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0 PRELIMINARIES 0.1 Real Numbers, Logic and Estimation 0.2 Inequalities and Absolute Values 0.3 The Rectangular Coordinate System 0.4 Graphs of Equations 0.5 Functions and Their Graphs 0.6 Operationson Functions 0.7 The Trigonometric Functions 1 LIMITS 1.1 Introduction to Limits 1.2 Rigorous Study of Limits 1.3 Limit Theorems 1.4 Limits Involving Trigonometric Functions 1.5 Limits at Infinity, Infinite Limits 1.6 Continuity of Functions 1.7 Chapter Review 2 THE DERIVATIVE 2.1 Two Problems with One Theme 2.2 The Derivative 2.3 Rules for Finding Derivatives 2.4 Derivatives of Trigonometric Functions 2.5 The Chain Rule 2.6 Higher-Order Derivatives 2.7 Implicit Differentiation 2.8 Related Rates 2.9 Differentials and Approximations 2.10 Chapter Review 3 APPLICATIONS OF THE DERIVATIVE 3.1 Maxima and Minima 3.2 Monotonicity and Concavity 3.3 Local Extrema and Extrema on Open Intervals 3.4 Graphing Functions Using Calculus 3.6 The Mean Value Theorem for Derivatives 3.7 Solving Equations Numerically 3.8 Antiderivatives 3.9 Introduction to Differential Equations 4 THE DEFINITE INTEGRAL 4.1 Introduction to Area 4.2 The Definite Integral 4.3 The 1st Fundamental Theorem of Calculus 4.4 The 2nd Fundamental Theorem of Calculus and the Method of Substitution 4.5 The Mean Value Theorem for Integrals & the Use of Symmetry 4.6 Numerical Integration 4.7 Chapter Review 5 APPLICATIONS OF THE INTEGRAL 5.1 The Area of a Plane Region 5.2 Volumes of Solids: Slabs, Disks, Washers 5.3 Volumes of Solids of Revolution: Shells 5.4 Length of a Plane Curve 5.5 Work and Fluid Pressure 5.6 Moments, Center of Mass 5.7 Probability and Random Variables 5.8 Chapter Review 6 TRANSCENDENTAL FUNCTIONS 6.1 The Natural Logarithm Function 6.2 Inverse Functions and Their Derivatives 6.3 The Natural Exponential Function 6.4 General Exponential & Logarithmic Functions 6.5 Exponential Growth and Decay 6.6 First-Order Linear Differential Equations 6.7 Approximations for Differential Equations 6.8 Inverse Trig Functions & Their Derivatives 6.9 The Hyperbolic Functions & Their Inverses 6.10 Chapter Review 7 TECHNIQUES OF INTEGRATION 7.1 Basic Integration Rules 7.2 Integration by Parts 7.3 Some Trigonometric Integrals 7.4 Rationalizing Substitutions 7.5 The Method of Partial Fractions 7.6 Strategies for Integration 7.7 Chapter Review 8 INDETERMINATE FORMS & IMPROPER INTEGRALS 8.1 Indeterminate Forms of Type 0/0 8.2 Other Indeterminate Forms 8.3 Improper Integrals: Infinite Limits of Integration 8.4 Improper Integrals: Infinite Integrands 8.5 Chapter Review 9 INFINITE SERIES 9.1 Infinite Sequences 9.2 Infinite Series 9.3 Positive Series: The Integral Test 9.4 Positive Series: Other Tests 9.5 Alternating Series, Absolute Convergence, and Conditional Convergence 9.6 Power Series 9.7 O97801312933110 PRELIMINARIES0.1Real Numbers, Logic and Estimation0.2Inequalities and Absolute Values0.3The Rectangular Coordinate System0.4Graphs of Equations0.5Functions and Their Graphs0.6Operations on Functions0.7The Trigonometric Functions1 LIMITS1.1Introduction to Limits1.2Rigorous Study of Limits1.3Limit Theorems1.4Limits Involving Trigonometric Functions1.5Limits at Infinity, Infinite Limits1.6Continuity of Functions1.7Chapter Review2 THE DERIVATIVE2.1Two Problems with One Theme2.2The Derivative2.3Rules for Finding Derivatives2.4Derivatives of Trigonometric Functions2.5The Chain Rule2.6Higher-OrderDerivatives2.7Implicit Differentiation2.8Related Rates2.9Differentials and Approximations2.10Chapter Review3 APPLICATIONS OF THE DERIVATIVE3.1Maxima and Minima3.2Monotonicity and Concavity3.3Local Extrema and Extrema on Open