bibliografia.bib

@book{apostol2007calculus,
  title={Calculus, Volume I},
  author={Apostol, Tom M},
  year={2007},
  publisher={John Wiley \& Sons}
}
@book{apostol2007calculus2,
  title={Calculus, Volume II},
  author={Apostol, Tom M},
  year={2007},
  publisher={John Wiley \& Sons}
}

@book{kay1988schaum,
  title={Schaum's Outline of Tensor Calculus},
  author={Kay, David},
  year={1988},
  publisher={McGraw Hill Professional}
}


@book{krantz2012implicit,
  title={The implicit function theorem: history, theory, and applications},
  author={Krantz, Steven G and Parks, Harold R},
  year={2012},
  publisher={Springer Science \& Business Media}
}

@book{lima2013analise,
  title={Analise real, volume 2: fun{\c{c}}{\~o}es de n vari{\'a}veis},
  author={Lima, Elon Lages},
  year={2013},
  publisher={Impa}
}


@book{guidorizzi2000curso,
  title={Um curso de C{\'a}lculo, vol. 2},
  author={Guidorizzi, Hamilton Luiz},
  year={2000},
  publisher={Grupo Gen-LTC}
}


@article{mcloughlin2012does,
  title={When Does a Cross Product on Rn Exist},
  author={McLoughlin, Peter F},
  journal={arXiv preprint arXiv:1212.3515},
  year={2012}
}


@book{musa2015multivariable,
  title={Multivariable and Vector Calculus: An Introduction},
  author={Musa, Sarhan M and Santos, David A},
  year={2015},
  publisher={Mercury Learning \& Information}
}

@book{winitzki2010linear,
  title={Linear algebra via exterior products},
  author={Winitzki, Sergei},
  year={2010},
  publisher={Sergei Winitzki}
}

@article{sharipov2004quick,
  title={Quick introduction to tensor analysis},
  author={Sharipov, Ruslan},
  journal={arXiv preprint math/0403252},
  year={2004}
}



@book{spivak1965calculus,
  title={Calculus on manifolds},
  author={Spivak, Michael},
  volume={1},
  year={1965},
  publisher={WA Benjamin New York}
}

@book{edwards2013advanced,
  title={Advanced calculus: a differential forms approach},
  author={Edwards, Harold M},
  year={2013},
  publisher={Springer Science \& Business Media}
}


@book{hubbard2015vector,
  title={Vector calculus, linear algebra, and differential forms: a unified approach},
  author={Hubbard, John H and Hubbard, Barbara Burke},
  year={2015},
  publisher={Matrix Editions}
}

@book{munkres1997analysis,
  title={Analysis on manifolds},
  author={Munkres, James R},
  year={1997},
  publisher={Westview Press}
}
@book{marsden2003vector,
  title={Vector calculus},
  author={Marsden, Jerrold Eldon and Tromba, Anthony},
  year={2003},
  publisher={Macmillan}
}
@book{lang1987calculus,
  title={Calculus of several variables},
  author={Lang, Serge},
  year={1987},
  publisher={Springer Science \& Business Media}
}


@book{corral2008vector,
  title={Vector Calculus},
  author={Corral, Michael and others},
  year={2008},
  publisher={Citeseer}
}
@book{matthews2012vector,
  title={Vector calculus},
  author={Matthews, Paul C},
  year={2012},
  publisher={Springer Science \& Business Media}
}
@book{spivak1984calculus,
  title={Calculus },
  author={Spivak, Michael},
  journal={Editorial Revert{\'e}, Barcelona},
  year={1984}
}

@book{@palumbo,
title={Curso de Cálculo de Uma Variável},
  author={Marco Aurélio Palumbo Cabral},
  year={2013}

}

@book{hartmanapex,
  title={APEX Calculus II},
  author={Hartman, Gregory},
  year={2015},
  school={University of Lethbridge}
}

@book{guichard2014calculus,
  title={Calculus: Early Transcendentals},
  author={Guichard, David and Koblitz, Neal and Keisler, H Jerome},
  year={2014},
  publisher={Whitman College}
}

@book{tan2010calculus,
  title={Calculus: Early Transcendentals},
  author={Tan, Soo},
  year={2010},
  publisher={Cengage Learning}
}

