How Long to Read An Introduction to Differential Geometry - With the Use of Tensor Calculus

How Long Does it Take to Read An Introduction to Differential Geometry - With the Use of Tensor Calculus?

It takes the average reader 5 hours and 20 minutes to read An Introduction to Differential Geometry - With the Use of Tensor Calculus by Luther Pfahler Eisenhart

Assuming a reading speed of 250 words per minute. Learn more

Description

AN INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH USE OF THE TENSOR CALCULUS By LUTHER PFAHLER EISENHART. Preface: Since 1909, when my Differential Geometry of Curves and Surfaces was published, the tensor calculus, which had previously been invented by Ricci, was adopted by Einstein in his General Theory of Relativity, and has been developed further in the study of Riemannian Geometry and various generalizations of the latter. In the present book the tensor calculus of cuclidean 3-space is developed and then generalized so as to apply to a Riemannian space of any number of dimensions. The tensor calculus as here developed is applied in Chapters III and IV to the study of differential geometry of surfaces in 3-space, the material treated being equivalent to what appears in general in the first eight chapters of my former book with such additions as follow from the introduction of the concept of parallelism of Levi-Civita and the content of the tensor calculus. LUTHER PFAHLER EISENHART. Contents include: CHAPTER I CURVES IN SPACE SECTION PAGE 1. Curves ami surfaces. The summation convention 1 2. Length of a curve. Linear element, 8 3. Tangent to a curve. Order of contact. Osculating plane 11 4. Curvature. Principal normal. Circle of curvature 16 5. TBi normal. Torsion 19 6r The Frenet Formulas. The form of a curve in the neighborhood of a point 25 7. Intrinsic equations of a curve 31 8. Involutes and evolutes of a curve 34 9. The tangent surface of a curve. The polar surface. Osculating sphere. . 38 10. Parametric equations of a surface. Coordinates and coordinate curves trT a surface 44 11. 1 Tangent plane to a surface 50 tSffDovelopable surfaces. Envelope of a one-parameter family of surfaces. . 53 CHAPTER II TRANSFORMATION OF COORDINATES. TENSOR CALCULUS 13. Transformation of coordinates. Curvilinear coordinates 63 14. The fundamental quadratic form of space 70 15. Contravariant vectors. Scalars 74 16. Length of a contravariant vector. Angle between two vectors 80 17. Covariant vectors. Contravariant and covariant components of a vector 83 18. Tensors. Symmetric and skew symmetric tensors 89 19. Addition, subtraction and multiplication of tensors. Contraction.... 94 20. The Christoffel symbols. The Riemann tensor 98 21. The Frenet formulas in general coordinates 103 22. Covariant differentiation 107 23. Systems of partial differential equations of the first order. Mixed systems 114 CHAPTER III INTRINSIC GEOMETRY OF A SURFACE 24. Linear element of a surface. First fundamental quadratic form of a surface. Vectors in a surface 123 25. Angle of two intersecting curves in a surface. Element of area 129 26. Families of curves in a surface. Principal directions 138 27. The intrinsic geometry of a surface. Isometric surfaces 146 28. The Christoffel symbols for a surface. The Riemannian curvature tensor. The Gaussian curvature of a surface 149 29. Differential parameters 155 30. Isometric orthogonal nets. Isometric coordinates 161 31...

How long is An Introduction to Differential Geometry - With the Use of Tensor Calculus?

An Introduction to Differential Geometry - With the Use of Tensor Calculus by Luther Pfahler Eisenhart is 320 pages long, and a total of 80,000 words.

This makes it 108% the length of the average book. It also has 98% more words than the average book.

How Long Does it Take to Read An Introduction to Differential Geometry - With the Use of Tensor Calculus Aloud?

The average oral reading speed is 183 words per minute. This means it takes 7 hours and 17 minutes to read An Introduction to Differential Geometry - With the Use of Tensor Calculus aloud.

What Reading Level is An Introduction to Differential Geometry - With the Use of Tensor Calculus?

An Introduction to Differential Geometry - With the Use of Tensor Calculus is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy An Introduction to Differential Geometry - With the Use of Tensor Calculus?

An Introduction to Differential Geometry - With the Use of Tensor Calculus by Luther Pfahler Eisenhart is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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