, Speed, Distance (Arc Length) for Parametric Eqs

36:10

Multivariable Calculus, Lec 2: Using Mathematica for Parametric Equations & Curves in 2D

28:13

Multivariable Calculus, Lecture 1: Parametric Curves in the Plane ℝ^2

30:24

Review Abstract Algebra in 30 Minutes

36:06

A Galois Group Isomorphic to the Symmetric Group S3

23:38

Find the Subfield Lattice of ℚ(√3,√5) over ℚ by Using Galois Theory!

29:33

Review All of Calculus 2 in 30 Minutes

23:41

Solve dy/dx = y^2 in TWO WAYS!! (Separation of Variables and Power Series Solution)

12:46

Damped Harmonic Oscillator with Complex Eigenvalues (Use Euler's Formula, Diff Eq for Calc 2, Pt 8A)

05:39

The Galois Group Gal(ℚ(∜2,i)/ℚ) has 8 Elements!

14:37

ℚ(∛2) is NOT a Galois Extension of ℚ (Fundamental Theorem of Galois Theory Does NOT Apply)

36:54

Galois Theory: Fundamental Definitions and a Basic Example

08:11

A Sneak Peek at Fourier Series by Playing Sound Waves in Wolfram Mathematica

25:45

How to Model Simple Harmonic Motion for Mass on a Spring (Diff Eqs for Calculus 2, Part 7B)

27:30

WOW! 4 Equilibrium Points! Logistic Growth Competing Species Model (Diff Eqs for Calc 2, Part 7A)

23:59

Galois Field GF(2^3) = GF(8)

27:20

Two Simple Finite Field Examples: ℤ2 and Galois Field GF(2^2) = GF(4)

16:59

Differential Equations for Calculus 2, Pt 6: Intro to Competing Species Model (use Mathematica)

12:28

Find a Splitting Field of x^3-1 over ℚ

20:26

ℚ(√2 + √3) = ℚ(√2,√3)...But WHY??? 🤔

17:32

ℚ(∛5) is an Algebraic Field Extension of ℚ of Degree 3 (so it's a finite degree extension too!)

18:47

Differential Equations for Calculus 2, Part 5B: Predator-Prey Model (Robins and Worms)

42:27

Differential Equations for Calculus 2, Part 5A: Logistic Model for Population Growth

22:56

Can a Polynomial Have Two Splitting Fields over ℚ???

34:01

Field Extensions and Kronecker's Theorem (Fundamental Theorem of Field Theory), including Examples

14:09

Differential Equations for Calculus 2, Part 4B: Free Fall with Air Resistance

18:15

Differential Equations for Calculus 2, Part 4A: Mixing Problem (Compartmental Analysis)

25:38

How to Avoid Going BROKE in Retirement with CALCULUS!

06:10

A Simple Field Extension! ℚ(√2) is a splitting field for f(x)=x^2-2 over the rational numbers ℚ

25:58

Vector Spaces in Linear Algebra vs Abstract Algebra

23:20

Differential Equations for Calculus 2, Part 3: Newton's Law of Cooling

32:25

The Calculus of Drug Dosing