Schaum's outlines : Calculus /
Frank Ayres, Jr., Elliott Mendelson.
- Sixth edition
- New York : McGraw-Hill, c2013.
- xii, 534 pages : illustrations; 28 cm.
- Schaum's outline series .
Revision of: Schaum's outline of theory and problems of differential and integral calculus. 3rd ed. c1990
Includes index
Linear coordinate systems. Absolute value. Inequalities Rectangular coordinate systems Lines Circles Equations and their graphs Functions Limits Continuity The derivative Rules for differentiating functions Implicit differentiation Tangent and normal lines Law of the mean. Increasing and decreasing functions Maximum and minimum values Curve sketching. Concavity. Symmetry Review of trigonometry Differentiation of trigonometric functions Inverse trigonometric functions Rectilinear and circular motion Related rates Differentials. Newton's method Antiderivatives The definite integral. Area under a curve The fundamental theorem of calculus The natural logarithm Exponential and logarithmic functions L'Hôpital's rule Exponential growth and decay Applications of integration I: area and arc length Techniques of integration I: Volume Techniques of integration II: trigonometric integrands and trigonometric substitutions Techniques of integration III: integration by partial fractions Techniques of integration IV: miscellaneous substitutions Improper integrals Applications of integration III: area of a surface of revolution Parametric representation of curves Curvature Plane vectors Curvilinear motion Polar coordinates Infinite sequences Infinite series Series with positive terms. The integral test. Comparison tests Alternating series. Absolute and conditional convergence. The ratio test Power series Taylor and Maclaurin series. Taylor's formula with remainder Partial derivatives Total differential. Differentiability. Chain rules Space vectors Surfaces and curves in space Directional derivatives. Maximum and minimum values Vector differentiation and integration Double and iterated integrals Centroids and moments of inertia of plane areas Double integration applied to volume under a surface and the area of a curved surface Triple integrals Masses of variable density Differential equations of the first and second order
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