Prerequisite Video Lectures
Essential mathematics for quantum mechanics: Linear Algebra and Multivariable Calculus
About These Resources
These carefully curated video lectures provide the mathematical foundation required to understand quantum mechanics. We recommend watching 3Blue1Brown series first for visual intuition, then diving into the MIT courses for rigorous understanding.
Study Path: Linear Algebra → Calculus → Tensors → Begin Quantum Mechanics Part I
Linear Algebra
Vectors, matrices, eigenvalues, and linear transformations
3Blue1Brown - Essence of Linear Algebra
16 videos • Visual intuition • Best starting point
Grant Sanderson's legendary series that makes linear algebra click visually. Covers vectors, linear transformations, matrices, determinants, eigenvalues, and change of basis with stunning animations.
Chapter 1: Vectors - What even are they?
Video Lecture
Vectors - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Chapter 2: Linear combinations, span, and basis vectors
Video Lecture
Linear Combinations - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Chapter 3: Linear transformations and matrices
Video Lecture
Linear Transformations - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Chapter 4: Matrix multiplication as composition
Video Lecture
Matrix Multiplication - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Chapter 5: Three-dimensional linear transformations
Video Lecture
3D Transformations - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Chapter 6: The determinant
Video Lecture
The Determinant - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Chapter 7: Inverse matrices, column space, and null space
Video Lecture
Inverse Matrices - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Chapter 9: Dot products and duality
Video Lecture
Dot Products - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Chapter 13: Change of basis
Video Lecture
Change of Basis - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Chapter 14: Eigenvectors and eigenvalues ⭐ ESSENTIAL
Video Lecture
Eigenvectors - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
MIT 18.06 - Linear Algebra (Gilbert Strang)
34 lectures • Complete university course
The legendary MIT course by Professor Gilbert Strang. Rigorous, comprehensive, and the standard for university linear algebra. Watch key lectures below or access the full playlist.
Lecture 1: The Geometry of Linear Equations
Video Lecture
MIT 18.06 Lecture 1
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Lecture 6: Column Space and Nullspace
Video Lecture
MIT 18.06 Lecture 6
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Lecture 17: Orthogonal Matrices and Gram-Schmidt
Video Lecture
MIT 18.06 Lecture 17
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Lecture 21: Eigenvalues and Eigenvectors ⭐ ESSENTIAL
Video Lecture
MIT 18.06 Lecture 21
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Lecture 22: Diagonalization and Powers of A
Video Lecture
MIT 18.06 Lecture 22
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Calculus
Derivatives, integrals, multivariable calculus, and vector calculus
3Blue1Brown - Essence of Calculus
12 videos • Visual intuition
Visual understanding of derivatives, integrals, and the fundamental theorem of calculus. Perfect for building intuition before diving into rigorous calculus.
Chapter 1: The essence of calculus
Video Lecture
Essence of Calculus - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Chapter 2: The paradox of the derivative
Video Lecture
Derivatives - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Chapter 3: Derivative formulas through geometry
Video Lecture
Derivative Formulas - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Chapter 8: Integration and the fundamental theorem ⭐
Video Lecture
Integration - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Chapter 11: Taylor series
Video Lecture
Taylor Series - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
MIT 18.02 - Multivariable Calculus (Denis Auroux)
35 lectures • Complete university course
Essential for quantum mechanics: partial derivatives, multiple integrals, gradient, divergence, curl, and coordinate systems. Professor Auroux is an excellent lecturer.
Lecture 1: Dot Product
Video Lecture
MIT 18.02 Lecture 1
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Lecture 8: Partial Derivatives ⭐ ESSENTIAL
Video Lecture
MIT 18.02 Lecture 8
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Lecture 12: Gradient ⭐ ESSENTIAL
Video Lecture
MIT 18.02 Lecture 12
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Lecture 16: Double Integrals
Video Lecture
MIT 18.02 Lecture 16
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Lecture 22: Divergence and Curl ⭐ ESSENTIAL
Video Lecture
MIT 18.02 Lecture 22
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
3Blue1Brown - Divergence and Curl
Visual explanation of vector calculus
Video Lecture
Divergence and Curl - 3Blue1Brown
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Tensors (Advanced)
Tensor notation and index manipulation for advanced QM
eigenchris - Tensors for Beginners
15 videos • Foundation for advanced physics
Excellent introduction to tensor notation, covariant/contravariant indices, and transformations. Essential for understanding advanced quantum mechanics, relativity, and QFT.
Tensor 1: What is a Tensor?
Video Lecture
What is a Tensor - eigenchris
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Tensor 2: Covariant and Contravariant Components
Video Lecture
Covariant Contravariant - eigenchris
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Tensor 5: Index Notation
Video Lecture
Index Notation - eigenchris
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Recommended Study Path
3Blue1Brown - Essence of Linear Algebra
Build visual intuition for linear algebra concepts
MIT 18.06 (Selected lectures)
Rigorous understanding and practice problems
3Blue1Brown - Essence of Calculus
Visual understanding of calculus fundamentals
MIT 18.02 - Multivariable Calculus
Partial derivatives, gradient, divergence, curl
eigenchris - Tensors (Optional)
Preparation for advanced topics