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Review of Engineering Mathematics Course Structure

Review of Engineering Mathematics Course Structure. Yun-Che Wang ( 王雲哲 ) Department of Civil Engineering National Cheng Kung University Tainan, Taiwan 70101. Outline. Why we need to improve ? What happened in the past ? How to improve ? Conclusions. Why we need to improve ?.

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Review of Engineering Mathematics Course Structure

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  1. Review of Engineering Mathematics Course Structure Yun-Che Wang (王雲哲) Department of Civil Engineering National Cheng Kung University Tainan, Taiwan 70101

  2. Outline • Why we need to improve ? • What happened in the past ? • How to improve ? • Conclusions

  3. Why we need to improve ? • Modernization of current technology requires more advanced mathematics and less irrelevant math! Pure mathematics Pure mathematics Mathematical physics Engineering mathematics Mathematical physics Engineering mathematics

  4. Why we need to improve ? (cont’d) • The root of engineering is in pure and apply mathematics • Modern engineering mathematics should contain more pure/applied mathematics • In the future, there may be no difference in engineering mathemtics and mathematical physics

  5. Why we need to improve ? (cont’d) Examples: • Calculus of variations • Asymptotic analysis (Perturbation theory) • Tensor analysis • Topology: differential topology • Nonlinear differential equation

  6. Why we need to improve ? (cont’d) Example ① : Calculus of variations NASA's Phoenix space craft 'on track' for Mars landing by Rich Bowden - May 22 2008, 21:20 Artist's impression of probe on Mars

  7. Why we need to improve ? (cont’d) Example ② : Asymptotic analysis (Perturbation theory) • Boundary layers of fluid flow

  8. Why we need to improve ? (cont’d) Example ② : Asymptotic analysis (Perturbation theory) • Insects fly Syrphid Flies Dragonflies These large insects may be seen soaring and darting about near and over ponds and streams in a manner to arouse the envy of the most daredevil aviator. They both catch and eat their insect prey while flying. Mosquitoes and other flies make up a large part of their diet. Syrphid flies are commonly called flower flies - they may be brightly colored and many resemble wasps and bees hovering over flowers. However, they do not sting. The larvae of most species are predaceous feeding on aphids or the young of termites, ants or bees.

  9. Why we need to improve ? (cont’d) Example ③ : Tensor analysis black hole

  10. Why we need to improve ? (cont’d) Example ④ : Topology: Differential topology • Seven Bridges of Königsberg  

  11. Why we need to improve ? (cont’d) Example ④ : Topology: Differential topology The most efficient way to pack different-sized circles together is not obvious. • packing – Sphere packing finds practical application in the stacking of oranges.

  12. Why we need to improve ? (cont’d) Example ⑤ : Nonlinear differential equation pendulum Topology and nonlinear differential equations form the basis of studying nonlinear dynamics, as pioneered by H. Poincare

  13. What happened in the past ? • We choose the 7 colleges and 20 departments to compare the difference. Internal Abroad

  14. ME ME ME ME ME ME ME CE CE CE CE CE CE CE Abroad Internal EE EE EE EE EE PHY Berkeley NCKU MIT NTU Manchester NTKU Singapore

  15. What happened in the past ? (cont.) Textbooks:

  16. Common Topics:

  17. Ｖ－ Subject Ｏ － Option

  18. Ｖ－ Subject Ｏ － Option

  19. Ｖ－ Subject Ｏ － Option ＊ － Graduate

  20. Ｖ－ Subject

  21. How to improve ? Methods: • Offer more math courses. • Computer-aided math courses • Restructure math courses.

  22. How to improve ? (cont.) Method① : Offer more math courses. Counter example – Special functions: • Bessel function • Bernoulli function • Legendre function • hypergeometric function • Hermite function

  23. How to improve ? (cont.) Method② : Computer-aided mathematics MathematicaTM MatlabTM Proponents of this idea emphasize the concepts of mathematics; not the hand-writing of equations

  24. How to improve ? (cont.) Method③ : Restructure math courses. — Embed math into engineering or physics courses. Ex1. Electrical Dynamics  potential solution technology to PDE, Fourier transform, …… Ex2. General Relativity  tensor, differential topology, ……

  25. Conclusions • Construct solid pathways from pure/applied mathematics to engineering mathematics • Increase learning motivations by using specific physical examples • Increase learning efficiency by less focusing outdated solution techniques • Emphasize mathematical concepts through familiarizing solution techniques • Re-structure engineering math course framework

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