Applied Analysis
Recommended Texts or Study Materials
- D Massatt and S P Shipman: Math 7382: Introduction to Applied Mathematics
- O Gonzalez and A M Stuart: A First Course in Continuum Mechanics
- P D Lax: Functional Analysis
- M Reed and B Simon: Methods of Modern Mathematical Physics, Volume I: Functional Analysis
- R S Strichartz: A Guide to Distribution Theory and Fourier Transforms
- Renardy and Rogers: An Introduction to Partial Differential Equations
Foundational Tools/Techniques/Ideas:
Tools
- Tensor and vector calculus
- Equations of continuum mechanics (including elasticity and electromagnetics)
- Fourier analysis
- Theory of distributions
Ideas
- For some reason, vector calculus is difficult. If you practice it a lot, it will become a powerful tool for all of applied math.
- Gaining intuition for the equations of continuum mechanics will go a long way.
- Fourier analysis is a fundamental "tool" in all of mathematics and never ceases to amaze.
- Distributions are the tool that allows a rigorous treatment of solutions to differential equations where the coefficients are not even differentiable. A typical application is solving the elasticity equations in a medium that is porous at a fine scale.
Common Advisors and Committee Members
| Advisor |
Committee Member 1 |
Committee Member 2 |
| Dr. Advisor Professor 1 |
Dr. Professor 2 |
Dr. Professor 3 |
Previously asked questions
