13 signed decks · Multivariable geometry · 2024
Use consistent visuals to explain space in 2D and 3D.
A parametric curve is located inside the surface it follows.
01 · Context + problem
In Calculus II, I help learners reason across two- and three-dimensional representations while notation changes from one coordinate system to another.
A spectacular 3D image can still fail instructionally if the axes, basis vectors and differential elements are not introduced in a stable sequence.
02 · Constraints
03 · How it was built
I reuse color, notation and page anatomy across the whole series.
I move from an object, to its coordinate description, to the integral it supports.
I choose views that preserve orientation and scale cues.
04 · Content produced
Six slides drawn from three of the thirteen decks I authored and produced for Calculus II, from parametrized curves to integrals in spherical coordinates.
08 visuals
A secant construction makes the vector derivative visible before formalization.
The moving orthonormal frame is attached directly to the parametrized curve.
The force field, tangent and polygonal approximation share one spatial frame.
The geometric setup resolves into two equivalent line-integral formulas.
The spherical basis is derived from visible angles and moving directions.
A differential wedge makes the spherical Jacobian readable in three dimensions.
Basis vectors are anchored directly to the geometry.
A counterexample makes orientation concrete.
05 · Work and scope
The excerpts come from the series I authored in 2024. They illustrate its notation and visual composition.
The presentation concerns the materials produced, without a study of their effect on learning.
These excerpts show the scope and visual authorship of the series; they are not a complete presentation of the course.
06 · Relevance for your organisation
I can produce a consistent set of figures and slides for a course taught by several instructors. Your team directs the teaching sequence and approves the subject matter; together we choose the templates, formats and documentation needed for future updates.
07 · Technical approach
Axes, basis vectors, surfaces and differential elements are authored from mathematical sources rather than flattened into screenshots.
LaTeX · TikZ · PGFPlots
Why it mattersNotation, views and geometric cues can be revised while preserving consistency across the series.
Curves, sliced solids and the Frenet–Serret frame are computed before they are rendered as figures or animations.
Python · NumPy · Matplotlib · SymPy
Why it mattersThe visual explanation stays tied to the mathematical object instead of a manually drawn approximation.
Vector figures support close reading, while animation is used when orientation or motion must unfold over time.
SVG · Matplotlib
Why it mattersEach idea is presented in a medium that preserves the cues learners need.