@book{stewart2015calculus,
  title={Calculus: Early Transcendentals},
  author={Stewart, James},
  year={2015},
  publisher={Cengage Learning}
}

@book{leithold1972calculus,
  title={The Calculus with Analytic Geometry},
  author={Leithold, Louis},
  volume={1},
  year={1972},
  publisher={Harper \& Row}
}

@book{kline1998calculus,
  title={Calculus: An Intuitive and Physical Approach},
  author={Kline, Morris},
  year={1998},
  publisher={Courier Corporation}
}

@book{edwards1982calculus,
  title={Calculus and Analytic Geometry},
  author={Edwards, Charles Henry and Penney, David E},
  year={1982},
  publisher={Prentice-Hall}
}


@book{courant2011differential,
  title={Differential and Integral Calculus},
  author={Courant, Richard},
  volume={2},
  year={2011},
  publisher={John Wiley \& Sons}
}

@book{spivak1995hitchhiker,
  title={The Hitchhiker's Guide to Calculus},
  author={Spivak, Michael},
  year={1995},
  publisher={Mathematical Assn of America}
}




@book{malta2002calculo,
  title={C{\'a}lculo a Uma Vari{\'a}vel},
  author={Malta, Iaci and Pesco, Sin{\'e}sio and Lopes, H{\'e}lio},
  journal={Uma Introdu{\c{c}}{\~a}o ao},
  year={2002}
}


@book{simmons1985calculus,
  title={Calculus with Analytic Geometry},
  author={Simmons, George F},
  journal={AMC},
  volume={10},
  pages={12},
  year={1985}
}
@book{swokowski1979calculus,
  title={Calculus with Analytic Geometry},
  author={Swokowski, Earl William},
  year={1979},
  publisher={Taylor \& Francis}
}


@article{de2013implicit,
  title={The Implicit and Inverse Function Theorems: Easy Proofs},
  author={de Oliveira, Oswaldo and others},
  journal={Real Analysis Exchange},
  volume={39},
  number={1},
  pages={207--218},
  year={2013},
  publisher={Michigan State University Press}
}

@book{Schoenfeld1978,
  title={Presenting a Strategy for Indefinite Integration},
  author={Schoenfeld, Alan H},
  journal={American Mathematical Monthly},
  pages={673--678},
  year={1978},
  publisher={JSTOR}
}

@book{guidorizzi2001curso,
  title={Um Curso de C{\'a}lculo},
  author={Guidorizzi, Hamilton Luiz},
  year={2001},
  publisher={Livros T{\'e}cnicos e Científicos Editora}
}

@book{dence2009advanced,
  title={Advanced Calculus: A Transition to Analysis},
  author={Dence, Thomas P and Dence, Joseph B},
  year={2009},
  publisher={Academic Press}
}

@book{demidovitch1977problemas,
  title={Problemas e Exercícios de An{\'a}lise Matem{\'a}tica},
  author={Demidovitch, Boris},
  journal={Editora Mir},
  year={1977}
}


@book{fitzpatrick2006advanced,
  title={Advanced Calculus},
  author={Fitzpatrick, Patrick},
  volume={5},
  year={2006},
  publisher={American Mathematical Soc.}
}



@misc{lima2008analise,
  title={Análise Real Volume 1},
  author={Lima, Elon Lages},
  year={2008},
  publisher={Rio de Janeiro: IMPA}
}



@book{mercer2014more,
  title={More Calculus of a Single Variable},
  author={Mercer, Peter R},
  year={2014},
  publisher={Springer}
}

@book{krantz2011integral,
  title={The Integral: a Crux for Analysis},
  author={Krantz, Steven G},
  journal={Synthesis Lectures on Mathematics and Statistics},
  volume={4},
  number={1},
  pages={1--105},
  year={2011},
  publisher={Morgan \& Claypool Publishers}
}


@article{kallam1996investigation,
  title={An Investigation into a Problem-Solving Strategy for Indefinite Integration and Its Effect on Test Scores of General Calculus Students.},
  author={Kallam, Linda G and Kallam, Michael},
  year={1996},
  publisher={ERIC}
}

@book{do2012differential,
  title={Differential forms and applications},
  author={Do Carmo, Manfredo P},
  year={2012},
  publisher={Springer Science \& Business Media}
}

