Multivariable Calculus/Calculus & Geometry textbook suggestions

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The discussion centers on finding suitable textbooks for a university course in multivariable calculus, particularly after a previous experience without adequate resources. Suggestions include well-regarded texts such as "Multivariable Calculus" by Edwards and Penney, Courant, and Apostol, noted for their mathematical rigor. Alternatives like "Div, Grad, Curl and All That" by Schey and "Vector Calculus" by Marsden and Tromba are recommended for more intuitive understanding. Participants also mention "Stewart's Multivariable Calculus" for its accessibility and Howard Anton's "Calculus: A New Horizon" for practical applications. Additionally, a free online resource covering relevant topics is provided, ensuring a comprehensive study approach.
chris_0101
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Hello all,

I am currently in University and I am retaking a course that I dropped last year due to the fact that there was no textbook and the time I spent in the course was a frantic scramble for reliable information and attempting to understand what the professor was teaching. I have looked before and the only textbook that I found that was remotely close to the material that is covered in the course is Multivariable Calculus by Edwards and Penney. I am asking the community for any suggestions for textbooks that cover most, if not all of the topics listed below:

- Differentiation in Several Variables
Partial derivatives, directional derivatives, del operator, Mean-value theorem for a function of several variables, differentiation through an integral, Leibniz's Rule 2nd order derivatives and Clairaut's theorem, Hessian Matrix. Functions from several variables to several variables, Jacobian Matrix

- Inverse - and Implicit functions in several variables
Inverse function theorem
Implicit function theorem

- Quadratic forms
Matrix Representation
Change of variable & diagonalization by congruence
Positive & Negative definiteness, Semi-definieness, determinantal criteria
Sylvester's Theorem

- Extrema
Local extrema-critical points, local max, local min, saddle points, determinantal tests on the Hessian Matrix
Global extrema-existence for continuous functwions on closed, bounded sets, finiding constrained extrema by the method of Lagrange multipliers

- Curves and Surfaces
Space curves defined parametrically-tangent, normal, binormal, arc length, curvature, torsion
Surfaces-implicit and parametric definitions-tangent plane, normal line
Space curves defined as intersecting surgaces, related quadratic & cubic forms

- Integration in several Variables
Multiple and iterated integrals
Change of order of variables
Change of variable formula in general
Polar, cylindrical & spherical coordinates
Line integrals, consecutive and non-consecutive vector fields, curl operator
Surface integrals, projection onto a plane, parametric surgace integrals
Stokes' theorem, boundary curve, orientation
Gauss' theorem, boundary surgace, div operator

Any suggestions will be greatly appreciated and sorry for the long list, I didn't want to leave anything out.
 
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I fully second Apostol and Courant.
 
Apostol and Courant are excellent but they are mathematically rigorous and I don't know if that is what you want. If not, then there is the book by Schey Div, Grad, Curl and All That for intuition; Marsden and Tromba Vector Calculus is an intermediate sort of book; and the old favourite is Stewart Multivariable Calculus or the relevant chapters in his Calculus. Stewart gives the simplest presentation of calculus.

I suggest going to the library and looking through all these books and deciding for yourself which one best suites your needs.
 
any multivariable calculus text will fit your description..
 
I agree that Courant and Apostol are NOT light reads. Stewart has an excellent MV book that is good for all audiences. A lesser known book is Howard Anton's Calculus, A new horizon, which has a lot of good applications of calc added in. Of course the Khan Academy has very easy-to-understand lectures, but not in all of the above mentioned topics.
 

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