Uploads from MathTheBeautiful

Watch and track your favorite playlist.

Curated by: MathTheBeautiful (655 videos)

Currently Playing: Areas and the trouble with √2. Lesson 2 of a complete course on Differential Geometry

Complete playlist: https://www.youtube.com/watch?v=W2uOamkVAFw&list=PLlXfTHzgMRUKG7lkye7DQAmNB0cfWNgWG&index=1 https://grinfeld.org https://www.patreon.com/PavelGrinfeld https://grinfeld.org/books/An-Introduction-To-Tensor-Calculus/ https://grinfeld.org/books/A-Tensor-Description-Of-Surfaces-And-Curves/

Tracks in this Playlist

Euler's Formula
De Moivre's Formula and a Trigonometric Sum
De Moivre's Formula and Trigonometric Identities
Extraction of Complex Roots
Multiplication of Complex Numbers in Polar Form
The SEVENTH of the seven beauties: the derivation of the integral of signed curvature
The SEVENTH of the seven beauties: The integral of signed curvature over a closed curve
The Polar Form of Complex Numbers
De Moivre's Formula for Complex Numbers: A Precursor to Euler's Formula
The Elementary Properties of Complex Numbers According to Hamilton
Accepting Complex Numbers: Hamilton vs Euler
The Birth of Complex Numbers and Tartaglia's Formula
Tartaglia's Formula in Action and Numbers of the form a+b√5
Tartaglia's Formula in Action: Two Examples
Euler's Derivation of the Tartaglia-Cardano Formula
Polynomial Equations and the Fundamental Theorem of Algebra
The SIXTH of the seven beauties. The integral of position vector dotted with unit normal.
The FIFTH of the seven beauties. The integral of position vector dotted with unit tangent.
The FOURTH of the seven beauties. The integral of position vector dotted curvature normal.
The THIRD of the seven beauties. The integral of unit normal over a curve.
The SECOND of the seven beauties! The integral of curvature normal over a curve.
A brief review of curves and integration over curves.
The FIRST of the seven beauties! The integral of unit tangent over a curve.
The Expression for the Arc Length of a Curve in Cartesian Coordinates
The Geometric Expression for the Arc Length of a Curve
From Physical to Arithmetic Integrals - Achieving Complete Agreement with Intuition
Hate most advanced math books? These words of encouragement are for you
From Physical to Arithmetic Integrals - How to Achieve Invariance
Converting a Physical Integral into an Arithmetic One: Identifying the Challenge
Why Change of Variables Is Often an Inherently Ambiguous Task
The Derivative of the Inverse Function, or How to Reparameterize a Curve
The Derivative of the Inverse Function - Why It Is Confusing (and how to eventually fix it)
Formula = Immortality
Integration by Substitution Is an Application of the Chain Rule
The Need for Arbitrary Parameterizations of Curves
Arithmetic Integrals And the Fundamental Theorem of Calculus
Geometric Integrals - a Fundamental Concept to Be Accepted on an Intuitive Basis
Hypersurfaces, Unit Normals, and Signed Curvature
The Curvature of a Curve, Its Principal Normal, And Its Osculating Plane
The Torsion of a Curve
Linear Decomposition by the Dot Product
The Arc Length Parameterization
The Analysis of the Unit Circle as a Planar Curve in Differential Geometry.
The Closest Point on a Curve to a Given Point: Combing Calculus And Geometry
Kinematic Analysis of a Rigid Bar
Classical Euclidean Geometry Is Limited to Three Dimensions
Constant Speed Motion - Analysis via differentiation of vector-valued functions
The Properties of Vector Differentiation
The Main Intuitive Idea of Calculus (applied to curves in Differential Geometry)
The Geometric Interpretation of the DERIVATIVE of a Vector-Valued Function
The Geometric Interpretation of a Vector-Valued Function: It's a curve - end of story.
