Teaching the module multivariable calculus led me to compile a set of problems with fairly detailed solutions covering the basic topics of multivariable calculus: functions of several variables, partial derivatives, extreme value problems and double integrals.
The module covered chapters 15, 16 and 17 of
- J. Marsden, A. Weinstein, Calculus III . Springer, 1985.
The sections of the problem set are in correspondence with the sections of the textbook. Other textbooks that served as source and inspiration are
- M. Corral, Vector Calculus . 2008.
- G. Hartman, APEX Calculus III . Version 3.0, 2015.
- D. Guichard, Single and Multivariable Calculus . 2016.
- J. Stewart, Calculus. 8th edition. Cengage Learning, 2015.
- G. Thomas, Thomas' Calculus. Twelfth edition. Addison-Wesley, 2010.
Here are the problems and solutions in one file each.
- Functions, graphs, and level surfaces [pdf]
- Introduction to partial derivatives [pdf]
- Linear approximations and tangent planes [pdf]
- The chain rule [pdf]
- Gradients and directional derivatives [pdf]
- Gradients and level surfaces [pdf]
- Maxima and minima [pdf]
- Constrained extrema and Lagrange multipliers [pdf]
- Review exercises [pdf]
- The double integral and iterated integrals [pdf]
- The double integral over general regions [pdf]
- Polar coordinates and the change of coordinates [pdf]
- Applications of the double integral [pdf]
LaTeX SourceThe LaTeX source files are available on GitHub. Two external programs are needed to compile them. To create 3D figures I used Asymptote and 2D figures were created using TikZ with some external calls to gnuplot.
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