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The ideal review for your calculus course More than 40 million students have trusted Schaum's Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in this field, Schaum's Outline of Calculuscovers what you need to know for your course and, more important, your exams. Step-by-step, the authors walk you through coming up with solutions to exercises in this topic. Outline format supplies a concise guide to the standard college course in calculus 1,103 problems solved step-by-step Clear, concise explanations of all calculus concepts Appropriate for the following courses: Calculus I, Calculus II, Calculus III, AP Calculus, Precalculus Supports all the major calculus textbooks
Table of Contents
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 • Differential Equations of First and Second Order