2 - Symbolic mathematics and mathematical functions

Abstract

This chapter discusses symbolic mathematical operations, including algebraic operations on real scalar variables, algebraic operations on real vector variables, and algebraic operations on complex scalar variables. The concept of a mathematical function is explained and trigonometric functions, logarithms and the exponential function are described in this section. The principal facts and ideas behind trigonometric functions, vectors, and algebra are also listed in this segment. Algebraic operations on real scalar variables are first discussed in the chapter. The basics of algebra are briefly reviewed and algebraic manipulations are further described in another segment of the chapter. Trigonometric functions include information on trigonometric identities, mathematical limits and a useful approximation, general properties of trigonometric functions, and inverse trigonometric functions. Vectors and coordinate systems is the next section of the chapter. It describes vectors in two dimensions, vector algebra in two dimensions, vectors and coordinate systems in three dimensions, and vector algebra in three dimensions. Imaginary and complex numbers and problem solving and symbolic mathematics are the other topics discussed in a section that forms a part of the chapter. The chapter basically introduces symbolic mathematics, which involves the manipulation of symbols instead of performing numerical operations. It presents the algebraic tools needed to manipulate expressions containing real scalar variables, real vector variables, and complex scalar variables. It also introduces ordinary and hyperbolic trigonometric functions, exponentials, and logarithms. A brief introduction to the techniques of problem solving is also included in the chapter.