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Why Computational/Applied Mathematics? 
Jon M. Ernstberger 
January, 2010
The Origins of Calculus 
I Who are the two people credited with the origination of 
calculus?
The Origins of Calculus 
I Who are the two people credited with the origination of 
calculus? Hint: Gravity
The Origins of Calculus 
I Who are the two people credited with the origination of 
calculus? Hint: Gravity 
Newton and Leibniz!
The Origins of Calculus 
I Who are the two people credited with the origination of 
calculus? Hint: Gravity 
Newton and Leibniz! 
I Why?
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!
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?
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.
What are Applied and Computational Mathematics? 
I Applied Mathematics: The branches of mathematics which 
deal with the application of well-de
ned mathematical 
techniques to solve modern problems.
What are Applied and Computational Mathematics? 
I Applied Mathematics: The branches of mathematics which 
deal with the application of well-de
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 are Applied and Computational Mathematics? 
I Applied Mathematics: The branches of mathematics which 
deal with the application of well-de
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?
What are Applied and Computational Mathematics? 
I Applied Mathematics: The branches of mathematics which 
deal with the application of well-de
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!
What are Applied and Computational Mathematics? 
I Applied Mathematics: The branches of mathematics which 
deal with the application of well-de
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!
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.
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).
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
t that data!). 
I Turn this all into a handheld device for instant identi

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Why Computational/Applied Mathematics?

  • 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