Technical Books

This note contains below topics, Ideas and approach, Convergence of sequences of real numbers, Convergence in vector and function spaces, Hilbert spaces and their properties, Linear operators, Eigenvalues and eigenfunctions of compact Hermitian operators, Inner products based on positive Hermitian operators, Singularvalue decomposition, Concluding remarks, Proofs of specific mathematical theorems, Index of definitions.

Covered topics are: Historical origins of fractional calculus, Fractional integral according to Riemann-Liouville, Caputo fractional derivative, Riesz-Feller fractional derivative, Grunwal-Letnikov, Integral equations, Relaxation and oscillation equations, Fractional diffusion equation, A nonlinear fractional differential equation, Stochastic solution, Geometrical interpretation of fractional integration

This book covers the following topics about Fractional Calculus: Elementary preliminaries, Grunwald�s construction, The Riemann-Liouville construction, Abel�s solution of the tautochrone problem, Heaviside�s solution of the diffusion equation, Application to the differention of fractal curves, Charge density on a needle, Eigenfunctions of derivative operators of integral/fractional order, Applications to analysis.

This note covers the following topics: Introduction To Fractional Calculus, Fractional Integral Equations, Fractional Differential Equations and The Mittag-leffler Type Functions.

Fractional calculus is a recent field of mathematical analysis and it is a generalization of integer differential calculus, involving derivatives and integrals of real or complex order. This PDF book covers the following topics related to Fractional Calculus : Fractional calculus, The calculus of variations, Expansion formulas for fractional derivatives, The fractional calculus of variations.

This note explains the following topics: historical notes and introduction to fractional calculus, The Liouville weyl fractional calculus, The riesz feller fractional calculus, The Riemann Liouville fractional calculus, The Grunwald letnikov fractional calculus, The mittag Leffler function, The wright functions.

We are working on the detailed description of this book, we will update this section soon.

We are working on the detailed description of this book, we will update this section soon.

This note covers the following topics: Thomasina's Geometry of Irregular Forms, The Chaos Game, The Sierpinski Hexagon, Thomasina's Fern and Valentine's Grouse.

This note covers the following topics: Rigidity and inflexibility in conformal dynamics, Hausdorff dimension and conformal dynamics: Strong convergence of Kleinian groups, Geometrically finite rational maps and Computation of dimension.

This book is an introduction to the theory of iteration of expanding and nonuniformly expanding holomorphic maps and topics in geometric measure theory of the underlying invariant fractal sets. Major topics covered: Basic examples and definitions, Measure preserving endomorphisms, Ergodic theory on compact metric spaces, Distance expanding maps, Thermodynamical formalism, Expanding repellers in manifolds and Riemann sphere, preliminaries, Cantor repellers in the line, Sullivan�s scaling function, application in Feigenbaum universality, Fractal dimensions, Sullivan�s classification of conformal expanding repellers, Conformal maps with invariant probability measures of positive, Lyapunov exponent and Conformal measures.

Goal of this course note is primarily to develop the foundations of geometric measure theory, and covers in detail a variety of classical subjects. A secondary goal is to demonstrate some applications and interactions with dynamics and metric number theory.

This book is devoted to a phenomenon of fractal sets, or simply fractals. Topics covered includes: Sierpinski gasket, Harmonic functions on Sierpinski gasket, Applications of generalized numerical systems, Apollonian Gasket, Arithmetic properties of Apollonian gaskets, Geometric and group-theoretic approach.

This PDF book covers the following topics related to Fractals in Probability and Analysis : Minkowski and Hausdorff dimensions, Self-similarity and packing dimension, Frostman�s theory and capacity, Self-affine sets, Graphs of continuous functions, Brownian motion, Random walks, Markov chains and capacity, Besicovitch�Kakeya sets, The Traveling Salesman Theorem.

This note is an overview of some basic notions is given, especially with an eye towards somewhat fractal examples, such as infinite products of cyclic groups, padic numbers, and solenoids. Topics covered includes, Fourier series, Topological groups, Commutative groups, The Fourier transform, Banach algebras, pAdic numbers, rAdic integers and solenoids, Compactifications and Completeness.