Cálculo de Una Variable: Trascendentes Tempranas – James Stewart – 9na Edición

Chapter 1: Functions and Models
1.1 Four Ways to Represent a Function
1.2 Mathematical Models: A Catalog of Essential Functions
1.3 New Functions from Old Functions
1.4 Exponential Functions
1.5 Inverse Functions and Logarithms
1 Review
Principles of Problem Solving

Chapter 2: Limits and Derivatives
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of a Limit
2.5 Continuity
2.6 Limits at Infinity, Horizontal Asymptotes
2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function
2 Review
Problems Plus

Chapter 3: Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions
3.7 Rates of Change in the Natural and Social Sciences
3.8 Exponential Growth and Decay
3.9 Related Rates
3.10 Linear Approximations and Differentials
3.11 Hyperbolic Functions
3 Review
Problems Plus

Chapter 4: Applications of Differentiation
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 What Derivatives Tell Us about the Shape of a Graph
4.4 Indeterminate Forms and l'Hospital's Rule
4.5 Summary of Curve Sketching
4.6 Graphing with Calculus and Technology
4.7 Optimization Problems
4.8 Newton's Method
4.9 Antiderivatives
4 Review
Problems Plus

Chapter 5: Integrals
5.1 The Area and Distance Problems
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
5.5 The Substitution Rule
5 Review
Problems Plus

Chapter 6: Applications of Integration
6.1 Areas between Curves
6.2 Volumes
6.3 Volumes by Cylindrical Shells
6.4 Work
6.5 Average Value of a Function
6 Review
Problems Plus

Chapter 7: Techniques of Integration
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
7.6 Integration Using Tables and Technology
7.7 Approximate Integration
7.8 Improper Integrals
7 Review
Problems Plus

Chapter 8: Further Applications of Integration
8.1 Arc Length
8.2 Area of a Surface of Revolution
8.3 Applications to Physics and Engineering
8.4 Applications to Economics and Biology
8.5 Probability
8 Review
Problems Plus

Chapter 9: Differential Equations
9.1 Modeling with Differential Equations
9.2 Direction Fields and Euler's Method
9.3 Separable Equations
9.4 Models for Population Growth
9.5 Linear Equations
9.6 Predator-Prey Systems
9 Review
Problems Plus

Chapter 10: Parametric Equations and Polar Coordinates
10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves
10.3 Polar Coordinates
10.4 Calculus in Polar Coordinates
10.5 Conic Sections
10.6 Conic Sections in Polar Coordinates
10 Review
Problems Plus

Chapter 11: Sequences, Series, and Power Series
11.1 Sequences
11.2 Series
11.3 The Integral Test and Estimates of Sums
11.4 The Comparison Tests
11.5 Alternating Series and Absolute Convergence
11.6 The Ratio and Root Tests
11.7 Strategy for Testing Series
11.8 Power Series
11.9 Representations of Functions as Power Series
11.10 Taylor and Maclaurin Series
11.11 Applications of Taylor Polynomials
11 Review
Problems Plus

Appendixes
Appendix A: Numbers, Inequalities, and Absolute Values
Appendix B: Coordinate Geometry and Lines
Appendix C: Graphs of Second-Degree Equations
Appendix D: Trigonometry
Appendix E: Sigma Notation
Appendix F: Proofs of Theorems
Appendix G: The Logarithm Defined as an Integral
Appendix H: Answers to Odd-Numbered Exercises
Index