The reader is familiar with the Maclaurin's expansion of a function f (x) in
series of integral powers of x._ Such a series is called a power series. In the present chapter, we consider expansions of f (x) in series containing sine and cosine functions. Such series are called Trigonometric Fourier Series. As a prologue, we give in Section 1.1 a brief Introductory Note on the topics of Sequences a
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This chapter is a continuation of Chapter 4 of Part II. Here, we consider
the method of solving one-dimensional wave equation, one-dimensional heat equation and two-dimensional Laplace equation by separation of variables. The D'Alembert's solution for one-dimensional wave equation is also included.

In this chapter, we introduce some basic notions of the Optimization Theory which deals with the act of obtaining best results under given circumstances. Linear programming is an important topic in the optimization theory, and our discussion is confined to an elementary exposition of this topic.

In this chapter we first present some numerical methods of solving algebraic and transcendental equations. Then we consider the Gauss-Seidel method and the Relaxation method of solving systems of linear equations. Lastly, we consider the power method of finding the largest eigenvalue of a square matrix.

In Chapter 3, we obtained Fourier series solutions to one-dimensional heat
equation, one-dimensional wave equation and two-dimensional Laplace equation. In this chapter we present some Numerical solutions to these equations.

In Chapters 7 and 8 of Part II and Chapter 2 of this book, we presented an
elementary treatment of Laplace Transforms and Fourier Transforms. In the present chapter we consider another transform, known as the Z - transform, which is closely related to the Laplace Transform. Whereas the Laplace transform is defined through an infinite integral, the Z-transform is defined through an infinite series
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Pages: 60

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