IFC1
IFC2
IFC3
Half Title
Title
Statement
Copyright
Contents
Preface
Additional Resources
Acknowledgements
Your Course.Your Way.
P: Preparation for Calculus
P.1 Graphs and Models
P.1 Exercises
P.2 Linear M
...
IFC1
IFC2
IFC3
Half Title
Title
Statement
Copyright
Contents
Preface
Additional Resources
Acknowledgements
Your Course.Your Way.
P: Preparation for Calculus
P.1 Graphs and Models
P.1 Exercises
P.2 Linear Models and Rates of Change
P.2 Exercises
P.3 Functions and Their Graphs
P.3 Exercises
P.4 Fitting Models to Data
P.4 Exercises
Review Exercises
P.S. Problem Solving
Ch 1: Limits and Their Properties
1.1 A Preview of Calculus
1.1 Exercises
1.2 Finding Limits Graphically and Numerically
1.2 Exercises
1.3 Evaluating Limits Analytically
1.3 Exercises
1.4 Continuity and One-Sided Limits
1.4 Exercises
1.5 Infinite Limits
1.5 Exercises
Review Exercises
P.S. Problem Solving
Ch 2: Differentiation
2.1 The Derivative and the Tangent Line Problem
2.1 Exercises
2.2 Basic Differentiation Rules and Rates of Change
2.2 Exercises
2.3 Product and Quotient Rules and Higher-Order Derivatives
2.3 Exercises
2.4 The Chain Rule
2.4 Exercises
2.5 Implicit Differentiation
2.5 Exercises
2.6 Related Rates
2.6 Exercises
Review Exercises
P.S. Problem Solving
Ch 3: Applications of Differentiation
3.1 Extrema on an Interval
3.1 Exercises
3.2 Rolle’s Theorem and the Mean Value Theorem
3.2 Exercises
3.3 Increasing and Decreasing Functions and the First Derivative Test
3.3 Exercises
3.4 Concavity and the Second Derivative Test
3.4 Exercises
3.5 Limits at Infinity
3.5 Exercises
3.6 A Summary of Curve Sketching
3.6 Exercises
3.7 Optimization Problems
3.7 Exercises
3.8 Newton’s Method
3.8 Exercises
3.9 Differentials
3.9 Exercises
Review Exercises
P.S. Problem Solving
Ch 4: Integration
4.1 Antiderivatives and Indefinite Integration
4.1 Exercises
4.2 Area
4.2 Exercises
4.3 Riemann Sums and Definite Integrals
4.3 Exercises
4.4 The Fundamental Theorem of Calculus
4.4 Exercises
4.5 Integration by Substitution
4.5 Exercises
4.6 Numerical Integration
4.6 Exercises
Review Exercises
P.S. Problem Solving
Ch 5: Logarithmic, Exponential, and Other Transcendental Functions
5.1 The Natural Logarithmic Function: Differentiation
5.1 Exercises
5.2 The Natural Logarithmic Function: Integration
5.2 Exercises
5.3 Inverse Functions
5.3 Exercises
5.4 Exponential Functions: Differentiation and Integration
5.4 Exercises
5.5 Bases Other than e and Applications
5.5 Exercises
5.6 Inverse Trigonometric Functions: Differentiation
5.6 Exercises
5.7 Inverse Trigonometric Functions: Integration
5.7 Exercises
5.8 Hyperbolic Functions
5.8 Exercises
Review Exercises
P.S. Problem Solving
Ch 6: Differential Equations
6.1 Slope Fields and Euler’s Method
6.1 Exercises
6.2 Differential Equations: Growth and Decay
6.2 Exercises
6.3 Separation of Variables and the Logistic Equation
6.3 Exercises
6.4 First-Order Linear Differential Equations
6.4 Exercises
Review Exercises
P.S. Problem Solving
Ch 7: Applications of Integration
7.1 Area of a Region Between Two Curves
7.1 Exercises
7.2 Volume:The Disk Method
7.2 Exercises
7.3 Volume: The Shell Method
7.3 Exercises
7.4 Arc Length and Surfaces of Revolution
7.4 Exercises
7.5 Work
7.5 Exercises
7.6 Moments, Centers of Mass, and Centroids
7.6 Exercises
7.7 Fluid Pressure and Fluid Force
7.7 Exercises
Review Exercises
P.S. Problem Solving
Ch 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.1 Basic Integration Rules
8.1 Exercises
8.2 Integration by Parts
8.2 Exercises
8.3 Trigonometric Integrals
8.3 Exercises
8.4 Trigonometric Substitution
