Lectures from MIT OpenCourseWare and open textbooks, rebuilt frame by frame as animation. Eleven courses so far.
Force, momentum, energy, and the conservation laws that govern the motion of bodies.
An introduction to Newtonian mechanics: units and estimation, vectors and kinematics, Newton's laws and the force laws, circular motion and universal gravitation, momentum and the center of mass, work and energy, and the conservation of mechanical energy.
Open course→Oscillators, Fourier series, Laplace transforms, and phase planes — MIT 18.03.
An introduction to ordinary differential equations: first-order equations, second-order linear equations and resonance, Fourier series, the Laplace transform, linear systems, and the phase-plane analysis of nonlinear systems.
Open course→Charges, fields, potential, circuits, magnetism, induction, and the electromagnetic waves that unite them — MIT 8.02.
An introduction to electricity and magnetism: fields and the vector calculus behind them, Coulomb's law and the electric field, Gauss's law, electric potential, capacitance and dielectrics, current and direct-current circuits, magnetic fields and forces, the Biot–Savart and Ampère laws, Faraday's law and inductance, LC, RLC and alternating-current circuits, Maxwell's equations and electromagnetic waves, and interference and diffraction.
Open course→Present value, fixed income, equities, options, portfolios, and the CAPM — MIT 15.401.
An introduction to the theory of finance: present value and the valuation of fixed-income and equity securities, forwards, futures, and options, portfolio theory and the capital asset pricing model, capital budgeting, and the efficient and adaptive markets hypotheses.
Open course→Optimization, graphs, simulation, statistics, and machine learning in Python — MIT 6.0002.
The sequel to Introduction to Computer Science using Python: using computation to model and understand the world — optimization and the knapsack problem, dynamic programming, graph search, stochastic thinking and random walks, Monte Carlo simulation, sampling and confidence intervals, experimental data and curve fitting, machine learning with clustering and classification, and the statistical sins that mislead.
Open course→Algorithms, types, expressions, and your first Python programs — all in the browser.
An introduction to computer science and programming in Python: computation and algorithms, types and control flow, floating-point numbers and bisection search, functions and scope, lists and mutation, comprehensions and testing, exceptions, dictionaries, recursion, and classes and objects.
Open course→Declensions, conjugations, and translation — learned by hand, the old way.
A first course in classical Latin: the noun cases and the first four declensions, adjectives and pronouns, the four conjugations across six tenses in the active and passive voices, the infinitive and the imperative, and expressions of place.
Open course→Vectors, matrices, spans, and transformations.
An introduction to linear algebra: systems of equations and elimination, vector spaces and the four fundamental subspaces, orthogonality and least squares, determinants, eigenvalues and diagonalization, symmetric and positive definite matrices, the singular value decomposition, and linear transformations.
Open course→Proof-first: definitions, then theorems, then proofs. Starts from scratch, but usually taken second — the abstract companion to our computational Linear Algebra.
A proof-based second course in linear algebra built on abstract vector spaces and linear maps rather than matrix computation: vector spaces and subspaces, span, bases and dimension, linear maps and matrices, quotients and duality, polynomials, eigenvalues and the minimal polynomial, inner product spaces, the spectral theorem and the singular value decomposition, Jordan form, and multilinear algebra with determinants and tensor products.
Open course→Keys, mining, wallets, and the mechanics of a peer-to-peer ledger.
How Bitcoin works from the inside: keys and addresses, wallets, transactions and Script, SegWit and Taproot, signatures and fees, the peer-to-peer network, blockchain structure, mining and consensus, security, and second-layer applications such as the Lightning Network.
Open course→Logic, proof methods, induction, sets, functions and relations — learning to construct a proof and write it up. The course to take before Linear Algebra Done Right.
An introduction to mathematical proof: statements and logic, direct proofs, the contrapositive, contradiction and proofs by cases, mathematical induction, sets and set operations, functions, injections, surjections and inverses, and relations, equivalence classes and modular arithmetic.
Open course→Vectors, partial derivatives, multiple integrals, and vector fields — MIT 18.02.
Calculus in two and three dimensions: vectors and matrices, partial derivatives and optimization, double and triple integrals, and the vector calculus of line and surface integrals through Green's theorem, Stokes' theorem, and the divergence theorem.
Open course→Limits, derivatives, integration, and infinite series — MIT 18.01.
A first course in the calculus of one variable: limits and derivatives, the applications of differentiation, integration and its techniques, improper integrals, and infinite series through Taylor expansions.
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