1 - Mathematics

Abstract

This chapter provides basic ideas and guidelines on mathematical functions of various branches of mathematics such as geometry, algebra, trigonometry, differential and integral calculus, analytical geometry, numerical methods, applied statistics, and computer applications. The first section of the chapter discusses sets and functions. A set is a collection of distinct objects or elements. A function can be defined as a set of ordered pairs, denoted as (x, y) such that no two such pairs have the same first element. The chapter also discusses Geometry that deals with angles, polygons, triangles, quadrilaterals, circles and spheres, arcs of circles, concurrencies, similarities, prisms and pyramids, coordinate systems, graphs, vectors, and lengths and areas of plane figures. The chapter describes operator precedence and notation, fractions, rules of addition, rules of multiplication and simple factoring, exponents, logarithms, binomial theorems, progressions, sums of the first “n” natural numbers, solution of different equations, and determinants. The chapter also describes basic trigonometric functions, graphs of trigonometric functions, inverse trigonometric functions, trigonometric properties, solution of plane triangles, hyperbolic functions, and polar coordinate system. The chapter further discusses different orders of derivatives, maxima and minima, different types of differentials and integrals, differential equations, methods of solving ordinary differential equations, and the Laplace Transformation. It discusses analytical geometry—both 2D and 3D—and provides information on symmetry, intercepts, asymptotes, and different forms of equations of straight line, plane, curves, and solids.