Bers, Lipman. creator text xxu New York Hdt,Rinehart Winton ink. 1969 monographic eng

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xiii, 566p.: ill.; 25cm. Contents: Numbers: Rational numbers The need for extending the concept of numbers -- Addition and multiplication -- Inequalities -- Decimal representation of rational numbers -- Real numbers -- Completeness of the real numbers. Induction -- Approximate calculations -- Rational and irrational numbers problems -- Coordinates: Coordinates of a point. Distance formula -- Straight lines -- Circles -- Parabolas -- Squaring the parabola -- Geometry and numbers problems -- Functions: Functions and graphs -- Polynomial, Rational, and Radical functions. Introduction to limits -- Continuous functions -- Limits -- One-sided limits, infinite limits, and limits at infinity -- Proofs of some continuity theorems -- Proof of the intermediate value theorem problems -- Derivatives: The derivative of a function. tangents. velocity -- Differentiation -- Higher derivatives. Acceleration -- Signs of derivative. Maxima and minima -- Primitives functions -- Proofs of differentiation rules -- One-sided derivation. Infinite derivatives. Differentiable and Nondifferentiable Function -- Proof of some Theorems about Derivatives problems -- Integrals: The integral of a function. The area under the curve -- The fundamental theorem of calculus -- Integration -- Area. Volume. Length -- Energy -- Improper Integrals -- Proof of the fundamental theorem -- Existence of integrals -- Existence of improper integrals problems -- Transcendental Functions: Sines and Cosines -- The tangent and the Arc tangent -- Other circular functions -- Logarithms -- The exponential function -- Other application of the exponential function -- Some nonelementary functions -- Techniques of integration: Numerical integration -- Integration of rational functions -- Rationalizable integrals -- Reduction formulas -- A collection of integration formulas -- Series: Mean value theorems -- Taylor's Theorem -- Infinite sequences -- Infinite series -- Power series -- L'Hospital's rule -- Convergence proofs -- Radius of convergence -- The truncation error in numerical integration. Includes Index. QA303.B54 0030652405 180418