Dimensional Analysis: Scaling and Theorems

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Calculus of Variations: Euler's Elastica

Covers Euler's Elastica and the equilibrium shape of a bent beam using variational/energy methods.

Dimensional Analysis of Explosions

Explores dimensional analysis of large explosions using recorded images to predict outcomes based on known parameters.

Dimensional Analysis: Gravitational Constant

Corrects exercise 3 on dimensional analysis using the gravitational constant as an example.

Dimensional Analysis & Scaling Laws

Covers dimensional analysis, physical similarity, and structural mechanics, emphasizing the importance of scaling laws in solving complex problems.

Resonant Sensors: Mass Flow and Measurement

Explores resonant sensors for mass flow and measurement, emphasizing stability and precision.

Understanding Units and the SI System

Explores the importance of units, the development of the SI system, and the shift towards defining units based on physical constants.

Differential Equations: General Solutions and Methods

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Matter and Volume: Atoms and Density

Explains matter, atoms, volume, and density, including characteristics of materials and density calculation.

Linear Second Order ODEs

Covers the solution of linear second order ODEs with constant coefficients and explores the method of variation of parameters.

Dimensional Analysis and Scalings

Covers fundamental concepts of dimensional analysis, physical similarity, and scalings, exploring the importance of expressing physical laws independently of units and the process of parameterizing problems.