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 Roytvarf, Alexander A.
 New York : Birkhäuser, c2013.
 Description
 Book — xxxvii, 405 p. : ill. ; 25 cm.
 Summary

 Section I. Problems.
 1. Jacobi Identities and Related Combinatorial Formulas.
 2. A Property of Recurrent Sequences.
 3. A Combinatorial Algorithm in Multiexponential Analysis.
 4. A Frequently Encountered Determinant.
 5. A Dynamical System with a Strange Attractor.
 6. Polar and Singular Value Decomposition Theorems.
 7. 2X2 Matrices Which Are Roots of 1.
 8. A Property of Orthogonal Matrices.
 9. Convexity and Related Classical Inequalities.
 10. OneParameter Groups of Linear Transformations.
 11. Examples of Generating Functions in Combinatorial Theory and Analysis.
 12. Least Squares and Chebyshev Systems.
 Section II. Hints.
 1. Jacobi Identities and Related Combinatorial Formulas.
 2. A Property of Recurrent Sequences.
 3. A Combinatorial Algorithm in Multiexponential Analysis.
 4. A Frequently Encountered Determinant.
 5. A Dynamical System with a Strange Attractor.
 6. Polar and Singular Value Decomposition Theorems.
 7. 2X2 Matrices Which Are Roots of 1.
 8. A Property of Orthogonal Matrices.
 9. Convexity and Related Classical Inequalities.
 10. OneParameter Groups of Linear Transformations.
 11. Examples of Generating Functions in Combinatorial Theory and Analysis.
 12. Least Squares and Chebyshev Systems.
 Section III. Explanations.1. Jacobi Identities and Related Combinatorial Formulas.
 2. A Property of Recurrent Sequences.
 3. A Combinatorial Algorithm in Multiexponential Analysis.
 4. A Frequently Encountered Determinant.
 5. A Dynamical System with a Strange Attractor.
 6. Polar and Singular Value Decomposition Theorems.
 7. 2X2 Matrices Which Are Roots of 1.
 8. A Property of Orthogonal Matrices.
 9. Convexity and Related Classical Inequalities.
 10. OneParameter Groups of Linear Transformations.
 11. Examples of Generating Functions in Combinatorial Theory and Analysis.
 12. Least Squares and Chebyshev Systems.
 Section IV. Full Solutions.
 1. Jacobi Identities and Related Combinatorial Formulas.
 2. A Property of Recurrent Sequences.
 3. A Combinatorial Algorithm in Multiexponential Analysis.
 4. A Frequently Encountered Determinant.
 5. A Dynamical System with a Strange Attractor.
 6. Polar and Singular Value Decomposition Theorems.
 7. 2X2 Matrices Which Are Roots of 1.
 8. A Property of Orthogonal Matrices.
 9. Convexity and Related Classical Inequalities.
 10. OneParameter Groups of Linear Transformations.
 11. Examples of Generating Functions in Combinatorial Theory and Analysis.
 12. Least Squares and Chebyshev Systems.
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QA9 .R777 2013  Unknown 
 Gustafson, Karl E.
 New Jersey : World Scientific, 2012.
 Description
 Book — xiv, 244 p. : ill ; 24 cm.
 Summary

 The Essentials of Antieigenvalue Theory Convexity in Norm Geometry The MinMax Theorem The Euler Equation Higher Antieigenvalues Applications in Numerical Analysis Applications in Wavelets, Control, and Scattering The Trigonometry of Matrix Statistics Bell's Inequalities, Penrose Twistors, and Quantum Trigonometry Trigonometry of Financial Instruments.
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QA300 .G795 2012  Unknown 
 Mathews, John H., 1943
 6th ed.  Sudbury, MA : Jones & Bartlett Learning, c2012.
 Description
 Book — xvi, 645 p. : ill. (some col.) ; 25 cm.
 Summary

