- #1
osnarf
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Sorry if this is in the wrong forum, it wouldn't let me post in the forum i tried first.
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I'm just about to finish up with Spivak's Calculus, and I'm trying to figure out where I should go to next. I've taken Calculus 1-3 and Differential Equations (just an introductory class to ODE's), and would like to repeat this sequence (with more rigor) before I progress any further (I would like to study advanced calc afterwards), which is why i started with Spivak (Seemed to cover Calculus 1-2). I would like to get to differential equations as soon as possible though (unless its not a good idea) because I have some classes coming up in engineering and physics that make use of them. I've pretty much decided on using Morris Tenenbaum and Harry Pollard's Ordinary Differential Equations, but am always open to suggestions.
The likely option for Calculus 3 seemed to be calculus on manifolds at first, but I read more about it and am not so sure anymore. As I understand it, the book is about differential forms, not vector calculus. Is this still multi-variable calculus, just a different way of thinking, or is it something new altogether? More importantly, if it is just a different way of doing multi-variable calc, if I go this route, would I still be well equipped to handle an ODE book and then a PDE book, or should I try to find a good book on vector multi-variable calculus instead?
Also, I was told that in order to study multi-variable calculus from a rigorous standpoint, it is beneficial to study linear algebra first. I've never taken a course on this, so would it be a good idea to go through a linear algebra book before I move to a multi-variable calculus book or is it something the book will develop along the way as needed and i can do linear algebra later?
So, to summarize:
- what are the differences between differential forms and vector calc, and will they both allow me to progress equally in differential equations after?
- is it necessary to study linear algebra first before multi-variable calc or would i be alright to
do linear algebra at a later time?
- what is your suggestion of which books to read and in which order? (In order to get to diff eq as soon as possible, and after multi-variable calc and diff eq be ready to do advanced calc).
Thank you for your help, I appreciate it
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I'm just about to finish up with Spivak's Calculus, and I'm trying to figure out where I should go to next. I've taken Calculus 1-3 and Differential Equations (just an introductory class to ODE's), and would like to repeat this sequence (with more rigor) before I progress any further (I would like to study advanced calc afterwards), which is why i started with Spivak (Seemed to cover Calculus 1-2). I would like to get to differential equations as soon as possible though (unless its not a good idea) because I have some classes coming up in engineering and physics that make use of them. I've pretty much decided on using Morris Tenenbaum and Harry Pollard's Ordinary Differential Equations, but am always open to suggestions.
The likely option for Calculus 3 seemed to be calculus on manifolds at first, but I read more about it and am not so sure anymore. As I understand it, the book is about differential forms, not vector calculus. Is this still multi-variable calculus, just a different way of thinking, or is it something new altogether? More importantly, if it is just a different way of doing multi-variable calc, if I go this route, would I still be well equipped to handle an ODE book and then a PDE book, or should I try to find a good book on vector multi-variable calculus instead?
Also, I was told that in order to study multi-variable calculus from a rigorous standpoint, it is beneficial to study linear algebra first. I've never taken a course on this, so would it be a good idea to go through a linear algebra book before I move to a multi-variable calculus book or is it something the book will develop along the way as needed and i can do linear algebra later?
So, to summarize:
- what are the differences between differential forms and vector calc, and will they both allow me to progress equally in differential equations after?
- is it necessary to study linear algebra first before multi-variable calc or would i be alright to
do linear algebra at a later time?
- what is your suggestion of which books to read and in which order? (In order to get to diff eq as soon as possible, and after multi-variable calc and diff eq be ready to do advanced calc).
Thank you for your help, I appreciate it