Calculus: The Classic Edition
1. PRECALCULUS REVIEW. Algebra. Functions. Trigonometry. 2. LIMITS OF FUNCTIONS. Introduction to Limits. Definition of Limits. Techniques for Finding Limits. Limits Involving Infinity. Continuous Functions. Review Exercises. 3. THE DERIVATIVE. Tangent Lines and Rates of Change. Definition of Derivative. Techniques of Differentiation. Derivatives of the Trigonometric Functions. Increments and Differentials. The Chain Rule. Implicit Differentiation. Related Rates. Review Exercises. 4. APPLICATIONS OF THE DERIVATIVE. Extrema of Functions. The Mean Value Theorem. The First Derivative Test. Concavity and the Second Derivative Test. Summary of Graphical Methods. Optimization Problems. Rectlinear Motion and Other Applications. Newton's Method. Review Exercises. 5. INTEGRALS. Antiderivatives and Indefinite Integrals. Change of Variables in Indefinite Integrals. Summation Notation and Area. The Definite Integral. Properties of the Definite Integral. The Fundamental Theorem of Calculus. Numerical Integration. Review Exercises. 6. APPLICATIONS OF THE DEFINITE INTEGRAL. Area. Solids of Revolution. Volumes by Cylindrical Shells. Volumes by Cross Sections. Arc Length and Surfaces of Revolution. Work. Moments and Centers of Mass. Other Applications. Review Exercises. 7. LOGARITHMIC AND EXPONENTIAL FUNCTIONS. Inverse Functions. The Natural Logarithmic Function. The Natural Exponential Function. Integration. General Exponential and Logarithmic Functions. Laws of Growth and Decay. Review Exercises. 8. INVERSE TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS. Inverse Trigonometric Functions. Derivative and Integrals. Hyperbolic Functions. Inverse Hyperbolic Functions. Review Exercises. 9. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals. Trigonometric Substitutions. Integrals of Rational Functions. Integrals Involving Quadratic Expressions. Miscellaneous Substitutions. Tables of Integrals. Review Exercises. 10. INDETERMINATE FORMS AND IMPROPER INTEGRALS. The Indeterminate Forms 0/0 and / . Other Indeterminate Forms. Integrals with Infinite Limits of Integration. Integrals with Discontinuous Integrands. Review Exercises. 11. INFINITE SERIES. Sequences. Convergent of Divergent Series. Positive-Term Series. The Rational and Root Tests. Alternation Series and Absolute Convergence. Power Series. Power Series Representations of Functions. Maclaurin and Taylor Series. Applications of Taylor Polynomials. The Binomial Series. Review Exercises. 12. TOPICS FROM ANALYTIC GEOMETRY. Parabolas. Ellipses. Hyperbolas. Rotation of Axes. Review Exercises. 13. PLANE CURVES AND POLAR COORDINATES. Plane Curves. Tangent Lines and Arc Length. Polar Coordinates. Integrals in Polar Coordinates. Polar Equations of Conics. Review Exercises. 14. VECTORS AND SURFACES. Vectors in Two Dimensions. Vectors in Three Dimensions. The Dot Product. The Vector Product. Lines and Planes. Surfaces. Review Exercises. 15. VECTOR-VALUED FUNCTIONS. Vector-Valued Functions and Space Curves. Limits, Derivatives, and Integrals. Motion. Curvature. Tangential and Normal Components of Acceleration. Kepler's Laws. Review Exercises. 16. PARTIAL DIFFERENTIATION. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Increments and Differentials. Chain Rules. Directional Derivatives. Tangent Planes and Normal Lines. Extrema of Functions of Several Variables. Lagrange Multipliers. Review Exercises. 17. MULTIPLE INTEGRALS. Double Integrals. Area and Volume. Double Integrals in Polar Coordinates. Surface Area. Triple Integrals. Moments and Center of Mass. Cylindrical Coordinates. Spherical Coordinates. Change of Variables and Jacobians. Review Exercises. 18. VECTOR CALCULUS. Vector Fields. Line Integrals. Independence of Path. Green's Theorem. Surface Integrals. The Divergence Theorem. Stoke's Theorem. Review Exercises. 19. DIFFERENTIAL EQUATIONS. Seperable Differential Equations. First-Order Linear Differential Equations. Second-Order Linear Differential Equations. Nonhomogeneous Linear Differential Equations. Vibrations. Series Solutions. Review Exercises. Appendices I: Mathematical Induction. Appendices II: Theorems on Limits and Integrals. Appendices III: Tables. Appendices IV: Table Of Integrals. Answers To Odd-Numbered Exercises. Index.--This text refers to an alternateHardcoveredition.