3Blue1Brown Visual Mathematics¶

Interactive notebooks inspired by the 3Blue1Brown video series. Use these alongside the foundational notebooks for visual intuition.

Series¶

Essence of Calculus series

#	Notebook	Topics
01	Essence of Calculus	Geometric intuition for derivatives
02	Paradox of the Derivative	Instantaneous rate of change
03	Derivative Formulas	Power rule, sum rule, product rule
04	Chain & Product Rules	Composition of functions
05	Exponential Derivatives	e^x and natural logarithm
06	Implicit Differentiation	Differentiating implicit equations
07	Limits & L’Hopital	Formal definition, L’Hopital’s rule
08	Integration	Fundamental theorem of calculus
09	Area and Slope	Connection between integration and differentiation
10	Higher-Order Derivatives	Second derivatives, concavity
11	Taylor Series	Polynomial approximation of functions
12	What Makes e Special	Why e is the natural base

Essence of Linear Algebra series

#	Notebook	Topics
01	Vectors & Linear Combinations	Span, basis vectors
02	Linear Transformations & Matrices	Matrices as transformations
03	Matrix Multiplication	Composition of transformations
04	Determinants	Area/volume scaling factor
05	Eigenvalues & Eigenvectors	Invariant directions under transformation
06	Inverse Matrices & Systems	Solving Ax=b, invertibility
07	Dot Products & Duality	Geometric interpretation
08	Cross Products	3D perpendicular vectors
09	Change of Basis	Coordinate transformations
10	3D Transformations	Extending to three dimensions
12	Cramer’s Rule	Solving systems via determinants
13	Quick Eigenvalue Trick	Fast 2x2 eigenvalue computation
16	Abstract Vector Spaces	Functions as vectors

#	Notebook	Topics
01	Introduction	What are differential equations
02	Heat Equation	Partial differential equations
03	Solving Heat Equation	Separation of variables
04	Fourier Series	Decomposing periodic functions
05	Laplace Transforms	Algebraic approach to ODEs
06	Understanding Laplace	Intuition for the transform
07	Resonance	Driven oscillators
08	Matrix Exponents	e^(At) and systems of ODEs

#	Notebook	Topics
01	What is a Neural Network	Neurons, layers, activations
02	Gradient Descent	Learning by minimizing loss
03	Backpropagation	Chain rule through a network
04	Backprop Calculus	Formal derivation
05	GPT and LLMs	How large language models work
06	Attention & Transformers	Self-attention mechanism
07	Attention Deep Dive	Multi-head attention, QKV
08	How GPT Stores Facts	Knowledge in transformer weights
09	Diffusion Models	Denoising score matching

These notebooks complement the foundational/ course. When a concept feels abstract, find the matching 3Blue1Brown notebook for visual intuition: