leahgaeta / Mathematics-Mechanics

Lecture notes and materials from my Applied Mathematics in Mechanics course. Note that this is an ongoing course.

Applied Mathematics in Mechanics

These are lecture notes and other items from my Applied Mathematics in Mechanics course, taught by Professor Douglas Holmes at Boston University (ME 712). This is from the Fall 2020 semester.

Topics Include:

• Dimensional Analysis & Scaling
  • Dimensional Analysis
  • Nondimensionalization
• Perturbation Methods
  • Perturbation Methods
  • Regular Perturbation Methods (IVP)
  • Singular Perturbation
  • Multiple Boundary Layers Problem
  • Multiple Scales: Two-Timing
• Variational Calculus
  • Calculus of Variations
  • First Variations & Geodesics
  • Variational Calculus (Elastica)
  • Lagrange Multipliers
• Dynamical Systems & Stability (a small crash course)
  • Stability & Linearity
  • Stability & Bifurcation
• Differential Geometry (a small crash course)
  • Differential Geometry & Tensor Analysis
  • Differential Geometry & Curved Spaces

Mathematica Notebooks:

• Introduction & Basics - note that I did not create this notebook, Professor Holmes at BU did
• Perturbation Example - note that I did not create this notebook, Professor Holmes at BU did
• More Mathematica notebooks to come!

Literature Reviews:

• Bubble Collapse & Wrinkling
• Adhesion of a Tape Loop

Final Project:

• Presentation of Approximating the Stance Map fo the SLIP Runner Based on Perturbation Approach
  • If the Jupyter Notebook viewer is being weird, a PDF version of the cells as slides can be seen here
• Final Project Paper: Approximating the Stance Map fo the SLIP Runner Based on Perturbation Approach