Intended for the undergraduate student majoring in mathematics, physics or engineering, the Sixth Edition of Complex Analysis for Mathematics and Engineering continues to provide a comprehensive, studentfriendly presentation of this interesting area of mathematics. The authors strike a balance between the pure and applied aspects of the subject, and present concepts in a clear writing style that is appropriate for students at the junior/senior level. Through its thorough, accessible presentation and numerous applications, the sixth edition of this classic text allows students to work through even the most difficult proofs with ease. New exercise sets help students test their understanding of the material at hand and assess their progress through the course. Additional Mathematica and Maple exercises are available on the publishers website.
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QA331.7 .M38 2012  Unknown 
 Collinson, Matthew.
 London : College Publications, c2012.
 Description
 Book — xviii, 272 p. : ill. (some col.) ; 24 cm.
 Online
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Q295 .C645 2012  Unknown 
85. Lectures on real analysis [2012]
 Lectures. Selections
 Lárusson, Finnur, 1966
 Cambridge ; New York : Cambridge University Press, 2012, ©2012.
 Description
 Book — x, 117 pages : illustrations ; 24 cm
 Summary

 Preface To the student
 1. Numbers, sets, and functions
 2. The real numbers
 3. Sequences
 4. Open, closed, and compact sets
 5. Continuity
 6. Differentiation
 7. Integration
 8. Sequences and series of functions
 9. Metric spaces
 10. The contraction principle Index.
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QA300.5 .L37 2012  Unknown 
 Sakhnovich, L. A.
 Basel ; London : Birkhäuser, c2012.
 Description
 Book — ix, 245 p. ; 24 cm.
 Summary

 Introduction.
 1 Levy processes.
 2 The principle of imperceptibility of the boundary.
 3 Approximation of positive functions.
 4 Optimal prediction and matched filtering.
 5 Effective construction of a class of nonfactorable operators.
 6 Comparison of thermodynamic characteristics.
 7 Dual canonical systems and dual matrix string equations.
 8 Integrable operators and Canonical Differential Systems.
 9 The game between energy and entropy.
 10 Inhomogeneous Boltzmann equations.
 11 Operator Bezoutiant and concrete examples. Comments. Bibliography. Glossary. Index.
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QA274.73 .S25 2012  Unknown 
 Muldowney, P. (Patrick), 1946
 Hoboken, N.J. : Wiley, c2012.
 Description
 Book — xvi, 527 p. : ill. ; 24 cm.
 Summary

 Preface xi
 Symbols xiii
 1 Prologue
 1
 2 Introduction
 37
 3 InfiniteDimensional Integration
 83
 4 Theory of the Integral
 111
 5 Random Variability
 183
 6 Gaussian Integrals
 257
 7 Brownian Motion
 305
 8 Stochastic Integration
 383
 9 Numerical Calculation
 447 A Epilogue
 491 Bibliography
 505 Index 521.
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QA273 .M864 2012  Unknown 
88. Perspectives in analysis, geometry, and topology : on the occasion of the 60th birthday of Oleg Viro [2012]
 Marcus Wallenberg Symposium on Perspectives in Analysis, Geometry, and Topology (2008 : Stockholms universitet)
 New York : Birkhäuser, c2012.
 Description
 Book — xxxi, 464 p. : ill. ; 24 cm.
 Summary

