Sunday, June 24, 2012


Problems in Calculus of One Variable is an exhaustive reference on Calculus for students studying a preliminary course on Calculus. The book is intended as an introduction to calculus, helping students in class-11 and class-12 understand the mathematical basis required for an additional or more advanced course. The book covers mathematical analysis, limits of a function, differential calculus, integral calculus, applications of differentiation and integration and improper integrals among other associated topics. The book is an indispensable resource for students aspiring for admission into one of the Indian Institutes of Technology for a Bachelor program in Engineering. About I. A. Maron I. A. Maron was a Russian mathematician. His works on Calculus are used throughout the world as introductory books on the subject. Table of Contents From the Author 1. Introduction to Mathematical Analysis 1.1 Real Numbers, The Absolute Value of a Real Number 1.2 Function, Domain of Definition 1.3 Investigation of Functions 1.4 Inverse Function 1.5 Graphical Representation of Functions 1.6 Number Sequences, Limit of a Sequence 1.7 Evaluation of Limits of Sequences 1.8 Testing Sequences for Convergence 1.9 The Limit of a function 1.10 Calculation of Limits of Functions 1.11 Infinitesimal and Infinite Functions, their Definitions and Comparison 1.12 Equivalent infinitesimals, Application to Finding Limits 1.13 One-sided Limits 1.14 Continuity of a Function, Points of Discontinuity and Their Classification 1.15 Arithmetical Operations on Function, Continuity of a Composite Function 1.16 The Properties of a Function, Continuous a Closed Interval, Continuity of an Inverse Function 1.17 Additional Problems 2. Differentiation of Functions 2.1 Definition of the Derivative 2.2 Differentiation of Explicit Functions 2.3 Successive Differentiation of Explicit Functions, Leibnitz Formula 2.4 Differentiation of Inverse, Implicit and Parametrically Represented Functions 2.5 Applications of the Derivative 2.6 The Differential of a Function, Application to Approximate Problems 2.7 Additional Problems 3. Application of Differential Calculus to Investigation of Functions 3.1 Basic Theorems on Differentiable Functions 3.2 Evaluation of Indeterminate Forms, L'Hospital's Rule 3.3 Taylor's Formula, Application to Approximate Calculations 3.4 Application of Taylor's Formula to Evaluation of Limits 3.5 Testing a Function for Monotonicity 3.6 Maxima and Minima of a Function 3.7 Finding the Greatest and the Least Values of a Function 3.8 Solving Problems in Geometry and Physics 3.9 Convexity and Concavity of a Curve, Points of Inflection 3.10 Asymptotes 3.11 General Plan for Investigating Functions and Sketching Graphs 3.12 Approximate Solution of Algebraic and Transcendental Equations 3.13 Additional Problems 4. Indefinite Integrals, Basic Methods of Integration 4.1 Direct Integration and the Methods of Expansion 4.2 Integration by Substitution 4.3 Integration by Parts 4.4 Reduction Formula 5. Basic Classes of Integrable Functions 5.1 Integration of Rational Functions 5.2 Integration of Certain Irrational Expressions 5.3 Euler's Substitutions 5.4 Other Methods of Integrating Expressions 5.5 Integration of a Binomial Differential 5.6 Integration of Trigonometric and Hyperbolic Functions 5.7 Integration of Certain Irrational Functions with the Aid of Trigonometric or Other Transcendental Functions 5.8 Integration of Other Transcendental Functions 5.9 Methods of Integration (List of Basic Forms of Integrals) 6. The Definite Integrals 6.1 Statement of the Problem, The Lower and Upper Integral Sums 6.2 Evaluating Definite Integrals by the Newton-Leibnitz Formula 6.3 Estimating an integral, The Definite Integral as a Function of Its Limits 6.4 Changing the Variable in a Definite Integral 6.5 Simplification of Integrals Based on the Properties of Symmetry of Integrals 6.6 Integration by Parts, Reduction Formulas 6.7 Approximating Definite Integrals 6.8 Additional Problems 7. Applications of the Definite Integral 7.1 Computing the Limits of Sums with the Aid of Definite Integrals 7.2 Finding Average Values of a Function 7.3 Computing Areas in Rectangular Coordinates 7.4 Computing Areas with Parametrically Represented Boundaries 7.5 The Area of a Curvilinear Sector in Polar Coordinates 7.6 Computing the Volume of a Solid 7.7 The Arc Length of a Plane Curve in Rectangular Coordinates 7.8 The Arc Length of a Curve Represented parametrically 7.9 The Arc Length of a Curve in Polar Coordinates 7.10 Area of Surface of Revolution 7.11 Geometrical Applications of the Definite Integral 7.12 Computing Pressure, Work and Other Physical Quantities by the Definite Integrals 7.13 Computing Static Moments and Moments of Inertia, Determining Coordinates of the Centre of Gravity 7.14 Additional Problems 8. Improper Integrals 8.1 Improper Integrals with Infinite Limits 8.2 Improper Integrals of Unbounded Functions 8.3 Geometric and Physical Applications of Improper Integrals 8.4 Additional Problems Answer and Hints Attachment
Published by: Arihant
Date published: 03/03/2014
Edition: 4th
ISBN: 9351414876
Available in Ebook Paperback Hardcover


