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Curated by: MathTheBeautiful (655 videos)

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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