Mathematical Methods for Mechanics

1. Front Matter

   Pages I-XVI

   PDF

2. Mathematical Auxiliaries

   • Eckart W. Gekeler

   Pages 1-77

3. Numerical Methods

   • Eckart W. Gekeler

   Pages 79-142

4. Optimization

   • Eckart W. Gekeler

   Pages 143-192

5. Variation and Control

   • Eckart W. Gekeler

   Pages 193-240

6. The Road as Goal

   • Eckart W. Gekeler

   Pages 241-300

7. Mass Points and Rigid Bodies

   • Eckart W. Gekeler

   Pages 301-357

8. Rods and Beams

   • Eckart W. Gekeler

   Pages 359-386

9. Continuum Theory

   • Eckart W. Gekeler

   Pages 387-434

10. Finite Elements

    • Eckart W. Gekeler

    Pages 435-502

11. A Survey on Tensor Calculus

    • Eckart W. Gekeler

    Pages 503-559

12. Case Studies

    • Eckart W. Gekeler

    Pages 561-576

13. Appendix

    • Eckart W. Gekeler

    Pages 577-598

14. Back Matter

    Pages 599-624

    PDF

Mathematics is undoubtedly the key to state-of-the-art high technology. It is aninternationaltechnicallanguageandprovestobeaneternallyyoungscience to those who have learned its ways. Long an indispensable part of research thanks to modeling and simulation, mathematics is enjoying particular vit- ity now more than ever. Nevertheless, this stormy development is resulting in increasingly high requirements for students in technical disciplines, while general interest in mathematics continues to wane at the same time. This book and its appendices on the Internet seek to deal with this issue, helping students master the di?cult transition from the receptive to the productive phase of their education. The author has repeatedly held a three-semester introductory course - titled Higher Mathematics at the University of Stuttgart and used a series of “handouts” to show further aspects, make the course contents more motiv- ing, and connect with the mechanics lectures taking place at the same time. One part of the book has more or less evolved from this on its own. True to the original objective, this part treats a variety of separate topics of varying degrees of di?culty; nevertheless, all these topics are oriented to mechanics. Anotherpartofthisbookseekstoo?eraselectionofunderstandablereal- ticmodelsthatcanbeimplementeddirectlyfromthemultitudeofmathema- calresources.TheauthordoesnotattempttohidehispreferenceofNumerical Mathematics and thus places importance on careful theoretical preparation.

• MATLAB
• Mass point
• Mathematica
• algorithm
• algorithms
• finite elements
• learning
• mechanics
• modeling
• modelling
• numerical methods
• optimization

From the reviews:

"Gekeler (Universität Stuttgart, Germany) offers a quality handbook of advanced mathematical concepts as they apply to mechanics; the level and extent of mathematics presented here is not available in any other mechanics work … . The volume also covers numerical methods applied to mechanical problems with references to MATLAB code. … Includes 209 examples and 248 references. Summing Up: Recommended. Graduate students, researchers, and faculty." (J. D. Fehribach, Choice, Vol. 46 (11), July, 2009)

• Institut für Angewandte Analysis und Numerische Simulation (IANS), Universität Stuttgart, Germany

  Eckart W. Gekeler

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