ABSTRACT
The calculus established by Isaac Newton and Gottfried Wilhelm Leibniz is fundamental to many branches of sciences and engineering. In traditional calculus courses, limits, differentiations, integrals, series expansions such as Taylor series and Fourier series expansions for single-variable and multivariable functions are the main topics discussed. The analytical solutions to these problems can be obtained by the direct use of the corresponding functions provided by the Symbolic Math Toolbox of MATLAB which will be discussed in Section 3.1. The Taylor series expansions for single-and multivariable functions as well as the Fourier series expansions are discussed in Section 3.2. Moreover, the series summation and product problems are discussed. Sections 3.5 and 3.6 present methods for path integrals, line integrals and surface integrals. Most of the materials presented in this chapter are symbolicbased, which cannot be solved using conventional computer programming languages such as C for average users. Computer mathematics languages such as MATLAB should be used instead.
