Outlines theory and techniques of calculus, emphasizing strong understanding of concepts, and the basic principles of analysis. Reviews elementary and intermediate calculus and features discussions of elementary-point set theory, and properties of continuous functions.
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FUNDAMENTALS OF ELEMENTARY CALCULUS
THE REAL NUMBER SYSTEM
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absolute maximum absolutely convergent algebra apply assume calculate called chain rule Chapter closed interval co-ordinate system components consider constant continuous function corresponding curve definition denote differentiable function divergent dot product double integral dx dy equations Example Exercise exists expression finite number formula function defined function f geometrical given graph Green's theorem Hence improper integrals independent variable inequality infinite inverse Jacobian limit line integral linear transformation mapping matrix mean method neighborhood norm notation obtain open interval open set parameter partial derivatives plane point function point x0 positive integer positive number problem prove quadratic form radius radius of convergence real numbers rectangle rectangular co-ordinate region result satisfied scalar sequence Show solution student subinterval sufficiently Suppose surface tangent Theorem VIII uniform convergence vector field vector space write x-axis xy-plane z-axis zero