Bill Kinney

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In-depth mathematics lectures, math exam reviews, and shorter videos on a wide variety of topics in mathematics. Highlights include many videos about Real An...

Latest Videos

How i ROTATES the Complex Plane (with Linear Algebra Insight Vectors & Matrices)

The Power ⚡ of Complex CONJUGATES Algebra, Geometry, and Linear Algebra

What’s the DISTANCE Between Two COMPLEX Numbers Modulus, Norms, Metrics, Circles, & Lines

Complex Numbers ℂ as a Real VECTOR SPACE - Leads to VECTOR SUBTRACTION!

How Real Scalars Transform Complex Numbers (With Proof & Graphs!) Modulus of a Complex Number

Add Complex Numbers Using Geometry – It’s Beautiful!

What is a Complex Number

The MOST INTERESTING Basic Fact About the IMAGINARY UNIT i (Integer Powers of i Cycle)

Common Errors in Math sqrt(a^2+b^2) = a+b

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

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

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

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

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

Stokes' Theorem Example with Mathematica

Divergence Theorem Examples with Mathematica

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

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

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

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

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

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

What is the Idea of Cylindrical Coordinates for Triple Integrals

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

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

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

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

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

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

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