The Britannica guide to analysis and calculus 1st Edition by Britannica Educational Publishing ISBN 1615301232 9781615301232 by Gregersen E. (ed.) 9781615301232, 1615301232 instant download after payment.

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ISBN 10: 1615301232 
ISBN 13: 9781615301232
Author: Britannica Educational Publishing

The dynamism of the natural world means that it is constantly changing, sometimes rapidly, sometimes gradually. By mathematically interpreting the continuous change that characterizes so many natural processes, analysis and calculus have become indispensable to bridging the divide between mathematics and the sciences. This comprehensive volume examines the key concepts of calculus, providing students with a robust understanding of integration and differentiation. Biographies of important figures will leave readers with an increased appreciation for the sometimes competing theories that informed the early history of the field.

The Britannica guide to analysis and calculus 1st Table of contents:

CHAPTER 1 MEASURING CONTINUOUS CHANGE
BRIDGING THE GAP BETWEEN ARITHMETIC AND GEOMETRY
DISCOVERY OF THE CALCULUS AND THE SEARCH FOR FOUNDATIONS
NUMBERS AND FUNCTIONS
NUMBER SYSTEMS
FUNCTIONS
THE PROBLEM OF CONTINUITY
APPROXIMATIONS IN GEOMETRY
INFINITE SERIES
THE LIMIT OF A SEQUENCE
CONTINUITY OF FUNCTIONS
PROPERTIES OF THE REAL NUMBERS
CHAPTER 2 CALCULUS
DIFFERENTIATION
AVERAGE RATES OF CHANGE
INSTANTANEOUS RATES OF CHANGE
FORMAL DEFINITION OF THE DERIVATIVE
GRAPHICAL INTERPRETATION
HIGHER-ORDER DERIVATIVES
INTEGRATION
THE FUNDAMENTAL THEOREM OF CALCULUS
ANTIDIFFERENTIATION
THE RIEMANN INTEGRAL
CHAPTER 3 DIFFERENTIAL EQUATIONS
ORDINARY DIFFERENTIAL EQUATIONS
NEWTON AND DIFFERENTIAL EQUATIONS
DYNAMICAL SYSTEMS THEORY AND CHAOS
PARTIAL DIFFERENTIAL EQUATIONS
MUSICAL ORIGINS
PARTIAL DERIVATIVES
D’ALEMBERT’S WAVE EQUATION
TRIGONOMETRIC SERIES SOLUTIONS
FOURIER ANALYSIS
CHAPTER 4 OTHER AREAS OF ANALYSIS
COMPLEX ANALYSIS
FORMAL DEFINITION OF COMPLEX NUMBERS
EXTENSION OF ANALYTIC CONCEPTS TO COMPLEX NUMBERS
SOME KEY IDEAS OF COMPLEX ANALYSIS
MEASURE THEORY
FUNCTIONAL ANALYSIS
VARIATIONAL PRINCIPLES AND GLOBAL ANALYSIS
CONSTRUCTIVE ANALYSIS
NONSTANDARD ANALYSIS
CHAPTER 5 HISTORY OF ANALYSIS
THE GREEKS ENCOUNTER CONTINUOUS MAGNITUDES
THE PYTHAGOREANS AND IRRATIONAL NUMBERS
ZENO’S PARADOXES AND THE CONCEPT OF MOTION
THE METHOD OF EXHAUSTION
MODELS OF MOTION IN MEDIEVAL EUROPE
ANALYTIC GEOMETRY
THE FUNDAMENTAL THEOREM OF CALCULUS
