Varberg 8e-9e-ET Version Table of Contents Comparisons 8th Edition 9th Edition Early Transcendentals 9 Ch Sec Title Ch Sec Title Ch Sec Title 1 PRELIMINARIES 0 PRELIMINARIES 0 PRELIMINARIES 1.1 The Real Number System 0.1 Real Numbers, Logic and Estimation 0.1 Real Numbers, Logic and Estimation 1.2 Decimals, Calculators, Estimation 0.2 Inequalities and Absolute Values 0.2 Inequalities and Absolute Values 1.3 Inequalities 0.3 The Rectangular Coordinate System 0.3 The Rectangular Coordinate System 1.4 Absolute Values, Square Roots & Squares 0.4 Graphs of 0.4 Graphs of 1.5 The Rectangular Coordinate System 0.5 and Their Graphs 1.6 The Straight Line 0.6 Operations on 1 FUNCTIONS 1.7 Graphs of 0.7 The Trigonometric 1.1 and Their Graphs 1.8 Chapter Review 1.2 Operations on 2 FUNCTIONS AND LIMITS 1.3 Exponential and Logarithmic 1 LIMITS 1.4 The Trigonometric & Their Inverses 2.1 and Their Graphs 1.1 Introduction to Limits 1.5 Chapter Review 2.2 Operations on 1.2 Rigorous Study of Limits 2.3 The Trigonometric 1.3 Limit Theorems 2 LIMITS 2.4 Introduction to Limits 1.4 Limits Involving Trigonometric 2.1 Introduction to Limits 2.5 Rigorous Study of Limits 1.5 Limits at Infinity, Infinite Limits 2.2 Rigorous Study of Limits 2.6 Limit Theorems 1.6 Continuity of 2.3 Limit Theorems 2.7 Limits Involving Trigonometric 1.7 Chapter Review 2.4 Limits Involving Transcendental 2.8 Limits at Infinity, Infinite Limits 2.5 Limits at Infinity, Infinite Limits 2.9 Continuity of 2.6 Continuity of 2.1 Chapter Review 2.7 Chapter Review 3 THE DERIVATIVE 2 THE DERIVATIVE 3 THE DERIVATIVE 3.1 Two Problems with One Theme 2.1 Two Problems with One Theme 3.1 Two Problems with One Theme 3.2 The Derivative 2.2 The Derivative 3.2 The Derivative 3.3 Rules for Finding 2.3 Rules for Finding 3.3 Rules for Finding 3.4 of Trigonometric 2.4 of Trigonometric 3.4 of Trigonometric 3.5 The Chain Rule 2.5 The Chain Rule 3.5 The Chain Rule 3.6 Leibniz Notation 2.6 Higher-Order 3.6 Higher-Order 3.7 Higher-Order 2.7 Implicit Differentiation 3.7 Implicit Differentiation 3.8 Implicit Differentiation 2.8 Related Rates 3.8 Related Rates
3.9 Related Rates 2.9 Differentials and Approximations 3.9 Differentials and Approximations 3.10 Differentials and Approximations 2.10 Chapter Review 3.10 Chapter Review 3.11 Chapter Review 3.12 Additional Problems 4 APPLICATIONS OF THE DERIVATIVE 3 APPLICATIONS OF THE DERIVATIVE 4 APPLICATIONS OF THE DERIVATIVE 4.1 Maxima and Minima 3.1 Maxima and Minima 4.1 Maxima and Minima 4.2 Monotonicity and Concavity 3.2 Monotonicity and Concavity 4.2 Monotonicity and Concavity 4.3 Local Maxima and Minima 3.3 Local Extrema and Extrema on Open 4.3 Local Extrema and Extrema on Open Intervals Intervals 4.4 More Max-Min Problems 3.4 Graphing Using 4.4 Graphing Using 4.5 Economic Applications 3.6 The Mean Value Theorem for 4.5 The Mean Value Theorem for 4.6 Sophisticated Graphing 3.7 Solving Numerically 4.6 Solving Numerically 4.7 The Mean Value Theorem 3.8 Antiderivatives 4.7 Antiderivatives 4.8 Chapter Review 3.9 Introduction to Differential 4.8 Introduction to Differential 4.9 Additional Problems 5 THE 4 THE DEFINITE 5 THE DEFINITE 5.1 Antiderivatives (Indefinite Integrals) 4.1 Introduction to Area 5.1 Introduction to Area 5.2 Introduction to Differential 4.2 The Definite Integral 5.2 The Definite