ABSTRACT
This chapter provides physicists through the steps of calculating derivatives and integrals. It discusses how to perform John R. Taylor series expansions, and apply the results to approximations where certain variables may be very small or very large. The chapter describes that many important functions cannot be integrated analytically and also discusses how to carry out numerical integration. Mathematica is aware of many special functions and their derivatives. Physics applications will often make use of derivative vector calculus with operators like gradient, divergence, curl, and the Laplacian. The indefinite integral, or antiderivative, of an expression or function is just as simple to take as a derivative. "Integrate" is used to compute definite integrals, but the second argument is a list that includes the lower and upper limits as well as the integration variable. Taylor's theorem, from mathematics, tells physicists that any differentiable function can be expressed in a power series expansion about some point.
