chapter I Mathematical foundation -- chapter 1 The foundations of calculus of variations -- chapter 2 Constrained variational problems -- chapter 3 Multivariate functionals -- chapter 4 Higher order derivatives -- chapter 5 The inverse problem of the calculus of variations -- chapter 6 Direct methods of calculus of variations -- chapter II Engineering applications -- chapter 7 Differential geometry -- chapter 8 Computational geometry -- chapter 9 Analytic mechanics -- chapter 10 Computational mechanics -- chapter Closing Remarks -- chapter Notation -- chapter List of Tables -- chapter List of Figures.