Download or read book Topology of Metric Spaces written by S. Kumaresan and published by Alpha Science Int'l Ltd.. This book was released on 2005 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Topology of Metric Spaces gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces and geometric ideas to encourage geometric thinking, to treat this as a preparatory ground for a general topology course, to use this course as a surrogate for real analysis and to help the students gain some perspective of modern analysis." "Eminently suitable for self-study, this book may also be used as a supplementary text for courses in general (or point-set) topology so that students will acquire a lot of concrete examples of spaces and maps."--BOOK JACKET.

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Download or read book A Textbook of Inorganic Chemistry Volume 1 written by Mandeep Dalal and published by Dalal Institute. This book was released on 2017-01-01 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced-level textbook of inorganic chemistry for the graduate (B.Sc) and postgraduate (M.Sc) students of Indian and foreign universities. This book is a part of four volume series, entitled "A Textbook of Inorganic Chemistry – Volume I, II, III, IV". CONTENTS: Chapter 1. Stereochemistry and Bonding in Main Group Compounds: VSEPR theory; dπ -pπ bonds; Bent rule and energetic of hybridization. Chapter 2. Metal-Ligand Equilibria in Solution: Stepwise and overall formation constants and their interactions; Trends in stepwise constants; Factors affecting stability of metal complexes with reference to the nature of metal ion and ligand; Chelate effect and its thermodynamic origin; Determination of binary formation constants by pH-metry and spectrophotometry. Chapter 3. Reaction Mechanism of Transition Metal Complexes – I: Inert and labile complexes; Mechanisms for ligand replacement reactions; Formation of complexes from aquo ions; Ligand displacement reactions in octahedral complexes- acid hydrolysis, base hydrolysis; Racemization of tris chelate complexes; Electrophilic attack on ligands. Chapter 4. Reaction Mechanism of Transition Metal Complexes – II: Mechanism of ligand displacement reactions in square planar complexes; The trans effect; Theories of trans effect; Mechanism of electron transfer reactions – types; outer sphere electron transfer mechanism and inner sphere electron transfer mechanism; Electron exchange. Chapter 5. Isopoly and Heteropoly Acids and Salts: Isopoly and Heteropoly acids and salts of Mo and W: structures of isopoly and heteropoly anions. Chapter 6. Crystal Structures: Structures of some binary and ternary compounds such as fluorite, antifluorite, rutile, antirutile, crystobalite, layer lattices- CdI2, BiI3; ReO3, Mn2O3, corundum, pervoskite, Ilmenite and Calcite. Chapter 7. Metal-Ligand Bonding: Limitation of crystal field theory; Molecular orbital theory: octahedral, tetrahedral or square planar complexes; π-bonding and molecular orbital theory. Chapter 8. Electronic Spectra of Transition Metal Complexes: Spectroscopic ground states, Correlation and spin-orbit coupling in free ions for Ist series of transition metals; Orgel and Tanabe-Sugano diagrams for transition metal complexes (d1 – d9 states); Calculation of Dq, B and β parameters; Effect of distortion on the d-orbital energy levels; Structural evidence from electronic spectrum; John-Tellar effect; Spectrochemical and nephalauxetic series; Charge transfer spectra; Electronic spectra of molecular addition compounds. Chapter 9. Magantic Properties of Transition Metal Complexes: Elementary theory of magneto - chemistry; Guoy’s method for determination of magnetic susceptibility; Calculation of magnetic moments; Magnetic properties of free ions; Orbital contribution, effect of ligand-field; Application of magneto-chemistry in structure determination; Magnetic exchange coupling and spin state cross over. Chapter 10. Metal Clusters: Structure and bonding in higher boranes; Wade’s rules; Carboranes; Metal carbonyl clusters - low nuclearity carbonyl clusters; Total electron count (TEC). Chapter 11. Metal-π Complexes: Metal carbonyls: structure and bonding; Vibrational spectra of metal carbonyls for bonding and structure elucidation; Important reactions of metal carbonyls; Preparation, bonding, structure and important reactions of transition metal nitrosyl, dinitrogen and dioxygen complexes; Tertiary phosphine as ligand.

