- 1. Why Computational/Applied Mathematics? Jon M. Ernstberger January, 2010
- 2. The Origins of Calculus I Who are the two people credited with the origination of calculus?
- 3. The Origins of Calculus I Who are the two people credited with the origination of calculus? Hint: Gravity
- 4. The Origins of Calculus I Who are the two people credited with the origination of calculus? Hint: Gravity Newton and Leibniz!
- 5. The Origins of Calculus I Who are the two people credited with the origination of calculus? Hint: Gravity Newton and Leibniz! I Why?
- 6. The Origins of Calculus I Who are the two people credited with the origination of calculus? Hint: Gravity Newton and Leibniz! I Why? Algebra wasn't enough!
- 7. The Origins of Calculus I Who are the two people credited with the origination of calculus? Hint: Gravity Newton and Leibniz! I Why? Algebra wasn't enough! I Can algebra describe: 1. Planetary motion? 2. Area under a nonlinear curve? 3. Oscillation?
- 8. The Origins of Calculus I Who are the two people credited with the origination of calculus? Hint: Gravity Newton and Leibniz! I Why? Algebra wasn't enough! I Can algebra describe: 1. Planetary motion? 2. Area under a nonlinear curve? 3. Oscillation? What's the point? Mathematics has always had a purpose.
- 9. What are Applied and Computational Mathematics? I Applied Mathematics: The branches of mathematics which deal with the application of well-de
- 10. ned mathematical techniques to solve modern problems.
- 11. What are Applied and Computational Mathematics? I Applied Mathematics: The branches of mathematics which deal with the application of well-de
- 12. ned mathematical techniques to solve modern problems. I Computational Mathematics: The branch of applied mathematics which deals with the implementation of those techniques on computers to solve dicult problems.
- 13. What are Applied and Computational Mathematics? I Applied Mathematics: The branches of mathematics which deal with the application of well-de
- 14. ned mathematical techniques to solve modern problems. I Computational Mathematics: The branch of applied mathematics which deals with the implementation of those techniques on computers to solve dicult problems. What's the big deal?
- 15. What are Applied and Computational Mathematics? I Applied Mathematics: The branches of mathematics which deal with the application of well-de
- 16. ned mathematical techniques to solve modern problems. I Computational Mathematics: The branch of applied mathematics which deals with the implementation of those techniques on computers to solve dicult problems. What's the big deal? I These softwares are everywhere!
- 17. What are Applied and Computational Mathematics? I Applied Mathematics: The branches of mathematics which deal with the application of well-de
- 18. ned mathematical techniques to solve modern problems. I Computational Mathematics: The branch of applied mathematics which deals with the implementation of those techniques on computers to solve dicult problems. What's the big deal? I These softwares are everywhere! I Jobs abound for people with these skills!
- 19. What You Can Do: Jet Propulsion Laboratories (JPL) Figure: Images courtesy NASA/JPL-Caltech. Top: Panoramic view from the rover. Lower-right: Overhead shot of Mars Rover. Mathematicians work on: 1. Optimal scheduling of transmissions. 2. Ecient resource use (optimal control!). 3. Design of solar panels.
- 20. What You Can Do: NASA Figure: Courtesy of NASA. Top: Shuttle Discovery. Bottom: Shuttle tiles. I Recall the explosion of the shuttle Columbia on February 1, 2003. I Due to foam insulation o the main tank striking the left wing. I Launched a frenzy over Non-Destructive Evaluation (NDE).
- 21. What You Can Do: NASA(2) Non-Destructive Evaluation Involves: I The use of Tera-Hertz waves (THz). There were only two of these in the U.S. Both owned by NASA. I HIGHLY nonlinear numerical optimization. (If you have data, make a model
- 22. t that data!). I Turn this all into a handheld device for instant identi
- 23. cation of the crack. I This is non-trivial problem with applications in aerospace and nautical engineering.
- 24. What You Can Do: Smart Materials I Nano-positioning (AFM, right top). I Sonar (Terfenol-D). I Jet-engine chevrons. I Energy harvesting (soldiers, ships, cars). Figure: Courtesy of http://www.hec.nasa.gov/ . Figure: Courtesy of http: //www.nanopicoftheday.org Figure: Courtesy of http://aml.seas.ucla.edu/
- 25. What You Can Do: Smart Materials (2) Working with smart materials often requires: I Numerical optimization. I Mathematical modeling.
- 26. What You Can Do: Biological Mathematics I Cancer Modeling (top) I HIV/AIDS Modeling (bottom-right) I Parkinson's Disease (bottom-left) I Heart disease, etc. Figure: Dopamine neuron courtesy of http://www.sciam.com/. Figure: Courtesy of http://www.intmath.com/.
- 27. What You Can Do: MORE! I Encryption I The NSA wants encryption experts. I RSA Encryption I Defense I Attack detection. I Vaccine production. I More BIO I High res. imaging. I Internal processes (circulatory system) I Search Engines (Google) I Computer Science I Parallel computing I Image De-blurring (right)
- 28. Sustainable Energy - Wave/Tidal Energy I Uses the kinetic energy in the waves to generate electricity! I One basically uses the perpetual energy of the moon to power national energy. I Several designs
- 29. What You Need to Know? I Calculus I Dierential Equations (Ordinary and Partial) I Mathematical Modeling I Numerical Analysis I Statistics and Statistical Inference I Abstract and Linear Algebra I Analysis I Intricate knowledge of a programming language. Guess What? The more you know about other mathematical
- 30. elds, the more apt you will be to solve your problem