DIFFERENTIALS AND INTEGRALS
DISCOVERY OF THE THEOREM
CALCULUS FLOURISHES
ELABORATION AND GENERALIZATION
EULER AND INFINITE SERIES
COMPLEX EXPONENTIALS
FUNCTIONS
FLUID FLOW
REBUILDING THE FOUNDATIONS
ARITHMETIZATION OF ANALYSIS
ANALYSIS IN HIGHER DIMENSIONS
CHAPTER 6 GREAT FIGURES IN THE HISTORY OF ANALYSIS
THE ANCIENT AND MEDIEVAL PERIOD
ARCHIMEDES
EUCLID
EUDOXUS OF CNIDUS
IBN AL-HAYTHAM
NICHOLAS ORESME
PYTHAGORAS
ZENO OF ELEA
THE 17TH AND 18TH CENTURIES
JEAN LE ROND D’ALEMBERT
ISAAC BARROW
DANIEL BERNOULLI
JAKOB BERNOULLI
JOHANN BERNOULLI
BONAVENTURA CAVALIERI
LEONHARD EULER
PIERRE DE FERMAT
JAMES GREGORY
JOSEPH-LOUIS LAGRANGE, COMTE DE L’EMPIRE
PIERRE-SIMON, MARQUIS DE LAPLACE
GOTTFRIED WILHELM LEIBNIZ
COLIN MACLAURIN
SIR ISAAC NEWTON
GILLES PERSONNE DE ROBERVAL
BROOK TAYLOR
EVANGELISTA TORRICELLI
JOHN WALLIS
THE 19TH AND 20TH CENTURIES
STEFAN BANACH
BERNHARD BOLZANO
LUITZEN EGBERTUS JAN BROUWER
AUGUSTIN-LOUIS, BARON CAUCHY
RICHARD DEDEKIND
JOSEPH, BARON FOURIER
CARL FRIEDRICH GAUSS
DAVID HILBERT
ANDREY KOLMOGOROV
HENRI-LÉON LEBESGUE
HENRI POINCARÉ
BERNHARD RIEMANN
STEPHEN SMALE
KARL WEIERSTRASS
CHAPTER 7 CONCEPTS IN ANALYSIS AND CALCULUS
ALGEBRAIC VERSUS TRANSCENDENTAL OBJECTS
ARGAND DIAGRAM
BESSEL FUNCTION
BOUNDARY VALUE
CALCULUS OF VARIATIONS
CHAOS THEORY
CONTINUITY
CONVERGENCE
CURVATURE
DERIVATIVE
DIFFERENCE EQUATION
DIFFERENTIAL
DIFFERENTIAL EQUATION
DIFFERENTIATION
DIRECTION FIELD
DIRICHLET PROBLEM
ELLIPTIC EQUATION
EXACT EQUATION
EXPONENTIAL FUNCTION
EXTREMUM
FLUXION
FOURIER TRANSFORM
FUNCTION
HARMONIC ANALYSIS
HARMONIC FUNCTION
INFINITE SERIES
INFINITESIMALS
INFINITY
INTEGRAL
INTEGRAL EQUATION
INTEGRAL TRANSFORM
INTEGRAPH
INTEGRATION
INTEGRATOR
ISOPERIMETRIC PROBLEM
KERNEL
LAGRANGIAN FUNCTION
LAPLACE’S EQUATION
LAPLACE TRANSFORM
LEBESGUE INTEGRAL
LIMIT
LINE INTEGRAL
MEAN-VALUE THEOREM
MEASURE
MINIMUM
NEWTON AND INFINITE SERIES
ORDINARY DIFFERENTIAL EQUATION
ORTHOGONAL TRAJECTORY
PARABOLIC EQUATION
PARTIAL DIFFERENTIAL EQUATION
PLANIMETER
POWER SERIES
QUADRATURE
SEPARATION OF VARIABLES
SINGULAR SOLUTION
SINGULARITY
SPECIAL FUNCTION
SPIRAL
STABILITY
STURM-LIOUVILLE PROBLEM
TAYLOR SERIES
VARIATION OF PARAMETERS
GLOSSARY
BIBLIOGRAPHY
NONTECHNICAL WORKS
TECHNICAL WORKS
CALCULUS AND REAL ANALYSIS
COMPLEX ANALYSIS
MEASURE THEORY
ORDINARY DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS
PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER ANALYSIS
OTHER AREAS OF ANALYSIS
INDEX
BACK COVER

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