 Preface.
 1 Selman Akbulut, Exotic structures on smooth 4manifolds.
 2 Kenneth Baker, John Etnyre, Rational linking and contact geometry.
 3 Robert Berman, JeanPierre Demailly, Regularity of plurisubharmonic upper envelopes in big cohomology classes.
 4 Alex Degtarev, Towards the generalized Shapiro and Shapiro conjecture.5 Alex Degtarev, Ilia Itenberg, Viatcheslav Kharlamov, On the number of components of a complete intersection of real quadrics.
 6 Tobias Ekholm, Rational Symplectic Field Theory and linearized Legendrian contact homology.
 7 Yakov Eliashberg, N. Mishachev, Wrinkling IV: Mappings with prescribed singularities.
 8 Michael Entov, Leonid Polterovich, Pierre Py, On continuity of quasimorphisms for symplectic maps. With an appendix by Michael Khanevsky.
 9 David Gay, Andras Stipsicz, On symplectic caps.
 10 Gennadi Henkin, CauchyPompeiu type formulas for a on affine algebraic Riemann surfaces and some applications.11 Kiumars Kaveh, A. G. Khovanskii, Algebraic equations and convex bodies.
 12 Louis Kauffman, Graphical Bracket Invariants of Virtual Links.
 13 Ciprian Manolescu, Christopher Woodward, Floer homology on the extended moduli space.
 14 Ngaiming Mok, Projectivealgebraicity of minimal compactifications of complexhyperbolic space forms of finite volume.
 15 Stepan Orevkov, Some examples of real algebraic and real pseudoholomorphic curves.
 16 Nicolai Reshetikhin, Topological invariants related to quantum groups at roots of unity.
 17 Alexander Shumakovitch: Khovanov Homology Theories and Their Applications.
 18 Eugenii Shustin, Patchworking theorem for tropical curves with multiple points.
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QA611 .A1 M37 2008  Unknown 
89. Champs de Hurwitz [2011]
 Bertin, José.
 Paris : Société mathématique de France, 2011.
 Description
 Book — 219 p. : ill. ; 24 cm
 Online
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Shelved by Series title N.S. NO.125/126  Unknown 
90. Convexity : an analytic viewpoint [2011]
 Simon, Barry, 1946
 Camrbridge ; New York : Cambridge University Press, 2011.
 Description
 Book — ix, 345 p. : ill. ; 24 cm.
 Summary

 Preface
 1. Convex functions and sets
 2. Orlicz spaces
 3. Gauges and locally convex spaces
 4. Separation theorems
 5. Duality: dual topologies, bipolar sets, and Legendre transforms
 6. Monotone and convex matrix functions
 7. Loewner's theorem: a first proof
 8. Extreme points and the KreinMilman theorem
 9. The strong KreinMilman theorem
 10. Choquet theory: existence
 11. Choquet theory: uniqueness
 12. Complex interpolation
 13. The BrunnMinkowski inequalities and log concave functions
 14. Rearrangement inequalities: a) BrascampLiebLuttinger inequalities
 15. Rearrangement inequalities: b) Majorization
 16. The relative entropy
 17. Notes References Author index Subject index.
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QA639.5 .S56 2011  Unknown 
 Stroock, Daniel W.
 New York : Springer, c2011.
 Description
 Book — xi, 243 p. ; 24 cm.
 Summary

 Preface.1. The Classical Theory.2. Measures. 3. Lebesgue Integration.4. Products of Measures.5. Changes of Variable.6. Basic Inequalities and Lebesgue Spaces.7. Hilbert Space and Elements of Fourier Analysis.8. The RadonNikodym Theorem, Daniell Integration, and Caratheodory's Extension Theorem.Index.
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QA312 .S876 2011  Unknown 
 Krajíček, Jan.
 Cambridge, UK ; New York : Cambridge University Press, 2011.
 Description
 Book — xvi, 247 p. ; 23 cm.
 Summary

 Preface Acknowledgements Introduction Part I. Basics:
 1. The definition of the models
 2. Measure on ss
 3. Witnessing quantifiers
 4. The truth in N and the validity in K(F) Part II. Second Order Structures:
 5. Structures K(F, G) Part III. AC0 World:
 6. Theories IDELTA0, IDELTA0(R) and V10
 7. Shallow Boolean decision tree model
 8. Open comprehension and open induction
 9. Comprehension and induction via quantifier elimination: a general reduction
 10. Skolem functions, switching lemma, and the tree model
 11. Quantifier elimination in K(Ftree, Gtree)
 12. Witnessing, independence and definability in V10 Part IV. AC0(2) World:
 13. Theory Q2V10
 14. Algebraic model
 15. Quantifier elimination and the interpretation of Q2
 16. Witnessing and independence in Q2V10 Part V. Towards Proof Complexity:
 17. Propositional proof systems
 18. An approach to lengthsofproofs lower bounds
 19. PHP principle Part VI. Proof Complexity of Fd and Fd(+):
 20. A shallow PHP model
 21. Model K(Fphp, Gphp) of V10
 22. Algebraic PHP model? Part VII. PolynomialTime and Higher Worlds:
 23. Relevant theories
 24. Witnessing and conditional independence results
 25. Pseudorandom sets and a LowenheimSkolem phenomenon
 26. Sampling with oracles Part VIII. Proof Complexity of EF and Beyond:
 27. Fundamental problems in proof complexity
 28. Theories for EF and stronger proof systems
 29. Proof complexity generators: definitions and facts
 30. Proof complexity generators: conjectures
 31. The local witness model Appendix. Nonstandard models and the ultrapower construction Standard notation, conventions and list of symbols References Name index Subject index.
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QA267.7 .K73 2011  Unknown 
93. Geometric aspects of analysis and mechanics : in honor of the 65th birthday of Hans Duistermaat [2011]
 New York : Birkhäuser, c2011.
 Description
 Book — xxxvi, 372 p. : ill. ; 24 cm.
 Summary