Integral 5.3 Sums and Sigma Notation 4.3 The 1st Fundamental Theorem of 5.3 The 1st Fundamental Theorem of 5.4 Introduction to Area 4.4 The 2nd Fundamental Theorem of 5.4 The 2nd Fundamental Theorem of 5.5 The Definite Integral and the Method of Substitution and the Method of Substitution 5.6 The 1st Fundamental Theorem of 4.5 The Mean Value Theorem for Integrals & the Use of Symmetry 5.5 The Mean Value Theorem for Integrals & the Use of Symmetry 5.7 The 2nd Fundamental Theorem of 4.6 Numerical Integration 5.6 Numerical Integration Calcu-lus & the Mean Value Th for Integrals 5.8 Evaluating Definite Integrals 4.7 Chapter Review 5.7 Chapter Review 5.9 Chapter Review 5.1 Additional Problems 6 APPLICATIONS OF THE 5 APPLICATIONS OF THE 6 APPLICATIONS OF THE 6.1 The Area of a Plane Region 5.1 The Area of a Plane Region 6.1 The Area of a Plane Region 6.2 Volumes of Solids: Slabs, Disks, Washers 5.2 Volumes of Solids: Slabs, Disks, Washers 6.3 Volumes of Solids of Revolution: Shells 5.3 Volumes of Solids of Revolution: Shells 6.2 Volumes of Solids: Slabs, Disks, Washers 6.3 Volumes of Solids of Revolution: Shells
6.4 Length of a Plane Curve 5.4 Length of a Plane Curve 6.4 Length of a Plane Curve 6.5 Work 5.5 Work and Fluid Pressure 6.5 Work and Fluid Pressure 6.6 Moments, Center of Mass 5.6 Moments, Center of Mass 6.6 Moments, Center of Mass 6.7 Chapter Review 5.7 Probability and Random Variables 6.8 Probability and Random Variables 6.8 Additional Problems 5.8 Chapter Review 6.8 Chapter Review 7 TRANSCENDENTAL FUNCTIONS 6 TRANSCENDENTAL FUNCTIONS 7 TECHNIQUES OF INTEGRATION & 7.1 The Natural Logarithm Function 6.1 The Natural Logarithm Function DIFFERENTIAL EQUATIONS 7.2 Inverse and Their 6.2 Inverse and Their 7.1 Basic Integration Rules 7.3 The Natural Exponential Function 6.3 The Natural Exponential Function 7.2 Integration by Parts 7.4 General Exponential & Logarithmic 6.4 General Exponential & Logarithmic 7.3 Some Trigonometric Integrals 7.5 Exponential Growth and Decay 6.5 Exponential Growth and Decay 7.4 Rationalizing Substitutions 7.6 First-Order Linear Differential 6.6 First-Order Linear Differential 7.5 The Method of Partial Fractions 7.7 Inverse Trig & Their 6.7 Approximations for Differential 7.6 Strategies for Integration 7.8 The Hyperbolic & Their 6.8 Inverse Trig & Their 7.7 Growth and Decay Inverses 7.9 Chapter Review 6.9 The Hyperbolic & Their 7.8 First-Order Linear Differential Inverses 7.10 Additional Problems 6.10 Chapter Review 7.9 Approximations for Differential 7.10 Chapter Review 8 TECHNIQUES OF INTEGRATION 7 TECHNIQUES OF INTEGRATION 8.1 Integration by Substitution 7.1 Basic Integration Rules 8.2 Some Trigonometric Integrals 7.2 Integration by Parts 8.3 Rationalizing Substitutions 7.3 Some Trigonometric Integrals 8.4 Integration by Parts 7.4 Rationalizing Substitutions 8.5 Integration of Rational 7.5 The Method of Partial Fractions 8.6 Chapter Review 7.6 Strategies for Integration 7.7 Chapter Review 9 INDETERMINATE FORMS & 8 INDETERMINATE FORMS & 8 INDETERMINATE FORMS & IMPROPER S IMPROPER S IMPROPER S 9.1 Indeterminate Forms of Type 0/0 8.1 Indeterminate Forms of Type 0/0 8.1 Indeterminate Forms of Type 0/0 9.2 Other Indeterminate Forms 8.2 Other Indeterminate Forms 8.2 Other Indeterminate Forms 9.3 Improper Integrals: Infinite Limits of 8.3 Improper Integrals: Infinite Limits of 8.3 Improper Integrals: Infinite Limits of Integration Integration Integration 9.4 Improper Integrals: Infinite Integrands 8.4 Improper Integrals: Infinite Integrands 8.4 Improper Integrals: Infinite Integrands
