000			02442nam a22001577a 4500
008			180418b xxu||||| |||| 00| 0 eng d
020			_a0030652405
050			_aQA303.B54
100			_aBers, Lipman.
245			_aCalculus. /
260			_aNew York: _bHdt,Rinehart Winton ink. , _c1969
300			_axiii, 566p.: _bill.; _c25cm.
500			_aIncludes Index.
505			_aContents: 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.
942			_2lcc _cBK
999			_c6595 _d14095