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Download or read book An Introduction to Probability Theory and Mathematical Statistics written by V. K. Rohatgi and published by Wiley-Interscience. This book was released on 1976-04-07 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sets and classes; Calculus; Linear Algebra; Probability; Random variables and their probability distributions; Moments and generating functions; Random vectors; Some special distributions; Limit theorems; Sample moments and their distributions; The theory of point estimation; Neyman-pearson theory of testing of hypotheses; Some further results on hypotheses testing; Confidence estimation; The general linear hypothesis; nonparametric statistical inference; Sequential statistical inference.

Download or read book Differential Calculus written by Shanti Narayan and published by S. Chand Publishing. This book was released on 2005-03 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook commences with a brief outline of development of real numbers, their expression as infinite decimals and their representation by points along a line. While the first part of the textbook is analytical, the latter part deals with the geometrical applications of the subject. Numerous examples and exercises have been provided to support student's understanding. This textbook has been designed to meet the requirements of undergraduate students of BA and BSc courses.

Download or read book IIT JAM Mathematics Solved Papers and Practice sets 2021 written by Neha Tyagi and published by Arihant Publications India limited. This book was released on 2020-08-14 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. IIT JAM Solved papers and Practice Sets are the preparatory guides for Physics, Chemistry,Biotechnology and Mathematics 2. IIT JAM Mathematics Solved papers and practice sets are designed as per latest pattern and Syllabus 3. 16 Previous Years’ Solved papers [2020-2005] for practice 4. 3 Practice Sets are given to track the progress 5. All the answers have been well explained with details for better understanding of the concepts Perusing MSc. form the institutes like IITs and IISCs is a great boom in ones career. Joint Admission Test for M.Sc. (JAM) is an all India admission test conducted every year for admission into M.Sc. and other post-graduate science programs at (IITs), (IISc,Bangalore),NITs etc. After all these institutions are of national importance and are well known, the world over, for quality education in engineering, science & technology and research in frontier areas. The new edition of IIT JAM Mathematics Solved Papers and Practice Sets has been designed as per the new exam pattern and syllabus. This book contains Previous Solved papers (2020 – 2005) all the questions have been provided with well explained with detailed answers which help students to understand the concepts and 3 Practice Sets has been designed as per existing test pattern that helps to keep the record of progress. A perfect combo of solved Papers and Practice Sets to increase the edificial knowledge of the aspirant, this book is for everyone who is preparing to ace the upcoming IIT JAM 2021. TABLE OF CONTENT Solved Papers [2020-2005], 3 Practice sets.