9.5 Chapter Review 8.5 Chapter Review 8.5 Chapter Review 9.5 Additional Problems 10 INFINITE SERIES 9 INFINITE SERIES 9 INFINITE SERIES 10.1 Infinite Sequences 9.1 Infinite Sequences 9.1 Infinite Sequences 10.2 Infinite Series 9.2 Infinite Series 9.2 Infinite Series 10.3 Positive Series: The Integral Test 9.3 Positive Series: The Integral Test 9.3 Positive Series: The Integral Test 10.4 Positive Series: Other Tests 9.4 Positive Series: Other Tests 9.4 Positive Series: Other Tests 10.5 Alternating Series, Absolute 9.5 Alternating Series, Absolute 9.5 Alternating Series, Absolute Convergence, Convergence, Convergence, and Conditional Convergence and Conditional Convergence and Conditional Convergence 10.6 Power Series 9.6 Power Series 9.6 Power Series 10.7 Operations on Power Series 9.7 Operations on Power Series 9.7 Operations on Power Series 10.8 Taylor and Maclaurin Series 9.8 Taylor and Maclaurin Series 9.8 Taylor and Maclaurin Series 10.9 Chapter Review 9.9 The Taylor Approximation to a 9.9 The Taylor Approximation to a Function Function 9.10 Chapter Review 9.10 Chapter Review 11 NUMERICAL METHODS, APPROXIMATIONS 11.1 The Taylor Approximation to a Function 11.2 Numerical Integration 11.3 Solving Numerically 11.4 The Fixed-Point Algorithm 11.5 Approximations for Differential 11.6 Chapter Review TP 11.1 TP 11.2 TP 11.3 Maclaurin Polynomials Numerical Integration Bisection, Newton's, and Fixed-Point Methods 12 CONICS AND POLAR COORDINATES 10 CONICS AND POLAR COORDINATES 10 CONICS AND POLAR COORDINATES 12.1 The Parabola 10.1 The Parabola 10.1 The Parabola 12.2 Ellipses and Hyperbolas 10.2 Ellipses and Hyperbolas 10.2 Ellipses and Hyperbolas 12.3 More on Ellipses and Hyperbolas 10.3 Translation and Rotation of Axes 10.3 Translation and Rotation of Axes 12.4 Translation of Axes 10.4 Parametric Representation of Curves 10.4 Parametric Representation of Curves 12.5 Rotation of Axes 10.5 The Polar Coordinate System 10.5 The Polar Coordinate System 12.6 The Polar Coordinate System 10.6 Graphs of Polar 10.6 Graphs of Polar 12.7 Graphs of Polar 10.7 in Polar Coordinates 10.7 in Polar Coordinates 12.8 in Polar Coordinates 10.8 Chapter Review 10.8 Chapter Review
12.9 Chapter Review 13 GEOMETRY IN THE PLANE, VECTORS 13.1 Plane Curves: Parametric Representation 13.2 Vectors in the Plane: Geometric Approach 11 GEOMETRY IN SPACE, VECTORS 11 GEOMETRY IN SPACE, VECTORS 13.3 Vectors in the Plane: Algebraic 11.1 Cartesian Coordinates in Three-Space 11.1 Cartesian Coordinates in Three-Space Approach 13.4 Vector-Valued & Curvilinear 11.2 Vectors 11.2 Vectors Motion 13.5 Curvature and Acceleration 11.3 The Dot Product 11.3 The Dot Product 13.6 Chapter Review 11.4 The Cross Product 11.4 The Cross Product 14 GEOMETRY IN SPACE, VECTORS 11.5 Vector Valued & Curvilinear 11.5 Vector Valued & Curvilinear Motion Motion 11.6 Lines in Three-Space 11.6 Lines in Three-Space 14.1 Cartesian Coordinates in Three-Space 11.7 Curvature and Components of 11.7 Curvature and Components of Acceleration Acceleration 14.2 Vectors in Three Space 11.8 Surfaces in Three