Differential Geometry of Surfaces

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Coordinate Systems: Polar, Cylindrical, Spherical

Covers position, velocity, and acceleration in polar, cylindrical, and spherical coordinate systems.

Tensors and Lorentz Transformations

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

Mechanics of Slender Structures: Final Review and Overview

Covers the main learning objectives of ME-411, focusing on dimensional analysis, scalings, and mechanical elements.

Structural Mechanics: Beam Bending and Boundary Conditions

Explores the moment-curvature relation for beams, emphasizing stress distribution and typical boundary conditions.

Continuum Mechanics: Mass Conservation

Explores mass conservation in continuum mechanics, covering stress, dynamics, constitutive laws, and solid deformation.

Mechanics of Slender Structure

Covers the expression of the Kirchhoff-St. Venant energy in a covariant setting and the equilibrium equations for spherical shells, among other topics.

Plates II: Föppl-von Kármán Equations

Explores the theory of plates, including bending and stretching energies, and the Föppl-von Kármán Equations.

Christoffel Symbols and Gravity Before Einstein

Introduces Christoffel symbols and gravity concepts before Einstein, discussing mathematical tensors and the Nobel Prize in Physics.

Differential Geometry: Surfaces

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

Stress Components & Transformation of Tensors

Covers stress components, tensor transformation, and invariants in continuum mechanics.