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Frank Ayres Jr., PhD, was a professor and a department head at Dickinson College in Carlisle, Pennsylvania.Elliott Mendelson, PhD, is a professor of mathematics at Queens College in New York City.
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. Newton뭩 Method � Antiderivatives � The Definite Integral. Area under a Curve � The Fundamental Theorem of Calculus � The Natural Logarithm � Exponential and Logarithmic Functions � L묱opital뭩 Rule � Exponential Growth and Decay � Applications of Integration I: Area and Arc Length � Applications of Integration II: Volume � Techniques of Integration I: Integration by Parts � Techniques of Integration II: Trigonometric Integrands and Trigonometric Substitutions � Techniques of Integration III: Integration by Partial Fractions � Miscellaneous Substitutions � Improper Integrals � Applications of Integration II: 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. Taylor뭩 Formula with Remainder � Partial Derivatives � Total Differential. Differentiability. Chain Rules � Space Vectors � Surface 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 First and Second Order