Calculus: Single and Multivariable

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Spis treści:
Preface.
Supplementary Resources.
Acknowledgments.
About the Authors.
C H A P T E R 1 Basics.
Preview.
1 Number Systems.
2 Planar Coordinates and Graphing in the Plane.
3 Lines and Their Slopes.
4 Functions and Their Graphs.
5 Combining Functions.
6 Trigonometry.
Summary of Key Topics.
Review Exercises.
Genesis & Development 1.
C H A P T E R 2 Limits.
Preview.
1 The Concept of Limit.
2 Limit Theorems.
3 Continuity.
4 Infinite Limits and Asymptotes.
5 Limits of Sequences.
6 Exponential Functions and Logarithms.
Summary of Key Topics.
Review Exercises.
Genesis & Development 2.
C H A P T E R 3 The Derivative.
Preview.
1 Rates of Change and Tangent Lines.
2 The Derivative.
3 Rules for Differentiation.
4 Differentiation of Some Basic Functions.
5 The Chain Rule.
6 Derivatives of Inverse Functions.
7 Higher Derivatives.
8 Implicit Differentiation.
9 Differentials and Approximation of Functions.
10 Other Transcendental Functions.
Summary of Key Topics.
Review Exercises.
Genesis & Development 3.
C H A P T E R 4 Applications of the Derivative.
Preview.
1 Related Rates.
2 The Mean Value Theorem.
3 Maxima and Minima of Functions.
4 Applied Maximum–Minimum Problems.
5 Concavity.
6 Graphing Functions.
7 l’Hoˆ pital’s Rule.
8 The Newton–Raphson Method.
9 Antidifferentiation and Applications.
Summary of Key Topics.
Review Exercises.
Genesis & Development 4.
C H A P T E R 5 The Integral.
Preview.
1 Introduction to Integration—Th e Area Problem.
2 The Riemann Integral.
3 Rules for Integration.
4 The Fundamental Theorem of Calculus.
5 A Calculus Approach to the Logarithm and Exponential Functions.
6 Integration by Substitution.
7 More on the Calculation of Area.
8 Numerical Techniques of Integration.
Summary of Key Topics.
Review Exercises.
Genesis & Development 5.
C H A P T E R 6 Techniques of Integration.
Preview.
1 Integration by Parts.
2 Powers and Products of Trigonometric Functions.
3 Trigonometric Substitution.
4 Partial Fractions—Linear Factors.
5 Partial Fractions—Irreducible Quadratic Factors.
6 Improper Integrals—Unbounded Integrands.
7 Improper Integrals—Unbounded Intervals.
Summary of Key Topics.
Review Exercises.
Genesis & Development 6.
C H A P T E R 7 Applications of the Integral.
Preview.
1 Volumes.
2 Arc Length and Surface Area.
3 The Average Value of a Function.
4 Center of Mass.
5 Work.
6 First Order Differential Equations—Separable Equations.
7 First Order Differential Equations—Linear Equations.
Summary of Key Topics.
Review Exercises.
Genesis & Development 7.
C H A P T E R 8 Infinite Series.
Preview.
1 Series.
2 The Divergence Test and the Integral Test.
3 The Comparison Tests.
4 Alternating Series.
5 The Ratio and Root Tests.
6 Introduction to Power Series.
7 Representing Functions by Power Series.
8 Taylor Series.
Summary of Key Topics.
Review Exercises.
Genesis & Development 8.
C H A P T E R 9 Vectors.
Preview.
1 Vectors in the Plane.
2 Vectors in Three–Dimensional Space.
3 The Dot Product and Applications.
4 The Cross Product and Triple Product.
5 Lines and Planes in Space.
Summary of Key Topics.
Review Exercises.
Genesis & Development 9.
C H A P T E R 1 0 Vector–Valued Functions.
Preview.
1 VectorR 11;Valued Functions—Limits, Derivatives, and Continuity.
2 Velocity and Acceleration.
3 Tangent Vectors and Arc Length.
4 Curvature.
5 Applications of Vector–Valued Functions to Motion.
Summary of Key Topics.
Review Exercises.
Genesis & Development 10.
C H A P T E R 1 1 Functions of Several Variables.
Preview.
1 Functions of Several Variables.
2 Cylinders and Quadric Surfaces.
3 Limits and Continuity.
4 Partial Derivatives.
5 Differentiability and the Chain Rule.
6 Gradients and Directional Derivatives.
7 Tangent Planes.
8 Maximum–Minimum Problems.
9 Lagrange Multipliers.
Summary of Key Topics.
Review Exercises.
Genesis & Development 11.
C H A P T E R 1 2 Multiple Integrals.
Preview.
1 Double Integrals Over Rectangular Regions.
2 Integration Over More General Regions.
3 Calculation of Volumes of Solids.
4 Polar Coordinates.
5 Integrating in Polar Coordinates.
6 Triple Integrals.
7 Physical Applications.
8 Other Coordinate Systems.
Summary of Key Topics.
Review Exercises.
Genesis & Development 12.
C H A P T E R 1 3 Vector Calculus.
Preview.
1 Vector Fields.
2 Line Integrals.
3 Conservative Vector Fields and Path Independence.
4 Divergence, Gradient, and Curl.
5 Green’s Theorem.
6 Surface Integrals.
7 Stokes’s Theorem.
8 The Divergence Theorem.
Summary of Key Topics.
Review Exercises.
Genesis & Development 13.
Table of Integrals.
Answers to Selected Exercises.
Index.