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This book contains the solutions of all the exercises of my book: Principles of Tensor Calculus. These solutions are sufficiently simplified and detailed for the benefit of readers of all levels particularly those at introductory levels.
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.
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.
The ideal review for your tensor calculus course More than 40 million students have trusted Schaum’s Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum’s Outlines cover everything from math to science, nursing to language. The main feature for all these books is the solved problems. Step-by-step, authors walk readers through coming up with solutions to exercises in their topic of choice. 300 solved problems Coverage of all course fundamentals Effective problem-solving techniques Complements or supplements the major logic textbooks Supports all the major textbooks for tensor calculus courses
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
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.
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.
Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.