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Introduction to the Mathematics of Variation
This book is about the calculus of variations which is a subject concerned mainly with optimization of functionals. However, because part of it is based on using ordinary calculus in solving optimization problems, "Calculus of Variations" in its original title is modified to become “Mathematics of Variation”. In fact, the book is essentially a collection of solved problems with rather modest theoretical background and hence it is based on the method of "learning by example and practice" which in our view is the most effective way for learning mathematics and overcoming its difficulties. The main merit of the book is its clarity, intuitive structure and rather inclusiveness as it includes...
Principles of Tensor Calculus
This book is based on my previous book: Tensor Calculus Made Simple, where the development of tensor calculus concepts and techniques are continued at a higher level. Unlike the previous book which is largely based on a Cartesian approach, the formulation in the present book is based on a general coordinate system. The book is furnished with an index as well as detailed sets of exercises to provide useful revision and practice. To facilitate linking related concepts and sections, cross referencing is used extensively throughout the book. The book also contains a number of graphic illustrations to help the readers to visualize the ideas and understand the subtle concepts. The book can be used as a text for an introductory or an intermediate level course on tensor calculus.
Introduction to Differential Geometry of Space Curves and Surfaces
This book is about differential geometry of space curves and surfaces. The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with an index, extensive sets of exercises and many cross references, which are hyperlinked for the ebook users, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.
The Mechanics of Lorentz Transformations
The subject of this book is the mechanics of Lorentz transformations which is commonly investigated under the title of special relativity theory. The motive for setting the subject of investigation as Lorentz transformations instead of special relativity is objectivity. However, we also investigate special relativity thoroughly as a possible interpretation of the mechanics of Lorentz transformations. The book originates from a collection of personal notes and tutorials about topics and applications related to modern physics and tensor calculus. The book includes many solved problems as well as extensive sets of exercises whose solutions are available in another book. The book also contains a...
Tensor Calculus Made Simple
This book is about tensor calculus. The language and method used in presenting the ideas and techniques of tensor calculus make it very suitable for learning this subject by the beginners who have not been exposed previously to this elegant branch of mathematics. Considerable efforts have been made to reduce the dependency on foreign texts by summarizing the main concepts needed to make the book self-contained. The book also contains a significant number of high-quality graphic illustrations to aid the readers and students in their effort to visualize the ideas and understand the abstract concepts. Furthermore, illustrative techniques, such as coloring and highlighting key terms by boldface fonts, have been employed. The book also contains extensive sets of exercises which cover most of the given materials. These exercises are designed to provide thorough revisions of the supplied materials. The solutions of all these exercises are provided in a companion book. The book is also furnished with a rather detailed index and populated with hyperlinks, for the ebook users, to facilitate referencing and connecting related subjects and ideas.
Solutions of Exercises of Introduction to Differential Geometry of Space Curves and Surfaces
This book contains the solutions of the exercises of my book: Introduction to Differential Geometry of Space Curves and Surfaces. These solutions are sufficiently simplified and detailed for the benefit of readers of all levels particularly those at introductory level.
Solutions of Exercises of General Relativity Simplified & Assessed
This book contains detailed solutions of all the 606 exercises of my book: General Relativity Simplified & Assessed. These exercises represent an integral part of the original book as they fill many gaps and provide essential extensions and elaborations.
Elementary Complex Analysis
This book is about complex analysis which is a vital and fascinating branch of mathematics that has many applications in pure and applied mathematics as well as science and engineering. The book is basically a collection of solved problems with a rather modest theoretical background presented in the main text and hence it is largely based on the method of "learning by example and practice". The book can be used as a text or as a reference for an introductory course on this subject as part of an undergraduate curriculum in physics or engineering or applied mathematics. The book can also be used as a source of supplementary pedagogical materials used in tutorial sessions associated with such a course.