8.4 Exercises
8.5 Partial Fractions
8.5 Exercises
8.6 Integration by Tables and Other Integration Techniques
8.6 Exercises
8.7 Indeterminate Forms and L’Hôpital’s Rule
8.7 Exercises
8.8 Improper Integrals
8.8 Exercises
Review Exercises
P.S. Problem Solving
Ch 9: Infinite Series
9.1 Sequences
9.1 Exercises
9.2 Series and Convergence
9.2 Exercises
9.3 The Integral Test and p-Series
9.3 Exercises
9.4 Comparisons of Series
9.4 Exercises
9.5 Alternating Series
9.5 Exercises
9.6 The Ratio and Root Tests
9.6 Exercises
9.7 Taylor Polynomials and Approximations
9.7 Exercises
9.8 Power Series
9.8 Exercises
9.9 Representation of Functions by Power Series
9.9 Exercises
9.10 Taylor and Maclaurin Series
9.10 Exercises
Review Exercises
P.S. Problem Solving
Ch 10: Conics, Parametric Equations, and Polar Coordinates
10.1 Conics and Calculus
10.1 Exercises
10.2 Plane Curves and Parametric Equations
10.2 Exercises
10.3 Parametric Equations and Calculus
10.3 Exercises
10.4 Polar Coordinates and Polar Graphs
10.4 Exercises
10.5 Area and Arc Length in Polar Coordinates
10.5 Exercises
10.6 Polar Equations of Conics and Kepler’s Laws
10.6 Exercises
Review Exercises
P.S. Problem Solving
Ch 11: Vectors and the Geometry of Space
11.1 Vectors in the Plane
11.1 Exercises
11.2 Space Coordinates and Vectors in Space
11.2 Exercises
11.3 The Dot Product of Two Vectors
11.3 Exercises
11.4 The Cross Product of Two Vectors in Space
11.4 Exercises
11.5 Lines and Planes in Space
11.5 Exercises
11.6 Surfaces in Space
11.6 Exercises
11.7 Cylindrical and Spherical Coordinates
11.7 Exercises
Review Exercises
P.S. Problem Solving
Ch 12: Vector-Valued Functions
12.1 Vector-Valued Functions
12.1 Exercises
12.2 Differentiation and Integration of Vector-Valued Functions
12.2 Exercises
12.3 Velocity and Acceleration
12.3 Exercises
12.4 Tangent Vectors and Normal Vectors
12.4 Exercises
12.5 Arc Length and Curvature
12.5 Exercises
Review Exercises
P.S. Problem Solving
Ch 13: Functions of Several Variables
13.1 Introduction to Functions of Several Variables
13.1 Exercises
13.2 Limits and Continuity
13.2 Exercises
13.3 Partial Derivatives
13.3 Exercises
13.4 Differentials
13.4 Exercises
13.5 Chain Rules for Functions of Several Variables
13.5 Exercises
13.6 Directional Derivatives and Gradients
13.6 Exercises
13.7 Tangent Planes and Normal Lines
13.7 Exercises
13.8 Extrema of Functions of Two Variables
13.8 Exercises
13.9 Applications of Extrema
13.9 Exercises
13.10 Lagrange Multipliers
13.10 Exercises
Review Exercises
P.S. Problem Solving
Ch 14: Multiple Integration
14.1 Iterated Integrals and Area in the Plane
14.1 Exercises
14.2 Double Integrals and Volume
14.2 Exercises
14.3 Change of Variables: Polar Coordinates
14.3 Exercises
14.4 Center of Mass and Moments of Inertia
14.4 Exercises
14.5 Surface Area
14.5 Exercises
14.6 Triple Integrals and Applications
14.6 Exercises
14.7 Triple Integrals in Other Coordinates
14.7 Exercises
14.8 Change of Variables: Jacobians
14.8 Exercises
Review Exercises
P.S. Problem Solving
Ch 15: Vector Analysis
15.1 Vector Fields
15.1 Exercises
15.2 Line Integrals
15.2 Exercises
15.3 Conservative Vector Fields and Independence of Path
15.3 Exercises
15.4 Green’s Theorem
15.4 Exercises
15.5 Parametric Surfaces
15.5 Exercises
15.6 Surface Integrals
15.6 Exercises
15.7 Divergence Theorem
15.7 Exercises
15.8 Stokes’s Theorem
15.8 Exercises
Review Exercises
P.S. Problem Solving
Appendices
A: Proofs of Selected Theorems
B: Integration Tables
Answers to Odd-Numbered Exercises
Index
IBC1
IBC2
IBC3
IBC4
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