**Introduction **

It is probably true to say that there is no branch of engineering, physics, economics, chemistry or computer Engineering which does not require the understanding of the basic laws of algebra, the laws of indices, thiamin pulsation of brackets, the ability to factories and the laws of precedence. This then leads to the solve simple, simultaneous and quadratic equations which occur so often. The study of algebra also revolves around using and manipulating polynomials. Polynomials are used in engineering, computer programming, software engineering, in management, and in business. Mathematicians, statisticians and engineers of all sciences employ the use of polynomials to solve problems; among them are aerospace engineers, chemical engineers, civil engineers, electrical engineers, environmental engineers, industrial engineers, materials engineers, mechanical engineers and nuclear engineers. The factor and remainder theorems are also employed in engineering software and electronic mathematical applications, through which polynomials of higher degrees and longer arithmetic structures are divided without any complexity. The study of algebra, equations, polynomial division and the factor and remainder theorems is therefore of some considerable importance in engineering.

**Table of Content**

**1 Algebra**

**2 Partial fractions **

**3 Logarithms**

**4 Exponential functions**

**5 Inequalities **

**6 Arithmetic and geometric progressions **

**7 The binomial series **

**8 Maclaurin’s series **

**9 Solving equations by iterative methods **

**10 Binary, octal and hexadecimal numbers **

**11 Boolean algebra and logic circuits **

**Section B Geometry and trigonometry **

**12 Introduction to trigonometry**

**13 Cartesian and polar co-ordinates**

**14 The circle and its properties **

**15 Trigonometric waveforms**

**16 Hyperbolic functions **

**17 Trigonometric identities and equations **

**18 The relationship between trigonometric and**

**hyperbolic functions **

**19 Compound angles **

**20 Functions and their curves**

**21 Irregular areas, volumes and mean values of**

**Waveforms**

**22 Complex numbers **

**23 De Moivre’s theorem **

**24 The theory of matrices and determinants **

**25 Applications of matrices and determinants **

**26 Vectors **

**27 Methods of adding alternating waveforms **

**28 Scalar and vector products **

**29 Methods of differentiation **

**30 Some applications of differentiation **

**31 Differentiation of parametric equations **

**32 Differentiation of implicit functions **

**33 Logarithmic differentiation**

**34 Differentiation of hyperbolic functions **

**35 Differentiation of inverse trigonometric and**

**hyperbolic functions **

**36 Partial differentiation **

**37 Total differential, rates of change and small**

**changes **

**38 Maxima, minima and saddle points for functions**

**of two variables **

**Standard integration**

**40 Some applications of integration **

**41 Integration using algebraic substitutions**

**42 Integration using trigonometric and hyperbolic**

**substitutions **

**43 Integration using partial fractions **

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