 Preface. About J.J. Duistermaat. Hans Duistermaat (19422010). Recollections of Hans Duistermaat. Recollections of Hans Duistermaat. Recollections of Hans Duistermaat. Classical Mechanics and Hans Duistermaat. DuistermaatHeckman formulas and index theory. Asymptotic equivariant index of Toeplitz operators and relative index of CR structures. A semiclassical inverse problem I: Taylor expansions. A semiclassical inverse problem II: reconstruction of the potential. On the solvability of systems of pseudodifferential operators. The Darboux process and a noncommutative bispectral problem: some explorations and challenges. Conjugation spaces and edges of compatible torus actions. NonAbelian localization for U(1) ChernSimons theory. Symplectic implosion and nonreductive quotients. Quantization of qHamiltonian SU(2)spaces. Wallcrossing formulas in Hamiltonian geometry. Eigenvalue distributions and Weyl laws for semiclassical nonselfadjoint operators in
 2 dimensions. Symplectic inverse spectral theory for pseudodifferential operators.
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QA300 .G466 2011  Unknown 
 Wang, Baoxiang.
 New Jersey : World Scientific Pub. Co., c2011.
 Description
 Book — xiv, 283 p. : ill. ; 24 cm.
 Summary

 Fourier Multiplier, Function Spaces NavierStokes Equation Strichartz Estimates for Linear Dispersive Equations Local and Global Wellposedness for Nonlinear Dispersive Equations The Low Regularity Theory for the Nonlinear Dispersive Equations FrequencyUniform Decomposition Method Conservations, Morawetz' Inequalities of NLS Boltzmann Equation without Angular Cutoff.
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QA403 .W358 2011  Unknown 
95. Introduction to classical and modern analysis and their application to group representation theory [2011]
 Basu, Debabrata.
 Singapore ; Hackensack, N.J. : World Scientific, c2011.
 Description
 Book — xvii, 367 p. : ill. ; 24 cm.
 Summary

 Convergence, Analytic Functions, Complex Integration, Residue Theorem, CauchyPochhammer Theory of Gamma, Beta and Zeta Function BargmanSegal Spaces, Elements of the Theory of Generalized Functions Regularizations and Cauchy's Theory of Analytic Continuation Gel'fandShilov Formulas for Gamma and Beta Function Lie Group and Invariant Measure Representations and Unitary Representation WignerEckart Theorem SU(2) Group Elements of SU(3) GellMann Basis and λMatrices GellMann Neeman Octet Model and Mass Formula Locally Compact Groups: SL(2, R) (SU(1,1)) Principal Exceptional, Positive and Negative Discreet Series and Their Canonical Carrier Spaces The ClebschGordan Problem: D+ X D+, c Dc X Dc, e Group Ring and Invariant Definition of Character Plancherel Formula as a Completeness Condition of Character The Group SL(2, C) and Its Unitary Representations Group Ring and Character Plancherel Formula SU(1,1) Content of SL(2, C) HeisenbergWeyl Group and Its Representations CoherentStates and BergmanSegal Spaces Bargmann's Integral Transform SU(1,1) Coherent States and Integral Transforms Connecting WellKnown Carrier Spaces of SU(1,1).
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QA176 .B37 2011  Unknown 
96. Introduction to real analysis [2011]
 Bartle, Robert Gardner, 1927
 4th ed.  Hoboken, NJ : John Wiley & Sons, c2011.
 Description
 Book — xiii, 402 p. : ill. ; 26 cm.
 Summary

