Mathematical and Numerical Methods for Partial Differential Equations

1. Front Matter

   Pages i-xiv

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2. Theory

   1. Front Matter

      Pages 1-1

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   2. Applications of Functional Analysis to Partial Differential Equations

      • Joël Chaskalovic

      Pages 3-61

   3. Finite-Element Method

      • Joël Chaskalovic

      Pages 63-109

3. Worked Problems

   1. Front Matter

      Pages 111-111

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   2. Variational Formulations of Problems with Elliptical Boundary Conditions

      • Joël Chaskalovic

      Pages 113-159

   3. Finite-Element Methods and Standard Differential Problems

      • Joël Chaskalovic

      Pages 161-211

   4. Mechanics of Deformable Solids

      • Joël Chaskalovic

      Pages 213-250

   5. Strength of Materials

      • Joël Chaskalovic

      Pages 251-311

   6. Nonlinear Problems

      • Joël Chaskalovic

      Pages 313-353

4. Back Matter

   Pages 355-358

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This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic.

• Deformable Solid Body Mechanics
• Elliptic Boundary Problems
• Finite-element Mathematics
• Non-linear Problems
• Strength of Materials
• differential Boundary Conditions
• partial differential equations

“This book is addressed and could be very useful to upper level undergraduate and beginning graduate students with a particular focus on degree courses in areas such as engineering, applied mathematics, and physics. The attention which is paid to the applications makes it valuable also for researchers and users of scientific computing. … This book certainly is a good addition to every engineering and computational mathematics library.” (Nicolae Tarfulea, Mathematical Reviews, April, 2015)

“The book can serve as a foundation for a three or four semester course for mechanics students or can be useful as support for all who are studying or teaching applications of mathematical and numerical methods for engineering sciences. It can be useful for all those who wish to see both the mathematical background of numerical algorithms on the one hand, and examples of its effective use in the solution of practical problems on the other hand.” (Iwan Gawriljuk, zbMATH, Vol. 1300, 2015)

• Institut Jean le Rond d'Alembert, University Pierre and Marie Curie, Paris, France

  Joël Chaskalovic

Joel Chaskalovic is a Professor of Applied Mathematics at the University Pierre and Marie Curie in Paris and has written books and published papers in highly ranked journals, including the French Sciences Academy Journal, Journal of Computational Physics, journals in medicine etc.

This reflects the wide spectrum of his research work, which focuses on non-linear mathematical modeling and data mining techniques applied to fluid and solid mechanics, numerical analysis, complexity and randomness, biology and medicine, marketing, media and communication. Professor Chaskalovic has held numerous lectures on all of these topics at conferences worldwide.

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