Space 11.8 Surfaces in Three Space 14.3 The Cross Product 11.9 Cylindrical and Spherical Coordinates 11.9 Cylindrical and Spherical Coordinates 14.4 Lines and Curves in Three-Space 11.10 Chapter Review 11.10 Chapter Review 14.5 Velocity, Acceleration, and Curvature 14.6 Surfaces in Three Space 14.7 Cylindrical and Spherical Coordinates 14.8 Chapter Review 15 THE DERIVATIVE IN n- SPACE 12 DERIVATIVES OF FUNCTIONS OF TWO OR MORE VARIABLES 12 DERIVATIVES OF FUNCTIONS OF TWO OR MORE VARIABLES 15.1 of Two or More Variables 12.1 of Two or More Variables 12.1 of Two or More Variables 15.2 Partial 12.2 Partial 12.2 Partial 15.3 Limits and Continuity 12.3 Limits and Continuity 12.3 Limits and Continuity 15.4 Differentiability 12.4 Differentiability 12.4 Differentiability 15.5 Directional and Gradients 12.5 Directional and Gradients 12.5 Directional and Gradients 15.6 The Chain Rule 12.6 The Chain Rule 12.6 The Chain Rule 15.7 Tangent Planes, Approximations 12.7 Tangent Planes, Approximations 12.7 Tangent Planes, Approximations 15.8 Maxima and Minima 12.8 Maxima and Minima 12.8 Maxima and Minima 15.9 Lagrange's Method 12.9 Lagrange Multipliers 12.9 Lagrange Multipliers 15.10 Chapter Review 12.10 Chapter Review 12.10 Chapter Review 16 THE IN n- 13 MULTIPLE 13 MULTIPLE
SPACE INTEGRATION INTEGRATION 16.1 Double Integrals over Rectangles 13.1 Double Integrals over Rectangles 13.1 Double Integrals over Rectangles 16.2 Iterated Integrals 13.2 Iterated Integrals 13.2 Iterated Integrals 16.3 Double Integrals over Nonrectangular 13.3 Double Integrals over Nonrectangular 13.3 Double Integrals over Nonrectangular Regions Regions Regions 16.4 Double Integrals in Polar Coordinates 13.4 Double Integrals in Polar Coordinates 13.4 Double Integrals in Polar Coordinates 16.5 Applications of Double Integrals 13.5 Applications of Double Integrals 13.5 Applications of Double Integrals 16.6 Surface Area 13.6 Surface Area 13.6 Surface Area 16.7 Triple Integrals (Cartesian 13.7 Triple Integrals (Cartesian 13.7 Triple Integrals (Cartesian 16.8 Triple Integrals (Cyl & Sph 13.8 Triple Integrals (Cyl & Sph 13.8 Triple Integrals (Cyl & Sph 16.9 Chapter Review 13.9 Change of Variables in Multiple Integrals 13.9 Change of Variables in Multiple Integrals 13.1 Chapter Review 13.1 Chapter Review 17 VECTOR CALCULUS 14 VECTOR CALCULUS 14 VECTOR CALCULUS 17.1 Vector Fields 14.1 Vector Fields 14.1 Vector Fields 17.2 Line Integrals 14.2 Line Integrals 14.2 Line Integrals 17.3 Independence of Path 14.3 Independence of Path 14.3 Independence of Path 17.4 Green's Theorem in the Plane 14.4 Green's Theorem in the Plane 14.4 Green's Theorem in the Plane 17.5 Surface Integrals 14.5 Surface Integrals 14.5 Surface Integrals 17.6 Gauss's Divergence Theorem 14.6 Gauss's Divergence Theorem 14.6 Gauss's Divergence Theorem 17.7 Stokes's Theorem 14.7 Stokes's Theorem 14.7 Stokes's Theorem 17.8 Chapter Review 14.8 Chapter Review 14.8 Chapter Review 18 DIFFERENTIAL EQUATIONS 18.1 Linear Homogeneous 18.2 Nonhomogeneous 18.3 Applications of Second-Order 18.4 Chapter Review APPENDIX APPENDIX APPENDIX A.1 Mathematical Induction A.1 Mathematical Induction A.1 Mathematical Induction A.2 Proofs of Several Theorems A.2 Proofs of Several Theorems A.2 Proofs of Several Theorems A.3 A Backward Look A.3 A Backward Look A.3 A Backward Look