1. College of Engineering and Science Louisiana Tech University College of Engineering and Science Connecting Mathematics with Engineering and the Sciences Bernd S. W. Schröder Program of Mathematics and Statistics (Chautauqua workshop)

2. Goals. §Present examples and ideas. §Seed/generate further ideas. §Slides are available for the asking. College of Engineering and Science

3. Why is a soda can shaped that way? §Material savings §Schematic has actual industry specs College of Engineering and Science

4. Heights of towers. §How tall is that thing? College of Engineering and Science

5. What does this sign mean? §Is this really steep? §Careful with web references. College of Engineering and Science

6. Reading Oscilloscopes §Tell me the frequency and the amplitude of that voltage.  The x-axis is scaled in steps of 250 μ s. §The y-axis is scaled in steps of 1V. College of Engineering and Science

7. How’s it hanging? §Do we need the derivation? College of Engineering and Science

8. Checking the shape §Just match the shapes. College of Engineering and Science

9. Don’t believe that computer. §Find the quirks and weaknesses of your CAS (if there still are any) §Plot (2^4)^x – (2^x)^4 §Also, symbolic integration weaknesses. College of Engineering and Science

10. Volumes of rotation in daily life. College of Engineering and Science

13. Where do those formulas come from? §Do a decent center of mass formula, not the 1/2f^2 abomination. §p. 156 for moments §(algebra gets tough because the integral is not in the right form) College of Engineering and Science

14. Where do those formulas come from? §Motivate curvature via dynamics. §Double check: Compute normal component of the acceleration for a circle, compare with centripetal force from elementary physics. College of Engineering and Science

15. Applied Vector Fields §Vector fields §Gradient fields, physics §Line integrals, work, fundamental theorem §Surface integrals, throughput, Gauss’ and Stokes’ Theorems College of Engineering and Science

16. Conceptual Surface Integrals §Emphasis on throughput §Visualization with fluids, electricity, magnetism: “I’m in … engineering, now you’re speaking my language.” §Show motion §Conceptual  “Easy” (a-k study vs. employ) College of Engineering and Science

17. Motion, Motion, Motion §http://www2.latech.edu/~schroder/video.htm College of Engineering and Science

18. Find the mass of the earth. §p. 254 §Can also do geostationary orbit (in several ways, also see Stewart’s Kepler project) College of Engineering and Science

19. The Laplace Operator in Other Coordinate Systems §Don’t verify: derive. §(Careful with instructions. Sum. 2006) College of Engineering and Science

20. Where do the PDEs in Physics come from? §The divergence of the electric field is proportional to the charge density because … College of Engineering and Science

21. Quick Heat Equation §p.331 §Navier Stokes is overkill §Green’s Theorem is a curiosity? College of Engineering and Science

22. The power plant in Millinocket §Stewart. College of Engineering and Science

23. Let’s analyze that spring mass system. College of Engineering and Science

24. Analyzing the spring mass system §The measured period really is the predicted period (now talk design) College of Engineering and Science

25. Laplace Transforms and Circuits. §Can compute the voltage coming out of an AC/DC converter (p.142) §Requires students to pick up some ideas about circuits. §Why else do we do Laplace transforms? §What’s wrong with picture 2? College of Engineering and Science

26. How does a beam bend? §Real data would help College of Engineering and Science

27. Common sense question may be more effective than derivation? §Can all boundary conditions be combined? College of Engineering and Science

28. Oscillating strings §Flash photos match analytical solution (in Chautauqua directory). §Also have drum membranes. College of Engineering and Science