# Best Tensor Calculus Books 2020 | Enrich Your Mathematics Knowledge

The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra. Tensors are extensively used in physics as well as image analytics and subspace de-compositions.

Also, the study of mathematics and engineering remains incomplete without the study of tensor algebra. If you want to learn tensor algebra from the very beginning to advanced level. Below are the best tensor calculus books 2020 that will be the best choice for you.

## 1. Introduction to Tensor Analysis and the Calculus of Moving Surfaces

A complete textbook designed for advanced undergraduate and graduate students. The discussion of the calculus of moving surfaces is extended in this book. It provides you with an introduction to tensor analysis. It's very easy to read all about tensor analysis. Not much theory but enough discussion to get you to the point of doing some practical calculations.

What you'll learn-

• Differential geometry on manifolds
• Shape optimization
• Dynamic fluid film equations.
• Discussion of the interplay between algebra and geometry
• Fundamental geometry
• Various exciting applications
• Boundary perturbation of boundary value problems
• Geodesic equations
• Gauss-Bonnet theorem.

## 2. Schaums Outline of Tensor Calculus (Schaum's Outlines)

The book was published by famous Schaum's outline series. Written by the renowned expert and teachers. The main features of this book are helpful solved problems and step by step details on all solved problem.

What you'll learn-

• Around 300 solved problem
• Discussion about all course fundamentals
• Effective problem solving techniques
• Details on all major problems of tensor calculus

## 3. Tensor Analysis on Manifolds (Dover Books on Mathematics) Author: Richard L. Bishop,Samuel I. Goldberg
Published at: 01/12/1980
ISBN: 0486640396

This book introduces you to the essentials of modern vector, tensor analysis. No previous knowledge is needed. The topics are clearly arranged that you can easily find all the topics at a glance. Its essentials for the students of engineering and physics to learn about nature and applications of vectors and tensor analysis on manifolds

What you'll learn-

• Tensor analysis function-theoretical and algebraic aspects
• Vector analysis
• integration theory
• The special structure of tensor analysis
• Clarify the ideas of classical mechanics
• Numerous example and problems

## 4. Tensor Calculus Made Simple

A complete guide for tensor analysis. The method of presentation of ideas and techniques on tensor analysis makes it more preferable for students and researchers. You can use it as your reference book for an introductory course on tensor algebra.

What you'll learn-

• Fundamental equations of a surface
• General coordinate system
• Graphical illustrations of every problem
• Applications of tensor calculus
• Numerous problem and step by step solutions.

## 5. Vectors, Tensors and the Basic Equations of Fluid Mechanics (Dover Books on Mathematics) Author: Rutherford Aris,Mathematics
Published at: 01/01/1990
ISBN: 0486661105

This book introduces you to the essentials of modern vector, tensor, and fluid mechanics. No previous knowledge is needed. The topics are clearly arranged that you can easily find all the topics at a glance. Its essentials for the students of engineering and physics to learn about nature and applications of vectors and tensor.

What you'll learn-

• Calculus of partial differentiation and multiple integrations
• Calculus of Cartesian vectors and tensors
• Equations of motion and energy in cartesian coordinates
• Equations of fluid flow in Euclidean space.
• Equations of surface flow
• Equations for reacting fluids
• 3-dimensional coordinate geometry
• Details on fluid motion and stress in fluids

## 6. Applications of Tensor Analysis (Dover Books on Mathematics)

This amazing book helps you to learn the fundamental ideas and the notation of tensor theory. It covers the introduction of the theory of differentiation of tensors and applied mathematics with dynamics, electricity, elasticity, and hydrodynamics.
What you'll learn-

• Algebraic preliminaries
• Algebraic geometry
• Differential geometry
• Fundamental equations of a surface
• Dynamics of rigid bodies, electricity, and magnetism
• Mechanics of continuous media
• The special theory of relativity

## 7. The Absolute Differential Calculus (Calculus of Tensors) (Dover Books on Mathematics) Author: Tullio Levi-Civita
Published at: 17/04/2013
ISBN: 0486634019
This book was written by famous mathematicians of the twentieth century. The mathematical background is needed for understanding the tensor calculus. It provides introductory theories and basic discussion of fundamental quadratic forms. And it gives you details on absolute differential calculus and explores physical applications
What you'll learn-
• Functional determinants and matrics
• Linear partial determinants
• Algebraic functions
• Curvature-related Riemann's symbols and properties
• Intrinsic geometry
• Gravitational equations and general relativity

## 8. Principles of Tensor Calculus: Tensor Calculus

This well-decorated book helps you to clarify your basics of tensor calculus. No previous knowledge is needed. The topics are clearly arranged that you can easily find all the topics at a glance. It provides various techniques of the tensor equation and solved any kind of calculation problems easily

What you'll learn-

• Cartesian approaches
• General co-ordinate system
• Graphical illustrations of every problem
• Basics of tensor calculus

## 9. Manifolds, Tensors, and Forms: An Introduction for Mathematicians and Physicists

This book introduces you to the essentials of modern differential geometry and topology. Clear definitions and step by step details make it perfect for undergraduate and graduate students. It discusses the very basics of manifolds and tensor.

What you'll learn-

• Multi-linear algebra
• Homology
• Differentiation and integration on manifolds
• Cohomology
• Pseudo-Riemannian geometry
• 250 details exercise
• Classical mechanics
• General relativity and gauge theory
• Electromagnetism

## 10. A Student's Guide to Vectors and Tensors

The most powerful problem-solving tools on vector and tensor with applications of mechanics and electromagnetism. Its essentials for the students of engineering and physics to learn about nature and applications of vectors and tensor. This book provides all basic and practical applications of tensor for engineering students.

What you'll learn-

• Maxwell's equations
• Vector and vector calculus
• Matrices and their algebra
• Interactive solutions to all problems
• Graphical explanations of tensor

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