Intervals3.4Graphing Functions Using Calculus3.6The Mean Value Theorem for Derivatives3.7Solving Equations Numerically3.8Antiderivatives3.9Introduction to Differential Equations4 THE DEFINITE INTEGRAL4.1Introduction to Area4.2The Definite Integral4.3The 1st Fundamental Theorem of Calculus4.4The 2nd Fundamental Theorem of Calculusand the Method of Substitution4.5The Mean Value Theorem for Integrals & the Use of Symmetry4.6Numerical Integration4.7Chapter Review5 APPLICATIONS OF THE INTEGRAL5.1The Area of a Plane Region5.2Volumes of Solids: Slabs, Disks, Washers5.3Volumes of Solids of Revolution: Shells5.4Length of a Plane Curve5.5Work and Fluid Pressure5.6Moments, Center of Mass5.7Probability and Random Variables5.8Chapter Review6 TRANSCENDENTAL FUNCTIONS6.1The Natural Logarithm Function6.2Inverse Functions and Their Derivatives6.3The Natural Exponential Function6.4General Exponential & Logarithmic Functions6.5Exponential Growth and Decay6.6First-Order Linear Differential Equations6.7Approximations for Differential Equations6.8Inverse Trig Functions & Their Derivatives6.9The Hyperbolic Functions & Their Inverses6.10Chapter Review7 TECHNIQUES OF INTEGRATION7.1Basic Integration Rules7.2Integration by Parts7.3Some Trigonometric Integrals7.4Rationalizing Substitutions7.5The Method of Partial Fractions7.6Strategies for Integration7.7Chapter Review8 INDETERMINATE FORMS & IMPROPER INTEGRALS8.1Indeterminate Forms of Type 0/08.2Other Indeterminate Forms8.3Improper Integrals: Infinite Limits of Integration8.4Improper Integrals: Infinite Integrands8.5Chapter Review9 INFINITE 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 Review10 CONICS AND POLAR COORDINATES10.1The Parabola10.2Ellipses and Hyperbolas10.3Translation and Rotation of Axes10.4Parametric Representation of Curves10.5The Polar Coordinate System10.6Graphs of Polar Equations10.7Calculus in Polar Coordinates10.8Chapter Review11 GEOMETRY IN SPACE, VECTORS11.1Cartesian Coordinates in Three-Space11.2Vectors11.3The Dot Product11.4The Cross Product11.5Vector Valued Functions & Curvilinear Motion11.6Lines in Three-Space11.7Curvature and Components of Acceleration11.8Surfaces in Three Space11.9Cylindrical and Spherical Coordinates11.10Chapter Review12 DERIVATIVES OF FUNCTIONS OF TWO OR MORE VARIABLES12.1Functions of Two or More Variables12.2Partial Derivatives12.3Limits and Continuity12.4Differentiability12.5Directional Derivatives and Gradients12.6The Chain Rule12.7Tangent Planes, Approximations12.8Maxima and Minima12.9LagrangeMultipliers12.10Chapter Review13 MULTIPLE INTEGRATION13.1Double Integrals over Rectangles13.2Iterated Integrals13.3Double Integrals over Nonrectangular Regions13.4Double Integrals in Polar C9780131293311For freshman/sophomore-level courses treating calculus of both one and several variables. Clear and Concise! Varberg focuses on the most critical concepts freeing you to teach the way you want! This popular calculus text remains the shortest mainstream calculus book available - yet covers all the material needed by, and at an appropriate level for, students in engineering, science, and mathematics. It's conciseness and clarity helps students 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. The authors make effective use of computing technology, graphics, and applications. Ideal for instructors who want a no-nonsense, concisely written treatment. 9780131293311Intended for freshman/sophomore-level courses treating calculus of both one and several variables, this work helps students focus on, and understand vital concepts in calculus. It makes use of computing technology, graphics, and applications, and is useful for instructors.9780131293311