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Full Description
Clear and Concise. Varberg focuses on the most critical concepts. This popular calculus text remains the shortest mainstream calculus book available - yet covers all relevant material needed by, and appropriate to, the study of calculus at this level. It's conciseness and clarity helps you focus on, and understand, critical concepts in calculus without them getting bogged down and lost in excessive and unnecessary detail. It is accurate, without being excessively rigorous, up-to-date without being faddish.
Contents
1PRELIMINARIES1.1Real Numbers, Estimation, and Logic1.2Inequalities and Absolute Values1.3The Rectangular Coordinate System1.4Graphs of Equations1.5Functions and Their Graphs1.6Operations on Functions1.7Exponential and Logarithmic Functions1.8The Trigonometric Functions 1.9The Inverse Trigonometric Functions1.10Chapter Review2LIMITS2.1Introduction to Limits2.2Rigorous Study of Limits2.3Limit Theorems2.4Limits at Infinity; Infinite Limits2.5Limits Involving Trigonometric Functions2.6Natural Exponential, Natural Log, and Hyperbolic Functions2.7Continuity of Functions2.8Chapter Review3THE DERIVATIVE3.1Two Problems with One Theme3.2The Derivative3.3Rules for Finding Derivatives3.4Derivatives of Trigonometric Functions3.5The Chain Rule3.6Higher-Order Derivatives3.7Implicit Differentiation3.8Related Rates3.9Derivatives of Exponential and Logarithmic Functions3.10Derivatives of Hyperbolic and Inverse Trigonometric Functions3.11Differentials and Approximations3.12Chapter Review44.1Maxima and Minima4.2Monotonicity and Concavity4.3Local Extrema and Extrema on Open Intervals4.4Practical Problems4.5Graphing Functions Using Calculus4.6The Mean Value Theorem for Derivatives4.7Solving Equations Numerically4.8Antiderivatives4.9Introduction to Differential Equations4.10Exponential Growth and Decay4.11Chapter Review5THE DEFINITE INTEGRAL5.1Introduction to Area5.2The Definite Integral5.3The 1st Fundamental Theorem of Calculus5.4The 2nd Fundamental Theorem of Calculusand the Method of Substitution5.5The Mean Value Theorem for Integrals & the Use of Symmetry5.6Numerical Integration5.7Chapter Review66.1The Area of a Plane Region6.2Volumes of Solids: Slabs, Disks, Washers6.3Volumes of Solids of Revolution: Shells6.4Length of a Plane Curve6.5Work and Fluid Pressure6.6Moments and Center of Mass6.8Probability and Random Variables6.8Chapter Review7DIFFERENTIAL EQUATIONS7.1Basic Integration Rules7.2Integration by Parts7.3Some Trigonometric Integrals7.4Rationalizing Substitutions7.5Integration of Rational Functions Using Partial Fractions7.6Strategies for Integration7.7First-Order Linear Differential Equations7.8Approximations for Differential Equations7.9Chapter Review8INDETERMINATE FORMS & IMPROPER INTEGRALS8.1Indeterminate Forms of Type 0/08.2Other Indeterminate Forms8.3Improper Integrals: Infinite Limits of Integration8.4Improper Integrals: Infinite Integrands8.5Chapter Review9INFINITE SERIES9.1Infinite Sequences9.2Infinite Series9.3Positive Series: The Integral Test9.4Positive Series: Other Tests9.5Alternating Series, Absolute Convergence,and Conditional Convergence9.6Power Series9.7Operations on Power Series9.8Taylor and Maclaurin Series9.9The Taylor Approximation to a Function9.10Chapter Review10CONICS AND POLAR COORDINATES10.1The Parabola10.2Ellipses and Hyperbolas10.3Translation and Rotation of Axes10.4Parametric Representation of Curves in the Plane10.5The Polar Coordinate System10.6Graphs of Polar Equations10.7Calculus in Polar Coordinates10.8Chapter Review1111.1Cartesian Coordinates in Three-Space11.2Vectors11.3The Dot Product11.4The Cross Product11.5Vector Valued Functions & Curvilinear Motion11.6Lines and Tangent Lines in Three-Space11.7Curvature and Components of Acceleration11.8Surfaces in Three Space11.9Cylindrical and Spherical Coordinates11.10Chapter Review12DERIVATIVES FOR FUNCTIONS OF 12.1Functions of Two or More Variables12.2Partial Derivatives12.3Limits and Continuity12.4Differentiability12.5Directional Derivatives and Gradients12.6The Chain Rule12.7Tangent Planes and Approximations12.8Maxima and Minima12.9The Method of Lagrange Multipliers12.10Chapter Review13MULTIPLE INTEGRATION13.1Double Integrals over Rectangles13.2Iterated Integrals13.3Double Integrals over Nonrectangular Regions13.4Double Integrals in Polar Coordinates13.5Applications of Double Integrals13.6Surface Area13.7Triple Integrals (Cartesian Coordinates)13.8Triple Integrals (Cyl & Sph Coordinates)13.9Change of Variables in Multiple Integrals13.10Chapter Review14VECTOR CALCULUS14.1Vector Fields14.2Line Integrals14.3Independence of Path14.4Green's Theorem in the Plane14.5Surface Integrals14.6Gauss's Divergence Theorem14.7Stokes's Theorem14.8Chapter Review15DIFFERENTIAL EQUATIONS15.1Linear Homogeneous Equations15.2Nonhomogeneous Equations15.3Applications of Second-Order Equations15.4Chapter ReviewAPPENDIXA.1Mathematical InductionA.2Proofs of Several Theorems
