Author: fruity [ 31 Jul 2012, 18:55 ] Post subject: Chapter 10 - Problem with Xi Hi,At page 187, is introduced:But I'm not sure what is meant by this.Somewhere is written that but I simply don't understand this section. For example, doesn't return a vector, right? Why is then called a 'vector field'?Furthermore, I still wonder what is 'dx' and the '1-form'. I think, I miss anything to understand this section.Does anyone know how it works?Greetings,fruity

 Author: vasco [ 31 Jul 2012, 20:31 ] Post subject: Re: Chapter 10 - Problem with Xi You may or may not find it useful to read this discussion in the forum:viewtopic.php?f=4&t=1439

 Author: vasco [ 31 Jul 2012, 20:39 ] Post subject: Re: Chapter 10 - Problem with Xi here is an operator, so

 Author: vasco [ 31 Jul 2012, 20:58 ] Post subject: Re: Chapter 10 - Problem with Xi can be thought of as a vector since it is the derivative in the direction of the x axis.

 Author: fruity [ 31 Jul 2012, 22:31 ] Post subject: Re: Chapter 10 - Problem with Xi Thanks... I will have to think about it (,too).

 Author: fruity [ 01 Aug 2012, 07:47 ] Post subject: Re: Chapter 10 - Problem with Xi Ok, I what I've understood now: is the direction we want to calculate the slope in. is the covector to the vector along the contour, but I'm not sure. There is the equation , which says me that the slope vanishes when the vector points in the right direction (along the contour). also says me that has to be the covector of , right? I think I still miss something related to ...vasco wrote: here is an operator, so So this equation in the book didn't mean the vector but the operator or , which returns a number...Furthermore, is called a vector field. Is now an operator or a vector or a vector field?

 Author: vasco [ 01 Aug 2012, 11:50 ] Post subject: Re: Chapter 10 - Problem with Xi fruity wrote:Thanks... I will have to think about it (,too).fruity wrote:Ok, I what I've understood now: is the direction we want to calculate the slope in. is the covector to the vector along the contour, but I'm not sure. There is the equation , which says me that the slope vanishes when the vector points in the right direction (along the contour). also says me that has to be the covector of , right? I think I still miss something related to ... is not a vector, but a scalar field on S (see page 183 section 10.2 near the top), so you can't write . is also not a vector.

 Author: fruity [ 01 Aug 2012, 18:18 ] Post subject: Re: Chapter 10 - Problem with Xi Sorry, I meantand. What I still don't understand is why should "give the direction of the contours" (Fig. 10.8). Isn't it the same as ?

 Author: vasco [ 02 Aug 2012, 07:09 ] Post subject: Re: Chapter 10 - Problem with Xi Hi fruityBy the way I don't understand this topic either, I'm just hoping that by discussing it with someone else I might get there.

 Author: fruity [ 02 Aug 2012, 09:12 ] Post subject: Re: Chapter 10 - Problem with Xi Thanks for your help. I think what I know now is enough for reading the next chapters...Maybe the use of these things in later chapters will help, too.

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