Mathematical and Numerical Methods for Partial Differential Equations: Applications for Engineering Sciences (Mathematical Engineering)

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 From The Contents: Introduction To Functional Analytical Methods Of Partial Differential Equations -- The Finite Element Method -- Variational Formulations Of Elliptic Boundary Problems -- Finite Elements And Differential Introduction To Functional Analytical Methods Of Partial Differential Equations -- The Finite Element Method -- Variational Formulations Of Elliptic Boundary Problems. By Joël Chaskalovic. Front Matter....Pages i-xiv Front Matter....Pages 1-1 Applications of Functional Analysis to Partial Differential Equations....Pages 3-61 Finite-Element Method....Pages 63-109 Front Matter....Pages 111-111 Variational Formulations of Problems with Elliptical Boundary Conditions....Pages 113-159 Finite-Element Methods and Standard Differential Problems....Pages 161-211 Mechanics of Deformable Solids....Pages 213-250 Strength of Materials....Pages 251-311 Nonlinear Problems....Pages 313-353 Back Matter....Pages 355-358