 CHAPTER 1 PRELIMINARIES. 1.1 Sets and Functions. 1.2 Mathematical Induction. 1.3 Finite and Infinite Sets.
 CHAPTER 2 THE REAL NUMBERS. 2.1 The Algebraic and Order Properties of R. 2.2 Absolute Value and the Real Line. 2.3 The Completeness Property of R. 2.4 Applications of the Supremum Property. 2.5 Intervals.
 CHAPTER 3 SEQUENCES AND SERIES. 3.1 Sequences and Their Limits. 3.2 Limit Theorems. 3.3 Monotone Sequences. 3.4 Subsequences and the BolzanoWeierstrass Theorem. 3.5 The Cauchy Criterion. 3.6 Properly Divergent Sequences. 3.7 Introduction to Infinite Series.
 CHAPTER 4 LIMITS. 4.1 Limits of Functions. 4.2 Limit Theorems. 4.3 Some Extensions of the Limit Concept.
 CHAPTER 5 CONTINUOUS FUNCTIONS. 5.1 Continuous Functions. 5.2 Combinations of Continuous Functions. 5.3 Continuous Functions on Intervals. 5.4 Uniform Continuity. 5.5 Continuity and Gauges. 5.6 Monotone and Inverse Functions.
 CHAPTER 6 DIFFERENTIATION. 6.1 The Derivative. 6.2 The Mean Value Theorem. 6.3 L'Hospital's Rules. 6.4 Taylor's Theorem.
 CHAPTER 7 THE RIEMANN INTEGRAL. 7.1 Riemann Integral. 7.2 Riemann Integrable Functions. 7.3 The Fundamental Theorem. 7.4 The Darboux Integral. 7.5 Approximate Integration.
 CHAPTER 8 SEQUENCES OF FUNCTIONS. 8.1 Pointwise and Uniform Convergence. 8.2 Interchange of Limits. 8.3 The Exponential and Logarithmic Functions. 8.4 The Trigonometric Functions.
 CHAPTER 9 INFINITE SERIES. 9.1 Absolute Convergence. 9.2 Tests for Absolute Convergence. 9.3 Tests for Nonabsolute Convergence. 9.4 Series of Functions.
 CHAPTER 10 THE GENERALIZED RIEMANN INTEGRAL. 10.1 Definition and Main Properties. 10.2 Improper and Lebesgue Integrals. 10.3 Infinite Intervals. 10.4 Convergence Theorems.
 CHAPTER 11 A GLIMPSE INTO TOPOLOGY. 11.1 Open and Closed Sets in R. 11.2 Compact Sets. 11.3 Continuous Functions. 11.4 Metric Spaces. APPENDIX A LOGIC AND PROOFS. APPENDIX B FINITE AND COUNTABLE SETS. APPENDIX C THE RIEMANN AND LEBESGUE CRITERIA. APPENDIX D APPROXIMATE INTEGRATION. APPENDIX E TWO EXAMPLES. REFERENCES. PHOTO CREDITS. HINTS FOR SELECTED EXERCISES. INDEX.
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QA300 .B294 2011  Unknown 
 Tobisch, Elena, 1956
 Cambridge, UK ; New York : Cambridge University Press, 2011.
 Description
 Book — xv, 223 p. : ill. ; 26 cm.
 Summary

 1. Exposition
 2. Kinematics: wavenumbers
 3. Kinematics: resonance clusters
 4. Dynamics
 5. Mechanical playthings
 6. Wave turbulent regimes
 7. Epilogue Appendix: software Index.
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QA372 .K247 2011  Unknown 
98. Real analysis through modern infinitesimals [2011]
 Vakil, Nader.
 Cambridge [England] ; New York : Cambridge University Press, 2011.
 Description
 Book — xix, 565 p. : ill. ; 24 cm.
 Summary