An Introduction To Probability: Theory and Its Applications (Volume - 1) is the updated and revised 2008 version of the original, and an introductory level reference and guide book highly useful for undergraduate students of computer science and other disciplines that require a sound knowledge of the probability theory. Summary Of The Book An Introduction To Probability: Theory and Its Applications (Volume - 1) is exhaustive in content and in-depth in its approach, laying emphasis on both, theory and applications of probability. It has been designed as a textbook for students who want to grasp the basic conceptual knowledge of the probability theory and also apply it to practical problems. The book opens with the first chapter introducing students to the Nature of Probability Theory, as well as providing a summarised account of its background and history. Thereafter, the rest of the sixteen chapters provide a study into many topics including, random variables, expectation, renewal theory, branching processes, random walk and ruin problems, recurrent events, compound distribution, Markov chains, and laws of large numbers. The book is illustrated with practical examples to support and provide a better understanding of its theoretical concepts. An Introduction To Probability: Theory and Its Applications (Volume - 1) is a comprehensive textbook on probability that covers topics including the binomial and poisson distributions, the sample space, compound distributions, integral valued variables, and elements of combinatorial analysis, to name a few. Furthermore, all the problems asked in the book have their solutions provided at the end of the book. Also, certain omissions and inclusions have been made, keeping in mind the current relevance of topics. For instance, probabilistic arguments has been done away with in order to include combinatorial artifices. Branching processes, the De Moivre-Laplace Theorem, and Markov Chain are other new additions to this book. The book also lists out which topics are meant purely for reading and can otherwise be omitted. About William Feller Considered one of the greatest Probabilists of the twentieth century, noted mathematician William Feller (Vilibald Sre?ko Feller) was of Croatian-American descent and born in 1906. His writings in his books and papers pertain to subjects such as Theory of Measurement, Mathematical Analysis, Differential Equations, Functional Analysis, and Geometry. Feller finished his schooling from his birthplace, Zagreb, and studied Maths for two years. Thereafter, he left for Germany where he continued his higher education, obtaining a doctorate in 1926. Initially, he took up teaching positions at the Universities of Kiel, Stockholm, and Lund, respectively. Eventually, he moved to the United States, gained citizenship there, and taught at Brown University, Cornell University, and Princeton University. Considered instrumental in his role in the inclusion of Probability Theory as a branch of Mathematical Analysis, he was the recipient of the distinguished National Medal Of Science in 1969. William Feller died in New York in January, 1970. Table of Contents · Introduction: The Nature of Probability Theory · The Sample Space · Elements of Combinatorial Analysis · Fluctuations in Coin Tossing and Random Walks · Combination of Events · Conditional Probability · Stochastic Independence · The Binomial and Poisson Distributions · The Normal Approximation to the Binomial Distribution · Unlimited Sequences of Bernoulli Trials · Random Variables · Expectation · Laws of Large Numbers · Integral Valued Variables · Generating Functions · Compound Distributions · Branching Processes · Recurrent Events · Renewal Theory · Random Walk and Ruin Problems · Markov Chains · Algebraic Treatment of Finite Markov Chains · The Simplest Time-Dependent Stochastic Processes · Answers to Problems
Published by: Wiley India Pvt Ltd
Date published: 03/03/2008
Edition: Third
ISBN: 8126518057
Available in Ebook Paperback Hardcover


Higher Algebra is a comprehensive book for high school students. The book comprises of chapters on ration, proportion, arithmetical and geometrical progression, harmonic progression, scales of notation, permutations and combinations, partial fractions, theory of numbers, determinants. In addition, the book consists of several solved and unsolved questions for through practice and revision. Table of Contents Chapter 1: Ratio Chapter 2: Proportion Chapter 3: Variation Chapter 4: Arithmetical Progression Chapter 5: Geometrical Progression Chapter 6: Harmonical Progression Theorems Connected with the Progression Chapter 7: Scales of Notation Chapter 8: Surds and Imaginary Quantities Chapter 9: The Theory of Quadratic Equations Chapter 10: Miscellaneous Equations Chapter 11: Permutations and Combinations Chapter 12: Mathematical Induction Chapter 13: Binomial Theorem Positive Integral Index Chapter 14: Binomial Theorem, Any Index Chapter 15: Multinomial Theorem Chapter 16: Logarithms Chapter 17: Exponential and Logarithmic Series Chapter 18: Interest and Annuities Chapter 19: Inequalities Chapter 20: Limiting Values and Vanishing Fractions Chapter 21: Convergency and Divergency of Series Chapter 22: Undetermined Coefficients Chapter 23: Partial Fractions Chapter 24: Recurring Series Chapter 25: Continued Fractions Chapter 26: Indeterminate Equations of the First Degree Chapter 27: Recurring Continued Fractions Chapter 28: Indeterminate Equations of the Second Degree Chapter 29: Summation of Series Chapter 30: Theory of Numbers Chapter 31: The General Theories of Continued Fractions Chapter 32: Probability Chapter 33: Determinants Chapter 34: Miscellaneous Theorems and Examples Chapter 35: Theory of Equations You can easily download it via clicking the link below
Published by: Arihanth
Date published: 09/03/2013
Edition: 4th
ISBN: 9351414922
Available in Ebook Paperback Hardcover


Elements of Coordinate Geometry


Loney Plane Trigonometry


Inorganic Chemistry, 2nd Ed - Catherine E. Housecroft


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