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Download or read book A Textbook of Physical Chemistry Volume 1 written by Mandeep Dalal and published by Dalal Institute. This book was released on 2018-01-01 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced-level textbook of physical chemistry for the graduate (B.Sc) and postgraduate (M.Sc) students of Indian and foreign universities. This book is a part of four volume series, entitled "A Textbook of Physical Chemistry – Volume I, II, III, IV". CONTENTS: Chapter 1. Quantum Mechanics – I: Postulates of quantum mechanics; Derivation of Schrodinger wave equation; Max-Born interpretation of wave functions; The Heisenberg’s uncertainty principle; Quantum mechanical operators and their commutation relations; Hermitian operators (elementary ideas, quantum mechanical operator for linear momentum, angular momentum and energy as Hermition operator); The average value of the square of Hermitian operators; Commuting operators and uncertainty principle(x & p; E & t); Schrodinger wave equation for a particle in one dimensional box; Evaluation of average position, average momentum and determination of uncertainty in position and momentum and hence Heisenberg’s uncertainty principle; Pictorial representation of the wave equation of a particle in one dimensional box and its influence on the kinetic energy of the particle in each successive quantum level; Lowest energy of the particle. Chapter 2. Thermodynamics – I: Brief resume of first and second Law of thermodynamics; Entropy changes in reversible and irreversible processes; Variation of entropy with temperature, pressure and volume; Entropy concept as a measure of unavailable energy and criteria for the spontaneity of reaction; Free energy, enthalpy functions and their significance, criteria for spontaneity of a process; Partial molar quantities (free energy, volume, heat concept); Gibb’s-Duhem equation. Chapter 3. Chemical Dynamics – I: Effect of temperature on reaction rates; Rate law for opposing reactions of Ist order and IInd order; Rate law for consecutive & parallel reactions of Ist order reactions; Collision theory of reaction rates and its limitations; Steric factor; Activated complex theory; Ionic reactions: single and double sphere models; Influence of solvent and ionic strength; The comparison of collision and activated complex theory. Chapter 4. Electrochemistry – I: Ion-Ion Interactions: The Debye-Huckel theory of ion- ion interactions; Potential and excess charge density as a function of distance from the central ion; Debye Huckel reciprocal length; Ionic cloud and its contribution to the total potential; Debye - Huckel limiting law of activity coefficients and its limitations; Ion-size effect on potential; Ion-size parameter and the theoretical mean-activity coefficient in the case of ionic clouds with finite-sized ions; Debye - Huckel-Onsager treatment for aqueous solutions and its limitations; Debye-Huckel-Onsager theory for non-aqueous solutions; The solvent effect on the mobality at infinite dilution; Equivalent conductivity (Λ) vs. concentration c 1/2 as a function of the solvent; Effect of ion association upon conductivity (Debye- Huckel - Bjerrum equation). Chapter 5. Quantum Mechanics – II: Schrodinger wave equation for a particle in a three dimensional box; The concept of degeneracy among energy levels for a particle in three dimensional box; Schrodinger wave equation for a linear harmonic oscillator & its solution by polynomial method; Zero point energy of a particle possessing harmonic motion and its consequence; Schrodinger wave equation for three dimensional Rigid rotator; Energy of rigid rotator; Space quantization; Schrodinger wave equation for hydrogen atom, separation of variable in polar spherical coordinates and its solution; Principle, azimuthal and magnetic quantum numbers and the magnitude of their values; Probability distribution function; Radial distribution function; Shape of atomic orbitals (s,p & d). Chapter 6. Thermodynamics – II: Classius-Clayperon equation; Law of mass action and its thermodynamic derivation; Third law of thermodynamics (Nernest heat theorem, determination of absolute entropy, unattainability of absolute zero) and its limitation; Phase diagram for two completely miscible components systems; Eutectic systems, Calculation of eutectic point; Systems forming solid compounds Ax By with congruent and incongruent melting points; Phase diagram and thermodynamic treatment of solid solutions. Chapter 7. Chemical Dynamics – II: Chain reactions: hydrogen-bromine reaction, pyrolysis of acetaldehyde, decomposition of ethane; Photochemical reactions (hydrogen - bromine & hydrogen -chlorine reactions); General treatment of chain reactions (ortho-para hydrogen conversion and hydrogen - bromine reactions); Apparent activation energy of chain reactions, Chain length; Rice-Herzfeld mechanism of organic molecules decomposition(acetaldehyde); Branching chain reactions and explosions ( H2-O2 reaction); Kinetics of (one intermediate) enzymatic reaction : Michaelis-Menton treatment; Evaluation of Michaelis 's constant for enzyme-substrate binding by Lineweaver-Burk plot and Eadie-Hofstae methods; Competitive and non-competitive inhibition. Chapter 8. Electrochemistry – II: Ion Transport in Solutions: Ionic movement under the influence of an electric field; Mobility of ions; Ionic drift velocity and its relation with current density; Einstein relation between the absolute mobility and diffusion coefficient; The Stokes- Einstein relation; The Nernst -Einstein equation; Walden’s rule; The Rate-process approach to ionic migration; The Rate process equation for equivalent conductivity; Total driving force for ionic transport, Nernst - Planck Flux equation; Ionic drift and diffusion potential; the Onsager phenomenological equations; The basic equation for the diffusion; Planck-Henderson equation for the diffusion potential.