@online{WinNT,
  author = {Paul Dawkins},
  title = {Paul's Online Math Notes},
  urldate = {2015-12-02}
}



@book{abb,
 title = {Flatland},
 author = {E.A. Abbott},
 edition = 7,
 annote = {Classic tale about a creature living in a 2-dimensional world who encounters a higher-dimensional
           creature, with lots of humor thrown in.},
 publisher = {Dover Publications, Inc.},
 year = 1952,
 address = {New York}
}

@book{ar,
 title = {Elementary Linear Algebra: Applications Version},
 author = {H. Anton and C. Rorres},
 edition = 8,
 annote = {Standard treatment of elementary linear algebra.},
 publisher = {John Wiley \& Sons},
 year = 2000,
 address = {New York}
}

@book{arn,
 title = {Mathematical Methods of Classical Mechanics},
 author = {V.I. Arnold},
 edition = {},
 publisher = {Springer-Verlag},
 year = 1978,
 address = {New York}
}

@book{bow,
 title = {Introduction to Elliptic Functions, with Applications},
 author = {F. Bowman},
 edition = {},
 publisher = {Dover},
 year = 1961,
 address = {New York}
}

@book{bss,
 title = {Nonlinear Programming: Theory and Algorithms},
 author = {M.S. Bazaraa and H.D. Sherali and C.M. Shetty},
 edition = 2,
 annote = {Thorough treatment of nonlinear optimization.},
 publisher = {John Wiley \& Sons},
 year = 1993,
 address = {New York}
}

@book{cm,
 title = {A Mathematical Introduction to Fluid Mechanics},
 author = {A.J. Chorin and J.E. Marsden},
 edition = {},
 publisher = {Springer-Verlag},
 year = 1979,
 address = {New York}
}

@book{euc,
 title = {Euclid's Elements},
 author = {Euclid, translated by T.L. Heath},
 edition = {},
 publisher = {Green Lion Press},
 year = 2002,
 address = {Santa Fe, NM}
}

@book{far,
 title = {Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide},
 author = {G. Farin},
 edition = 2,
 annote = {An intermediate-level book on curve and surface design.},
 publisher = {Academic Press},
 year = 1990,
 address = {San Diego, CA}
}

@book{hec,
 title = {Optics},
 author = {E. Hecht},
 edition = 2,
 annote = {An intermediate-level book on optics, covering a wide range of topics.},
 publisher = {Addison-Wesley Publishing Co.},
 year = 1987,
 address = {Reading, MA}
}

@book{bishop2012tensor,
  title={Tensor analysis on manifolds},
  author={Bishop, Richard L and Goldberg, Samuel I},
  year={2012},
  publisher={Courier Corporation}
}
@book{abraham2012manifolds,
  title={Manifolds, tensor analysis, and applications},
  author={Abraham, Ralph and Marsden, Jerrold E and Ratiu, Tudor},
  volume={75},
  year={2012},
  publisher={Springer Science \& Business Media}
}

@article{borisenko1969vector,
  title={Vector and tensor analysis with applications},
  author={Borisenko, Aleksandr Ivanovich and Tarapov, Ivan Evgenʹevich and Balise, Peter L},
  journal={Physics Today},
  volume={22},
  number={2},
  pages={83--85},
  year={1969},
  publisher={AIP}
}


@book{hps,
 title = {Introduction to Probability Theory},
 author = {P.G. Hoel and S.C. Port and C.J. Stone},
 edition = {},
 annote = {An excellent introduction to elementary, calculus-based probability theory. Lots of good exercises.},
 publisher = {Houghton Mifflin Co.},
 year = 1971,
 address = {Boston, MA}
}

@book{fleming2012functions,
  title={Functions of several variables},
  author={Fleming, Wendell H},
  year={2012},
  publisher={Springer Science \& Business Media}
}

@book{hr,
 title = {Physics: Parts 1\&2 Combined},
 author = {D. Halliday and R. Resnick},
 edition = 3,
 publisher = {John Wiley \& Sons},
 year = 1978,
 address = {New York}
}

