Higher Mathematics for Science, Technology and Engineering

This chapter aims mainly to spot the lights on the basis of mathematics of function of one variable, different types, properties. Functions encountered nearly in everything in our daily live and even who works in the field of numerical analysis needs to be in a solid background of the mathematics of functions.

The basis of the derivative for functions of one variable is introduced herein. The chapter started from the basic definition of the derivative, geometric meaning and growing up to the derivatives of the basic functions. The rules of the derivatives are presented in some details so as the reader can be easily familiar with the different rules of derivatives.

The basis of the partial derivatives is the basis of the partial differential equations and their wide applications. The chapter started from the basic definition of the partial derivative, geometric meaning and their rules.

Equations arise in different branches of mathematics, and so the need of dealing with theory of equations as a separate topic of mathematics. In this chapter, the theory of equations are described and explained well and in a brief details. Operations related to equations and transformations are also explained well with detailed examples.

Determinants and matrices are very important subjects that are widely found in different branches and topics in mathematics. The present chapter deals with these two topics in some brief details starting the preliminary definitions of determinants and matrices, their properties. The linear system of equations from its mathematical constitution till different methods of solutions is also discussed in brief details.

Partial fractions encountered within theoretical and applied problems. Also, the partial fractions are good mathematical tools when solving complicated integrals. The main usage of the partial fractions can be considered as a simplified mathematical tool.

The topics vector differential and integral calculus arise in many practical and engineering applications. This chapter concerns mainly with these topics but few revision on the basis of vectors is introduced. Scalar and vector functions are also introduced due to their importance in numerical analysis.

Special functions are mostly wide and found in different branches of practical and engineering problems. No one can cover all different types and classifications of such functions. In the present chapter, we will do our best to cover most and famous special functions. This study will cover main topics in each type starting from the basic definition, mathematical formula, properties and more.

Fourier series is one of the topics that used in function approximation, especially when it is recommended using series expansion instead of using the function it-self. But one may ask himself just simple question, is the Fourier series can be good alternative than the original function?. The answer is actually no and no one can say we can get accurate approximation for the function but we can say Fourier series is quite approximation for the function within specified period under prescribed conditions related to the function itself.