A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing.
As a mathematical tool, wavelets can be used to extract information from many different kinds of data, including – but not limited to – audio signals and images. Sets of wavelets are needed to analyze data fully. "Complementary" wavelets decompose a signal without gaps or overlaps so that the decomposition process is mathematically reversible. Thus, sets of complementary wavelets are useful in wavelet based compression/decompression algorithms where it is desirable to recover the original information with minimal loss.
COURSE OUTCOME IS
CO 1:Explain the functions of bounded variations,rectifiable curves, paths and equivalence of paths.
CO2 : Illustrate the properties of Riemann-Stieljes integral.
CO 3: Analyze the uniform convergence of a sequence of functions with continuity, integrability, differentiability.
CO 4: Apply the properties of power series to exponential, logarithmic and trigonometric functions.
In this course we discuss functions of bounded variations, rectifiable curves, paths and equivalence of
paths as module -1. In the next module we develop the ideas of Riemann-Stieljes integral and discuss integration and
differentiation. In third module we assimilate the ideas of uniform convergence and continuity, uniform convergence and
integration, uniform convergence and differentiation. In the last module we explore power series, exponential and trigonometric functions.
The course aims to introduce Numerical Analysis, which palys a pivotal role in solving algebraic and transcendental equations. Numerical solutions of such equations are investigated. Application of methods of numerical analysis in Linear system of equations, matrices and ordinary differential equations are introduced. Solutions of differentiation and integration coupled with Interpolation and Extrapolation are examined.
Introduction to topological space – examples of topological spaces along with its properties are discussed