
MDU Mathematics III  Sem III Section A : Fourier Series and Fourier Transforms(Euler s formulae, conditions for a Fourier expansion, change of interval, Fourier expansion of odd and even functions, Fourier expansion of square wave, rectangular wave, sawtoothed wave, half and full rectified wave, half range sine and consine series Fourier integrals, Fourier transforms, Shifting theorem (both on time and frequency axes) Fourier transforms of derivatives, Fourier transforms of integrals, Convolution theorem, Fourier transform of Diracdelta function) 


1. Contents(Mathematics) 
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This book on Mathematics  IV covers the syllabus for the 2nd year 1st Semester course of B.E / B.Tech programmes offered by various major universities and autonomous colleges. It covers the following topics Functions of a Complex Variable, Complex Integration, Evaluation of Integrals, Fourier Series and Transforms and Applications of PDE.
Title: Mathematics IV
Published on: 27/03/20
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Pages:
10








2. Fourier Transform(Mathematics) 
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We have already seen that a periodic function can be represented by an infinite series known as Fourier series. Fourier transform deals with non periodic functions. It can be shown that the limiting form of Fourier series as the period tends to infinity is the Fourier integral and this suggests the idea of Fourier transform. This is useful in the solution of boundary value problems and also in oth
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Title: Engineering Mathematics  III





4. Contents(Mathematics) 
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The aim of this book is to provide a simplified form of the present syllabi of various Technical
Universities in Transforms and Partial Differential Equations for the IIIrd Semester B.E/B.Tech students. This book has been prepared with utmost care to make it extremely useful for the students. It is selfcontained and numerous examples have been given and sufficient number of problems have been in
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Title: Transforms and Partial Differential Equations  Second Edition
Published on: 06/05/20
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Pages:
4








5. Chapter 4 * Fourier Series and Transforms(Mathematics) 
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Introduction, Periodic functions, Fourier series of periodic function, Dirichletâ€™s conditions, Even and odd functions, Change of interval, Half range sine and cosine series. Fourier integral theorem (without proof), Fourier sine and cosine integrals, sine and cosine, transforms, properties, inverse transforms, Finite Fourier transforms.
Title: Mathematics IV
Published on: 27/03/20
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Pages:
346








6. Fourier Series(Mathematics III) 
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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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Title: Engineering Mathematics Part  III





8. Difference Equations and ztransforms(Mathematics) 
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Differential equations arise in the study of systems in which variables vary continuously. When the independent variable varies by taking discrete values, the systems are often characterised by difference equations. Also, most of the numerical methods of solutions of differential equations are based on finite difference methods and involve solutions of difference equations. Further, recurrence rel
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Title: Engineering Mathematics  III





10. Chapter 6 * The ContinuousTime Fourier Transform(Electronics and Communication) 
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Chapter 6 deals with Fourier transform of continuous time signals. It also
gives an introduction for modulation.
Title: Signals and Systems
Published on: 04/04/20
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Pages:
94








11. Power Series, the Exponential,Logarithmic and Trigonometric Functions (Mathematics) 
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In this unit we shall study an important class of series of functions called power series that possess properties that are not valid for general series of function s. At each point interior to the circle of convergence, the power series not only converges but converges absolutely. What is
very important about power series is that, in each circle concentric with the circle of convergence but of sm
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Title: Math 2.2 Real Analysis II




12. Fourier Transforms(Mathematics III) 
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In this chapter we present an elementary treatment of the topic of Infinite (or
complex) Fourier Transforms.
Title: Engineering Mathematics Part  III




13. Uniform Convergence and Continuity, Uniform Convergence and Differentiability, Uniform Convergence and Integrability (Mathematics) 
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Point wise convergence is not enough to preserve properties of sequences. In other words, if a sequence of functions has some property like continuity(or differentiablility or integrability) and converges pointwise, then the limit function mayor may not have the same property. But uniform continuity is good enough to preserve continuity, but does not preserve differentiability.
Title: Math 2.2 Real Analysis II





14. The Laurent Series, Partial Fractions,MittagLeffler's Theorem(Mathematics) 
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In this unit, we discuss the infinite product and their relations with infinite series. Further, we study Weierstrass Factorization theorem which deals with representation of meromorphic function as an infinite product. We also study canonical product.
Title: Math 2.3 Complex Analysis  II






17. Algebra of sets  Sigma Algebra and Borel Sets(Mathematics) 
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In this unit, we introduce the concept of algebra of sets. this unit also explains the concept of sigma algebra along with some examples. This unit provides an insight into Borel sets along with some examples.
Title: Math 3.2 Measure Theory




18. Metric Spaces, Completeness(Mathematics) 
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In this unit, we introduce the concept of metric spaces. We give the
properties of metric spaces and some theorems related to metric space.
Finally, we explain the Metric Completion Theorem.
Title: Math 3.3 Functional Analysis




19. The Weierstrass Theorem, the Taylor Series(Mathematics) 
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Sequence and series representation of a fun ct ion play very important role in many branches of Mathematics. In this unit, we discuss how an analytic function in an open disk can be represented as a Taylor series.
Title: Math 2.3 Complex Analysis  II




20. Multiplication of Series and Rearrangements(Mathematics) 
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This unit will be devoted to the study of absolute convergence, multiplication of series and re arrangements of the series.
Title: Math 1.2 Real Analysis  I




21. Outer measure and measurable sets(Mathematics) 
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This unit explains Lebesgue outer measure and its properties. It also explains Lebesgue measurable sets and its properties (Theorems).
Title: Math 3.2 Measure Theory






24. Everywhere Continuous but Nowhere Differentiable Functions, Stone Weierstrasstheorem(Mathematics) 
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In the early nineteenth century most mathematicians believed that a continuous function has derivatives at a significant set of points. But in 1872, in his presentation Berlin academy, Karl Weierstrass shocked the mathematics world by proving this conjecture is false. He presented a function which is continuous everywhere but differentiable nowhere. Because of the contribution of several mathemati
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Title: Math 2.2 Real Analysis II





25. Setting up of First Order Differential Equations and their Solutions(Mathematics) 
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Differential equations occur quite frequently in our daily life. The motion of an object can always be associated with a differential equation. The change in prices of commodities, the flow of fluids, the concentration of chemicals etc., often lead to differential equations. Such equations may depend on one or more independent variables. Further, it may include the derivatives of the first or high
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Title: Math 3.4 Mathematical Modeling






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