Structural Analysis: Bar Elements

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Rotation between Cartesian frames

Covers the rotation between Cartesian frames and their properties in SO(3) and Euler parameterization.

Virtual Work II: Examples of Potentials

Covers examples of potentials in virtual work for structural mechanics.

Optimization with Constraints

Covers the optimization with constraints and the KKT theorem.

Symmetries of Navier-Stokes Equations

Explores the symmetries of Navier-Stokes equations in periodic boxes, including translations, transformations, rotations, and scaling.

Geometric Transformations in the Plane: Examples

Explores geometric transformations in the plane through rotation and reflection examples, emphasizing analytical formulas and characteristic elements.

Isometries in Euclidean Spaces

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Runge Kutta Method

Covers the Runge Kutta method and its application to optimal control and neural networks.

Physics 1: Normal Acceleration and Spatial Rotations

Explores normal acceleration, spatial rotations, vector rotation, and angular speed concepts in physics.

Conformal Transformations: Part 1

Covers the topic of conformal transformations, including translations, dilations, rotations, and the conformal algebra.

Singular Value Decomposition: Applications and Theorems

Explores the applications and theorems of Singular Value Decomposition in linear algebra, including image processing, matrix rotation, and transition probabilities.