ABSTRACT
The calculus established by Isaac Newton and Gottfried Wilhelm Leibniz is fundamental to many branches of sciences and engineering. This chapter discusses Taylor series expansions for univariate and multivariate functions as well as the Fourier series expansions and also discusses the sum and product of sequences problems. It explains traditional calculus courses, limits, differentiations, integrals, series expansions such as Taylor series and Fourier series expansions for univariate and multivariate functions. The int() function provided in the Symbolic Math Toolbox of MATLAB can be used directly to evaluate the indefinite integrals to given functions. The definite integrals and improper integrals are also part of calculus. The chapter discusses Taylor series expansions to univariate and multivariate functions. It summarizes the concepts and integration method for path and line integrals. Path integrals are originated from the evaluation of the total mass of a spatial wire with unevenly distributed density.
