Learning Lab

Interactive visualizations of core concepts — Analysis II & Physics
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Vector Calculus

The Gradient ∇f

Direction of steepest ascent, perpendicularity to level curves, magnitude as rate of change.

Analysis II
2D 3D

Divergence ∇·F

Sources and sinks, infinitesimal flux, and the connection to the divergence theorem.

Analysis II
2D 3D

Curl ∇×F

Rotation and circulation, the paddle wheel test, and Stokes' theorem connection.

Analysis II
2D 3D

Green's Theorem

Line integrals equal area integrals — verify numerically with interactive closed curves.

Analysis II
2D

Stokes' Theorem

Surface integrals of curl equal line integrals around the boundary.

Analysis II
3D

Divergence Theorem

Volume integrals of divergence equal surface flux — Gauss's theorem in action.

Analysis II
3D
Mechanics

Strain Tensor

Deformable bodies, normal & shear strains, principal strains, Mohr's circle, volumetric/deviatoric decomposition.

Mechanics
2D 3D

Stress Tensor

Cauchy stress, traction vectors, normal & shear stresses, principal stresses, Mohr's circle, hydrostatic/deviatoric decomposition, von Mises.

Mechanics
2D 3D

Constitutive Laws (Stoffgesetze)

Hooke's law: stress ↔ strain via compliance & stiffness matrices. Young's modulus, Poisson's ratio, plane stress/strain.

Mechanics
2D 3D
Physics

1. Strom und Ladung

Current & charge, circuits, Ohm's law, Kirchhoff's laws, power, resistivity, exercises with solutions.

Physics
Open

2. Elektrisches Feld

E-Felder, Gauss, Potential, Coulomb, Kondensatoren, Ladevorgang, Dielektrikum, Kraft & Energie, Fluss.

Physics
Open

3. Magnetisches Feld

Magnetismus, Induktion, Wechselstrom

Physics
Open
Linear Algebra

1. Basics

Lineare Gleichungssysteme, Lösungsfälle, Rang, Determinante, Invertierbarkeit, Homogene Systeme.

Linear Algebra
Open

2. Matrizen

Multiplikation, Dreiecksmatrix, Transponierte, Inverse, Gauss-Jordan, Orthogonal, Symmetrisch, LR Zerlegung.

Linear Algebra
Open