@book{jac,
 title = {Classical Electrodynamics},
 author = {J.D. Jackson},
 edition = 2,
 annote = {An advanced book on electromagnetism, famous for being intimidating. Most of the mathematics
 will be understandable after reading the present book.},
 publisher = {John Wiley \& Sons},
 year = 1975,
 address = {New York}
}


@book{kui,
 title = {Quaternions and Rotation Sequences},
 author = {J.B. Kuipers},
 edition = {},
 publisher = {Princeton University Press},
 year = 1999,
 address = {Princeton, NJ}
}

@book{mar,
 title = {Classical Dynamics of Particles and Systems},
 author = {J.B. Marion},
 edition = 2,
 annote = {Standard intermediate-level treatment of classical mechanics. Very thorough.},
 publisher = {Academic Press},
 year = 1970,
 address = {New York}
}

@book{mtw,
 title = {Gravitation},
 author = {C.W Misner and K.S. Thorne and J.A. Wheeler},
 edition = {},
 publisher = {W.H. Freeman \& Co.},
 year = 1973,
 address = {New York}
}

@book{one,
 title = {Elementary Differential Geometry},
 author = {B. O'Neill},
 edition = {},
 annote = {Intermediate-level book on differential geometry, with a modern approach based on
           differential forms.},
 publisher = {Academic Press},
 year = 1966,
 address = {New York}
}

@book{pc,
 title = {Quantum Mechanics},
 author = {J.L. Powell and B. Crasemann},
 edition = {},
 publisher = {Addison-Wesley Publishing Co.},
 year = 1961,
 address = {Reading, MA}
}

@book{pm,
 title = {Analytic Geometry},
 author = {M.H. Protter and C.B. Morrey},
 edition = 2,
 annote = {Thorough treatment of elementary analytic geometry, with a rigor not found in most recent books.},
 publisher = {Addison-Wesley Publishing Co.},
 year = 1975,
 address = {Reading, MA}
}

@book{pog,
 title = {Analytical Geometry},
 author = {A.V. Pogorelov},
 edition = {},
 annote = {An intermediate/advanced book on analytic geometry.},
 publisher = {Mir Publishers},
 year = 1980,
 address = {Moscow}
}




@book{rmc,
 title = {Foundations of Electromagnetic Theory},
 author = {J.R. Reitz and F.J. Milford and R.W. Christy},
 edition = 3,
 annote = {Intermediate text on electromagnetism.},
 publisher = {Addison-Wesley Publishing Co.},
 year = 1979,
 address = {Reading, MA}
}

@book{rud,
 title = {Principles of Mathematical Analysis},
 author = {W. Rudin},
 edition = 3,
 publisher = {McGraw-Hill},
 year = 1976,
 address = {New York}
}

@book{sch,
 title = {Div, Grad, Curl, and All That: An Informal Text on Vector Calculus},
 author = {H.M. Schey},
 edition = {},
 annote = {Very intuitive approach to the subject, from a physicist's viewpoint. Highly recommended.},
 publisher = {W.W. Norton \& Co.},
 year = 1973,
 address = {New York}
}



@book{tm,
 title = {Advanced Calculus},
 author = {A.E. Taylor and W.R. Mann},
 edition = 2,
 annote = {Excellent treatment of {$n$}-dimensional calculus. A good book to study after the present book. Many
           intriguing exercises.},
 publisher = {John Wiley \& Sons},
 year = 1972,
 address = {New York}
}

@book{usp,
 title = {Theory of Equations},
 author = {J.V. Uspensky},
 edition = {},
 annote = {A classic on the subject, discussing many interesting topics.},
 publisher = {McGraw-Hill},
 year = 1948,
 address = {New York}
}

@book{wei,
 title = {A First Course in Partial Differential Equations},
 author = {H.F. Weinberger},
 edition = {},
 annote = {A good introduction to the vast subject of partial differential equations.},
 publisher = {John Wiley \& Sons},
 year = 1965,
 address = {New York}
}

@book{do1992riemannian,
  title={Riemannian geometry},
  author={do Carmo Valero, Manfredo Perdigao},
  year={1992}
}

@book{do1976differential,
  title={Differential geometry of curves and surfaces},
  author={Do Carmo, Manfredo Perdigao and Do Carmo, Manfredo Perdigao},
  volume={2},
  year={1976},
  publisher={Prentice-hall Englewood Cliffs}
}