 Preface Introduction Part I. Elements of Real Analysis:
 1. Internal set theory
 2. The real number system
 3. Sequences and series
 4. The topology of R
 5. Limits and continuity
 6. Differentiation
 7. Integration
 8. Sequences and series of functions
 9. Infinite series Part II. Elements of Abstract Analysis:
 10. Point set topology
 11. Metric spaces
 12. Complete metric spaces
 13. Some applications of completeness
 14. Linear operators
 15. Differential calculus on Rn
 16. Function space topologies Appendix A. Vector spaces Appendix B. The badic representation of numbers Appendix C. Finite, denumerable, and uncountable sets Appendix D. The syntax of mathematical languages References Index.
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QA300 .V28 2011  Unknown 
99. Advanced calculus : a geometric view [2010]
 Callahan, James (James J.)
 New York : Springer, c2010.
 Description
 Book — xvi, 526 p. : ill. ; 26 cm.
 Summary

 1 Starting Points.1.1 Substitution. Exercises. 1.2 Work and path integrals. Exercises. 1.3 Polar coordinates. Exercises.
 2 Geometry of Linear Maps. 2.1 Maps from R2 to R2. Exercises. 2.2 Maps from Rn to Rn. Exercises. 2.3 Maps from Rn to Rp, n 6= p. Exercises.
 3 Approximations. 3.1 Meanvalue theorems. Exercises. 3.2 Taylor polynomials in one variable. Exercises. 3.3 Taylor polynomials in several variables. Exercises.
 4 The Derivative. 4.1 Differentiability. Exercises. 4.2 Maps of the plane. Exercises. 4.3 Parametrized surfaces. Exercises. 4.4 The chain rule. Exercises.
 5 Inverses. 5.1 Solving equations. Exercises. 5.2 Coordinate Changes. Exercises. 5.3 The Inverse Function Theorem. Exercises.
 6 Implicit Functions. 6.1 A single equation. Exercises. 6.2 A pair of equations. Exercises. 6.3 The general case. Exercises.
 7 Critical Points. 7.1 Functions of one variable. Exercises. 7.2 Functions of two variables. Exercises. 7.3 Morse's lemma. Exercises.
 8 Double Integrals. 8.1 Example: gravitational attraction. Exercises. 8.2 Area and Jordan content. Exercises. 8.3 Riemann and Darboux integrals. Exercises.
 9 Evaluating Double Integrals. 9.1 Iterated integrals. Exercises. 9.2 Improper integrals. Exercises. 9.3 The change of variables formula. 9.4 Orientation. Exercises. 9.5 Green's Theorem. Exercises.
 10 Surface Integrals. 10.1 Measuring flux. Exercises. 10.2 Surface area and scalar integrals. Exercises. 10.3 Differential forms. Exercises.
 11 Stokes' Theorem. 11.1 Divergence. Exercises. 11.2 Circulation and Vorticity. Exercises. 11.3 Stokes' Theorem. 11.4 Closed and Exact Forms. Exercises.
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QA303.3 .C355 2010  Unknown 
100. Excursions in classical analysis : pathways to advanced problem solving and undergraduate research [2010]
 Chen, Hongwei.
 Washington, D.C. : Mathematical Association of America, c2010.
 Description
 Book — xiii, 301 p. : ill. ; 26 cm.
 Summary

 Preface
 1. Two classical inequalities
 2. A new approach for proving inequalities
 3. Means generated by an integral
 4. The L'Hopital monotone rule
 5. Trigonometric identities via complex numbers
 6. Special numbers
 7. On a sum of cosecants
 8. The gamma products in simple closed forms
 9. On the telescoping sums
 10. Summation of subseries in closed form
 11. Generating functions for powers of Fibonacci numbers
 12. Identities for the Fibonacci powers
 13. Bernoulli numbers via determinants
 14. On some finite trigonometric power sums
 15. Power series
 16. Six ways to sum (2)
 17. Evaluations of some variant Euler sums
 18. Interesting series involving binomial coefficients
 19. Parametric differentiation and integration
 20. Four ways to evaluate the Poisson integral
 21. Some irresistible integrals Solutions to selected problems.
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QA301 .C43 2010  Unknown 