Schaum's outline of calculus / Frank Ayres, Jr., Elliot Mendelson.

Rev. ed. 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'Hopital's 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. Taylor's 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 -- Differntial Equations of First and Second Order.

1103 fully solved problems; expert tips on the graphing calculaor; many math review sections; covers all course fundamentals, supplements any class text; the perfect aid for higher grades.