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Full Description
Essential Calculusgrowing demand for a more streamlined and faster paced text at a lower price for students. This text continues the Larson tradition by offering instructors proven pedagogical techniques and accessible content and innovative learning resources for student success.
Contents
Note1. Limits and Their Properties1.1 Linear Models and Rates of Change1.2 Functions and Their Graphs1.3 Inverse Functions1.4 Exponential and Logarithmic Functions1.5 Finding Limits Graphically and Numerically1.6 Evaluating Limits Analytically1.7 Continuity and One-Sided Limits1.8 Infinite Limits2. Differentiation2.1 The Derivative and the Tangent Line Problem2.2 Basic Differentiation Rules and Rates of Change2.3 Product and Quotient Rules and Higher-Order Derivatives2.4 The Chain Rule2.5 Implicit Differentiation2.6 Derivatives of Inverse Functions2.7 Related Rates2.8 Newton''s Method3. Applications of Differentiation3.1 Extrema on an Interval3.2 Rolle''s Theorem and the Mean Value Theorem3.3 Increasing and Decreasing Functions and the First Derivative Test3.4 Concavity and the Second Derivative Test3.5 Limits at Infinity3.6 Optimization Problems3.7 Differentials4. Integration4.1 Antiderivatives and Indefinite Integration4.2 Area4.3 Riemann Sums and Definite Integrals4.4 The Fundamental Theorem of Calculus4.5 Integration by Substitution4.6 Numerical Integration4.7 The Natural Logarithmic Function: Integration4.8 Inverse Trigonometric Functions: Integration4.9 Hyperbolic Functions5. Applications of Integration5.1 Area of a Region Between Two Curves5.2 Volume: The Disk Method5.3 Volume: The Shell Method5.4 Arc Length and Surfaces of Revolution5.5 Applications in Physics and Engineering5.6 Differential Equations: Growth and Decay6. Integration Techniques, L''Hopital''s Rule, and Improper Integrals6.1 Integration by Parts6.2 Trigonometric Integrals6.3 Trigonometric Substitution6.4 Partial Fractions6.5 Integration by Tables and Other Integration Techniques6.6 Indeterminate Forms and L''Hopital''s Rule6.7 Improper Integrals7. Infinite Series7.1 Sequences7.2 Series and Convergence7.3 The Integral and Comparison Tests7.4 Other Convergence Tests7.5 Taylor Polynomials and Approximations7.6 Power Series7.7 Representation of Functions by Power Series7.8 Taylor and Maclaurin Series8. Conics, Parametric Equations, and Polar Coordinates8.1 Plane Curves and Parametric Equations8.2 Parametric Equations and Calculus8.3 Polar Coordinates and Polar Graphs8.4 Area and Arc Length in Polar Coordinates8.5 Polar Equations and Conics and Kepler''s Laws9. Vectors and the Geometry of Space9.1 Vectors in the Plane9.2 Space Coordinates and Vectors in Space9.3 The Dot Product of Two Vectors9.4 The Cross Product of Two Vectors in Space9.5 Lines and Planes in Space9.6 Surfaces in Space9.7 Cylindrical and Spherical Coordinates10. Vector-Valued Functions10.1 Vector-Valued Functions10.2 Differentiation and Integration of Vector-Valued Functions10.3 Velocity and Acceleration10.4 Tangent Vectors and Normal Vectors10.5 Arc Length and Curvature11. Functions of Several Variables11.1 Introduction to Functions of Several Variables11.2 Limits and Continuity11.3 Partial Derivatives11.4 Differentials and the Chain Rule11.5 Directional Derivatives and Gradients11.6 Tangent Planes and Normal Lines11.7 Extrema of Functions of Two Variables11.8 Lagrange Multipliers12. Multiple Integration12.1 Iterated Integrals and Area in the Plane12.2 Double Integrals and Volume12.3 Change of Variables: Polar Coordinates12.4 Center of Mass and Moments of Inertia12.5 Surface Area12.6 Triple Integrals and Applications12.7 Triple Integrals in Cylindrical and Spherical Coordinates12.8 Change of Variables: Jacobians13. Vector Analysis13.1 Vector Fields13.2 Line Integrals13.3 Conservative Vector Fields and Independence of Path13.4 Green''s Theorem13.5 Parametric Surfaces13.6 Surface Integrals13.7 Divergence Theorem13.8 Stokes''s TheoremAppendix A Proofs of Selected TheoremsAppendix B Integration TablesAppendix C Business and Economic ApplicationsAnswers to Odd-Numbered ExercisesIndexAdditional AppendicesAppendix D Precalculus ReviewD.1 Real Numbers and the Real Number LineD.2 The Cartesian PlaneD.3 Review of Trigonometric FunctionsAppendix E Rotation and General Second-Degree EquationAppendix F Complex Numbers
