Calculus with Curvilinear Coordinates : Problems and Solutions

This book presents problems and solutions in calculus with curvilinear coordinates. Vector analysis can be performed in different coordinate systems, an optimal system considers the symmetry of the problem in order to reduce calculatory difficulty. The book presents the material in arbitrary orthogonal coordinates, and includes the discussion of parametrization methods as well as topics such as potential theory and integral theorems. The target audience primarily comprises university teachers in engineering mathematics, but the book may also be beneficial for advanced undergraduate and graduate students alike. Front Matter ....Pages i-xiv Arc Length and Tangent Vector (Markus Antoni)....Pages 1-38 Differentiation of Field Quantities (Markus Antoni)....Pages 39-56 Work, Line Integral and Potential (Markus Antoni)....Pages 57-74 Integral Theorems of Vector Analysis (Markus Antoni)....Pages 75-122 Back Matter ....Pages 123-124 Preface 5 Acknowledgements 7 Contents 8 Notation 9 List of Figures 10 1 Arc Length and Tangent Vector 12 2 Differentiation of Field Quantities 50 3 Work, Line Integral and Potential 68 4 Integral Theorems of Vector Analysis 86 Index 134