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This review of beginning calculus is updated to reflect the latest course scope and sequences, with expanded explanations of particularly difficult topics.
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Chapters include: Coordinate Systems on a Line * Coordinate Systems in a Plane * Graphs of Equations * Straight Lines * Intersections of Graphs * Symmetry * Functions and Their Graphs * Limits * Special Limits * Continuity * The Slope of a Tangent Line * The Derivative * More on the Derivative * Maximum and Minimum Problemse * The Chain Rule * Implicit Differentiation * The Mean-Value Theorem and the Sign of the Derivative * Rectilinear Motion and Instantaneous Velocity * Instantaneous Rate of Change * Related Rates * Approximation by Differentials; Newton's Method * Higher-Order Derivatives * Applications of the Second Derivative and Graph Sketching * More Maximum and Minimum Problems * Angle Measure * Sine and Cosine Functions * Graphs and Derivatives of Sine and Cosine Functions * The Tangent and Other Trigonometric Functions * Antiderivatives * The Definite Integral * The Fundamental Theorem of Calculus * Applications of Integration I: Area and Arc Length * Applications of Integration II: Volume * The Natural Logarithm * Exponential Functions * L'Hopital's Rule: Exponential Growth and Decay * Inverse Trigonometric Functions * Integration by Parts * Trigonometric Integrands and Trigonometric Substitutions * Integration of Rational Function: The Method of Partial Fractions
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