- #1

lee.spi

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thanks

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- Thread starter lee.spi
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In summary: Advanced-Calculus-Equations-Vector/dp/0198548176if you read his Advanced calculus book ,you'll get probably the prerequisites you need for it.

- #1

lee.spi

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thanks

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- #2

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If you're brand new to differential geometry, then you should start by learning about curves and surfaces. The prerequisities to this are (rigorous) calculus and linear algebra. Some books here are

- https://www.amazon.com/dp/0132125897/?tag=pfamazon01-20

- https://www.amazon.com/dp/184882890X/?tag=pfamazon01-20

- https://www.amazon.com/dp/0521721490/?tag=pfamazon01-20

Or the very excellent free lecture notes by Shifrin:

- http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf

The topics you should definitely cover are Gaussian curvature, the theorema egregium, the Gauss-Bonnet theorem.

After this, you can go for modern differential geometry. This requires a bit more prerequisites though. For example, you'll need to know basic real analysis, metric spaces and topology. One good book that teaches you the necessary topology is

- https://www.amazon.com/dp/1441979395/?tag=pfamazon01-20

After that you can go to Lee's other books:

https://www.amazon.com/dp/1441999817/?tag=pfamazon01-20

and

https://www.amazon.com/dp/0387983228/?tag=pfamazon01-20

- https://www.amazon.com/dp/0132125897/?tag=pfamazon01-20

- https://www.amazon.com/dp/184882890X/?tag=pfamazon01-20

- https://www.amazon.com/dp/0521721490/?tag=pfamazon01-20

Or the very excellent free lecture notes by Shifrin:

- http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf

The topics you should definitely cover are Gaussian curvature, the theorema egregium, the Gauss-Bonnet theorem.

After this, you can go for modern differential geometry. This requires a bit more prerequisites though. For example, you'll need to know basic real analysis, metric spaces and topology. One good book that teaches you the necessary topology is

- https://www.amazon.com/dp/1441979395/?tag=pfamazon01-20

After that you can go to Lee's other books:

https://www.amazon.com/dp/1441999817/?tag=pfamazon01-20

and

https://www.amazon.com/dp/0387983228/?tag=pfamazon01-20

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- #3

mathwonk

Science Advisor

Homework Helper

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here is a free one that is written by a very skillful writer and accomplished geometer:

I recommend it:

http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf

I recommend it:

http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf

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- #4

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mathwonk said:

I recommend it:

http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf

I already linked that.

Last edited by a moderator:

- #5

mathwonk

Science Advisor

Homework Helper

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ah yes! now i see it. i am glad you also like that one.

- #6

lee.spi

- 21

- 0

i was reading this book , it is a good book , thanks

- #7

NumericalFEA

- 57

- 5

lee.spi said:

thanks

Here is one with an emphasis on numerical methods of differential geometry (especially Chapter 5) with lots of source codes in C/C++:

https://www.amazon.com/dp/0646594044/?tag=pfamazon01-20

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- #8

whyevengothere

- 53

- 3

William L. Burke: Applied Differential Geometry if you know some physics.

- #9

fisicist

- 46

- 7

Shlomo Sternberg: Curvature in Mathematics and Physics

- #10

Daverz

- 1,003

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fisicist said:Shlomo Sternberg: Curvature in Mathematics and Physics

Not an introductory text. You really need to have some familiarity with differential geometry on manifolds to understand it.

- #11

whyevengothere

- 53

- 3

if you read his Advanced calculus book ,you'll get probably the prerequisites you need for it.Daverz said:Not an introductory text. You really need to have some familiarity with differential geometry on manifolds to understand it.

Differential Geometry is a branch of mathematics that studies the properties of curves and surfaces in multidimensional spaces. It uses techniques from calculus and linear algebra to analyze the geometric properties of these objects.

Differential Geometry has many applications in various fields such as physics, engineering, computer graphics, and robotics. It is used to model and analyze the shape and curvature of objects in these fields.

Some popular books for learning Differential Geometry include "Differential Geometry of Curves and Surfaces" by Manfredo do Carmo, "Curves and Surfaces for Computer-Aided Geometric Design" by Gerald Farin, and "Elementary Differential Geometry" by Barrett O'Neill.

Yes, a strong understanding of calculus and linear algebra is necessary for studying Differential Geometry. These concepts are the foundation for many of the techniques and formulas used in this field.

There are many online resources available for learning Differential Geometry, such as lecture notes, video lectures, and online courses. Some popular websites include MIT OpenCourseWare, Khan Academy, and Coursera.

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