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AuthorEdwards, Robert. author
TitleA Formal Background to Mathematics 2a [electronic resource] : A Critical Approach to Elementary Analysis / by Robert Edwards
ImprintNew York, NY : Springer New York, 1980
Connect tohttp://dx.doi.org/10.1007/978-1-4613-8096-2
Descript XLVIII, 606 p. online resource

CONTENT

VII: Convergence of Sequences -- Hidden hypotheses -- VII.1 Sequences convergent inR -- VII.2 Infinite limits -- VII.3 Subsequences -- VII.4 The Monotone Convergence Principle again -- VII.5 Suprema and infima of sets of real numbers -- VII.6 Exponential and logarithmic functions -- VII.7 The General Principle of Convergence -- VIII: Continuity and Limits of Functions -- and hidden hypotheses -- VIII.1 Continuous functions -- VIII.2 Properties of continuous functions -- VIII.3 General exponential, logarithmic and power functions -- VIII.4 Limit of a function at a point -- VIII.5 Uniform continuity -- VIII.6 Convergence of sequences of functions -- VIII.7 Polynomial approximation -- VIII.8 Another approach to expa -- IX: Convergence of Series -- and hidden hypotheses -- IX.1 Series and their convergence -- IX.2 Absolute and conditional convergence -- IX.3 Decimal expansions -- IX.4 Convergence of series of functions -- X: Differentiation -- and hidden hypotheses -- X.1 Derivatives -- X.2 Rules for differentiation -- X.3 The mean value theorem and its corollaries -- X.4 Primitives -- X.5 Higher order derivatives -- X.6 Extrema and derivatives -- X.7 A differential equation and the exponential function again -- X.8 Calculus in several variables -- XI: Integration -- XI.1 Integration and area -- XI.2 Analytic definition and study of integration -- XI.3 Integrals and primitives -- XI.4 Integration by parts -- XI.5 Integration by change of variable (or by substitution) -- XI.6 Termwise integration of sequences of functions -- XI.7 Improper integrals -- XI.8 First order linear differential equations -- XI.9 Integrals in several variables -- XII: Complex Numbers: Complex Exponential and Trigonometric Functions -- XII.1 Definition of complex numbers -- XII.2 Groups, subgroups and homomorphisms -- XII.3 Homomorphisms ofRinto ?; complex exponentials -- XII.4 The exponential function with domainC -- XII.5 The trigonometric functions cosine and sine -- XII.6 Further inverse trigonometric functions -- XII.7 The simple harmonic equation -- XII.8 Another differential equation -- XII.9 Matrices and complex numbers -- XII.10 A glance at Fourier series -- XII.11 Linear differential equations with constant coefficients -- XIII: Concerning Approximate Integration -- XIII.1 Quotes from syllabus notes -- XIII.2 Notation and preliminaries -- XIII.3 Precise formulation of statements XIII.1.1 โ{128}{147} XIII.1.3 -- XIII.4 Some corrected versions -- XIII.5 Falsity of statements XIII.3.1 โ{128}{147} XIII.3.3 -- XIII.6 The formulas applied to tabulated data -- XIV: Differential Coefficients -- XIV.1 The d-notation and differential coefficients -- XIV.2 The simple harmonic equation -- XV: Lengths of Curves -- XV.1 Quotes and criticisms -- XV.2 Paths -- XV.3 Lengths of paths -- XV.4 Path length as an integral -- XV.5 Ratio of arc length to chord length -- XV.6 Additivity of arc length -- XV.7 Equivalent paths; simple paths -- XV.8 Circular arcs; application to complex exponential and trigonometric functions -- XV.9 Angles and arguments -- XV.10 General remarks about curves


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