university levels of education Calculus III III
Calculus III, Deep Mastery Series — handmade, no ads, no sign-ups. Every lecture is kept whole and shown whole: nothing is summarised, so what you see is the lecture as it was written. 14,710 words across 20 lectures, from curves and surfaces in space to the theorems of Green, Stokes and Gauss. Twenty-one ways through the same text, forty-six palettes on a white default with dark a click away, twelve layouts and colours you can set yourself. The mathematics is typeset from the author's own LaTeX, so every formula renders as written.
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Lectures 1–10
Lectures 1 to 10. Vectors and Geometry in Three Dimensions, Vector-Valued Functions, Space Curves, Motion in Space, Arc Length, Curvature, and Torsion, Functions of Several Variables, Quadric Surfaces, Limits, Continuity, and Partial Derivatives, The Chain Rule, Gradient Vector, Directional Derivatives, Tangent Planes, and Implicit Differentiation, Multivariable Optimization, Hessian Matrix, Second Derivative Test, and Lagrange Multipliers and 5 more, ending on Triple Integrals in Cylindrical and Spherical Coordinates, Jacobians, Volume Computations, and Applications. 6,403 words across 10 lectures.
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Lectures 11–20
Lectures 11 to 20. Introduction to Vector Calculus: Vector Fields, Line Integrals, Work, Conservative Fields, and Potential Functions, The Del Operator, Gradient, Divergence, Curl, Laplacian, and Differential Operators, Green's Theorem: Circulation, Flux, Area, Conservative Fields, and Applications, Surface Integrals: Parameterized Surfaces, Surface Area, Scalar Surface Integrals, Flux Integrals, Normal Vectors, and Applications, Stokes' Theorem: Circulation, Curl, Oriented Surfaces, and Applications and 5 more, ending on Capstone Review: Unifying Multivariable Calculus, Vector Calculus, Differential Geometry, and Advanced Applications. 8,307 words across 10 lectures.
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The whole course
All 20 lectures, opened without a filter. 14,710 words, 8,417 blocks, 0 tables and 0 paired examples, with a glossary of 0 entries and a search index of 1,355 words. Twenty-one ways through the same text. Six read it — one lecture entire, an index of every lecture number down the left, a reader that hands you a single section at a time, a continuous scroll, an outline of the section headings, and a syllabus of the whole course. Eight take it apart — every Spanish line beside its English, the glossary lifted out of the tables, the tables on their own, flashcards Spanish side first, the practice questions, a drill that pulls a random example in either direction, and the objectives and closing summaries. Seven keep track — homework, cultural notes, an accent-insensitive search across every block, starred lines, a page of your own notes per lecture, a progress board, and a printable handout. Forty-six colour palettes on a white default with dark one click away, eight colour roles editable by hand, twelve page layouts from a narrow reading column through ruled notebook paper and two magazine columns to a monospaced terminal, seven typefaces with a separate face for the Spanish, and sliders for text size, leading and line length. The English can be hidden to read the Spanish cold, or the Spanish hidden to work back the other way. Progress, stars and notes autosave, with JSON export and import.
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