Differentiation of Vectors: What It Actually Means to DIfferentiate a Vector-Valued Function!
Why did the Russians hate Stalin? Norm McDonald would love this joke
My Proof of Pythagoras' Theorem is NOT circular!
The Heights of a Triangle Are Concurrent, a Vector-Based Proof That Does Not Require Any Ingenuity!
The Orthogonal Projection Expressed in Terms of The Dot Product
Ceva's Theorem, A Vector Based Proof - No Ingenuity Required! Concurrent Lines in a Triangle
The Bisector Theorem: A Vector-Based Proof - No Ingenuity Required!
The Medians of a Triangle Are Concurrent, A Vector-Based Proof - As Straightforward as It Gets!
Introduction to Affine Spaces: What you can do in Linear Algebra w/o inner products. Less Is More!
A Simple Solution to an Otherwise Challenging Problem - Algebra and Geometry Working Together!
The Vector Equation of a Straight Line. This will help us solve a number of difficult problems soon!
The Diagonals of a Rhombus Intersect at a Right Angle - A Dot Product Proof
The Dot Product Proof of the Pythagorean Theorem - The power of Vectors Is on Full Display!
The SIMPLEST proof ot the Pythagorean Theorem - a visual approach even a kindergartener would get!
The Dot Product and the Inner Product: Comparing These Key Concepts in Linear Algebra, Geometry, ℝⁿ
What Is a Vector? It depends! Geometric perspective vs Linear Algebra vs ℝⁿ
Mr. Tibbs, the Queen's butler in BFG made a math mistake. Did the Movie Get It Right? We Investigate
Squaring the Parabola by Means of Ordinary Calculus: A lesson in containing analytical calculations
A Lesson in Daring, Flair, and Beauty: Archimedes' Incredible Breakthrough in Squaring the Parabola
How Archimedes "Squared" the Sphere or One of the Greatest Unifying Moments in Science History
The Challenge of π or How Archimedes Squared the Circle. Introduction to Differential Geometry
Why Does Area Change Quadratically w/ Size? A Simple Question That Requires the Concept of Infinity
How the Greeks Approached the Concept of Area. Archimedes' Method of Exhaustions
Areas and the trouble with √2. Lesson 2 of a complete course on Differential Geometry
The MOST Fundamental Concepts in Differential Geometry, & SURPRISE: Math always start in the middle!
Gilbert Strang's Final MIT Lecture
The Strang Decomposition A = CR
The connection between the cross product and the determinant
An elementary surface integral formula you've never heard of
Vector Calculus 25: The Frenet Identities for a Planar Curve
Vector Calculus 24: The Principal Normal and Curvature of a Planar Curve
Vector Calculus 23: The Laws of Vector Differentiation
Vector Calculus 22: The Distance Between a Point and a Curve
Vector Calculus 20: Heron's Problem, a Vector-Analytic Solution
Vector Calculus 0: Why Vector Calculus?
Integral of e²ˣ/(еˣ+1) - Integration by Substitution, Calculus 2
Integral of 1/(eˣ + e⁻ˣ) - Integration by Substitution, Calculus 2
Integral of 1/(1+√x) - Integration by Substitution, Calculus 2
Integral of x⁷/√(1+x⁴) - Integration by Substitution, Calculus 2
Integral of (1+x)/(1+x^2) - Integration by Substitution, Calculus 2
Integral of tan(x) - Integration by Substitution, Calculus 2
Nothingburger integrals involving the natural logarithm - Integration by Substitution, Calculus 2
5. x⁵ √(x³+7)- Integration by Substitution, Calculus 2
Foreword to Integration by Partial Fractions (No examples in this video)
Integration by Partial Fractions, Integral of 1/(x²-1), Calculus 2
Integration by Partial Fractions, Integral of (x-1)/(x²-4x-12), Calculus 2
Integration by Partial Fractions, Integral of (6x+12)/(x²+x), Calculus 2
Integration by Partial Fractions, Integral of 1/ (x²+4x+5), Calculus 2
Integration by Partial Fractions, Integral of (2x+3)/x(x-1)², Calculus 2