Vectors and Tensors: Mathematical Preliminaries and Transformations

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Elements of Lie Groups and Algebras

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

Gaussian Curvature in Plates

Explores Gaussian curvature, principal curvatures, and nonlinear strain in thin elastic plates.

Laminate Analysis: Introduction

Introduces the theory behind laminates and their applications in different industries.

Tensors and Lorentz Transformations

Covers tensors, Lorentz transformations, and electrodynamics in relativistic notation.

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Mechanics of Kirchhoff Rods I

Explores the mechanics of slender structures, introducing concepts like finite strain and finite rotation theory.

Stress and Strain: Generalization to 3D

Covers stress equilibrium, strain, and the generalization of stress to 3D, introducing Hooke's Law and analyzing structures with axial loads.

Special and General Relativity

Introduces special and general relativity, Einstein equations, and gravitational dynamics.

Mechanics of Kirchhoff Rods I

Covers the mechanics of slender structures, focusing on exact kinematics and equilibrium equations of rods.