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This is the modified version of "Vector Calculus" by Michael Corral. The modifications were made by Anton Petrunin, while teaching a calculus course at Penn State, Fall 2016. This book covers calculus in two and three variables. It is suitable for a one-semester course, normally known as “Vector Calculus”, “Multivariable Calculus”, or simply “Calculus III”. The prerequisites are the standard courses in single-variable calculus (also known as Calculus I and II). The exercises are divided into three categories: A, B and C. The A exercises are mostly of a routine computational nature, the B exercises are slightly more involved, and the C exercises usually require some effort or insight to solve. A crude way of describing A, B and C would be “Easy”, “Moderate” and “Challenging”, respectively. However, many of the B exercises are easy and not all the C exercises are difficult. Answers and hints to most odd-numbered and some even-numbered exercises are provided in Appendix A.
There are a few exercises that require the student to write a computer program, for example, the Monte Carlo method for approximating multiple integrals, in Section 4.4. The code samples in the text are in the Java programming language, hopefully with enough comments so that the reader can figure out what is being done even without knowing Java. Those exercises do not mandate the use of Java, so students are free to implement the solutions using the language of their choice. While it would have been simple to use a scripting language like Python, and perhaps even easier with a functional programming language (such as Haskell or Scheme), Java was chosen due to its ubiquity, relatively clear syntax, and easy availability for multiple platforms.
Vectors in Euclidean Space.
Curves.
Functions of Several Variables.
Multiple Integrals.
Line and Surface Integrals.
Appendix A: Answers and Hints to Selected Exercises.
GNU Free Documentation License.
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