01:00

Common Errors in Math: Freshman's Dream (a+b)^2=a^2+b^2

23:51

What Did We Learn in MULTIVARIABLE CALCULUS? 25 Minute FINAL REVIEW of Course Content

09:14

Physical Interpretation of Curl of 2D Vector Field (Relate to Angular Velocity of Small Paddlewheel)

10:43

Show curl(grad f)=0 and div(curl f)=0 by Direct Calculation

12:11

What is the MEANING of DIVERGENCE of a Vector Field at a Point? You Need the Divergence Theorem!

26:50

Stokes' Theorem Example with Mathematica

40:48

Divergence Theorem Examples with Mathematica

25:55

Flux of a Vector Field Over a Parameterized Surface in ℝ^3 (Flux Surface Integral)

12:35

Surface Area Integral of Graph of z=x^2-y^2 over Disk (Use Polar Coords RIGHT AWAY, or at THE END??)

41:22

Parametric Surfaces and Surface Area Integrals (Mathematica is SO HELPFUL! )

39:08

General Change of Variables Integration Formula with Jacobian Determinant of the Transformation

11:00

Multi Calc, Exam Review Problem (Fundamental Thm of Line Integrals for Conservative Vector Fields)

27:52

Triple Integrals in Spherical Coordinates are WILD!!! 🔥🔥🔥

07:40

What is the Idea of Cylindrical Coordinates for Triple Integrals?

31:32

Area Between Two Polar Curves as Single Integral and as Double Integral (dA=rdrdθ)

19:21

∫𝓒F ∙ dr = ∫∫𝓓curl(F)dA, 𝓒 = ∂𝓓 | Green's Theorem Statement and a Detailed Example

25:17

Potential Function for Conservative Vector Field, Scalar Curl, Path Independence, Green's Theorem

10:59

What Happens When We Integrate the Gradient of a Function Around a Closed Curve?

32:03

Vector Line Integral as Work Done Along a Path 𝓒 by a Force Field (Use Two Parametrizations)

05:36

How to Set Up a Line Integral Over a Piecewise Smooth Oriented Curve 𝓒 = 𝓒1 + 𝓒2

21:21

Scalar Line Integral Meaning and Example (Parameterize by Arc Length and Simple Parametrization)

13:34

IMAGINE IT'S A FLUID! Explore Vector Fields with Mathematica (Intuitive Meaning of Curl and Div)

26:24

Introduction to Vector Fields in 2D and 3D (including Divergence and Curl)

16:29

Triple Integrals and Center of Mass of Solid Bodies

25:28

TRIPLE INTEGRALS ∫∫∫dV !!! 🔥🔥🔥

16:26

Mass, Moments, and Center of Mass for a Lamina using Double Integrals (Infinitesimal Approach)

14:43

Multi Calc, Lec 23C: Exam 3 Quick Summary of Topics

08:06

IMPOSSIBLE becomes EASY (Change the Order of Integration for Double Integrals in Calculus!)

18:20

TWO INTEGRALS BECOME ONE! Change Order of Integration dA=dxdy vs dA=dydx (w/ mass & center of mass)

13:52

How to Set Up a Double Integral with Variable Limits of Integration (Over Disk without Polar Coords)

17:59

Optimization and the Geometric Meaning of the Lagrange Multipliers Equation ∇f = λ∇g

19:05

What Are Double Integrals Used For? (Introduction to Double Integrals as Iterated Integrals)

07:27

Maximum Volume of a Box Inscribed in the Unit Sphere (use Lagrange Multipliers)

38:02

Multi Calc, Lec 20: Constrained Optimization and Lagrange Multipliers

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)

10:45

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)