  # University Calculus: Early Transcendentals, 4th edition

• Joel R. Hass,
• Christopher E. Heil,
• Przemyslaw Bogacki,
• Maurice D. Weir,
• George Thomas Thomas

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## Overview

University Calculus: Early Transcendentals helps you generalize and apply key ideas of calculus through clear and precise explanations, examples, figures, and exercise sets.

ISBN-13: 9780136880912

Subject: Calculus

Category: Calculus

1. Functions
1.1. Functions and Their Graphs
1.2. Combining Functions: Shifting and Scaling Graphs
1.3. Trigonometric Functions
1.4. Graphing with Software
1.5. Exponential Functions
1.6. Inverse Functions and Logarithms

2. Limits and Continuity
2.1. Rates of Change and Tangent Lines to Curves
2.2. Limit of a Function and Limit Laws
2.3. The Precise Definition of a Limit
2.4. One-Sided Limits
2.5. Continuity
2.6. Limits Involving Infinity: Asymptotes of Graphs
Practice Exercises

3. Derivatives
3.1. Tangent Lines and the Derivative at a Point
3.2. The Derivative as a Function
3.3. Differentiation Rules
3.4. The Derivative as a Rate of Change
3.5. Derivatives of Trigonometric Functions
3.6. The Chain Rule
3.7. Implicit Differentiation
3.8. Derivatives of Inverse Functions and Logarithms
3.9. Inverse Trigonometric Functions
3.10. Related Rates
3.11. Linearization and Differentials
Practice Exercises

4. Applications of Derivatives
4.1. Extreme Values of Functions on Closed Intervals
4.2. The Mean Value Theorem
4.3. Monotonic Functions and the First Derivative Test
4.4. Concavity and Curve Sketching
4.5. Indeterminate Forms and L′Hôpital′s Rule
4.6. Applied Optimization
4.7. Newton′s Method
4.8. Antiderivatives
Practice Exercises

5. Integrals
5.1. Area and Estimating with Finite Sums
5.2. Sigma Notation and Limits of Finite Sums
5.3. The Definite Integral
5.4. The Fundamental Theorem of Calculus
5.5. Indefinite Integrals and the Substitution Method
5.6. Definite Integral Substitutions and the Area Between Curves
Practice Exercises

6. Applications of Definite Integrals
6.1. Volumes Using Cross-Sections
6.2. Volumes Using Cylindrical Shells
6.3. Arc Length
6.4. Areas of Surfaces of Revolution
6.5. Work
6.6. Moments and Centers of Mass
Practice Exercises

7. Integrals and Transcendental Functions
7.1. The Logarithm Defined as an Integral
7.2. Exponential Change and Separable Differential Equations
7.3. Hyperbolic Functions
Practice Exercises

8. Techniques of Integration
8.1. Integration by Parts
8.2. Trigonometric Integrals
8.3. Trigonometric Substitutions
8.4. Integration of Rational Functions by Partial Fractions
8.5. Integral Tables and Computer Algebra Systems
8.6. Numerical Integration
8.7. Improper Integrals
Practice Exercises

9. Infinite Sequences and Series
9.1. Sequences
9.2. Infinite Series
9.3. The Integral Test
9.4. Comparison Tests
9.5. Absolute Convergence: The Ratio and Root Tests
9.6. Alternating Series and Conditional Convergence
9.7. Power Series
9.8. Taylor and Maclaurin Series
9.9. Convergence of Taylor Series
9.10. Applications of Taylor Series
Practice Exercises

10. Parametric Equations and Polar Coordinates
10.1. Parametrizations of Plane Curves
10.2. Calculus with Parametric Curves
10.3. Polar Coordinates
10.4. Graphing Polar Coordinate Equations
10.5. Areas and Lengths in Polar Coordinates
Practice Exercises

11. Vectors and the Geometry of Space
11.1. Three-Dimensional Coordinate Systems
11.2. Vectors
11.3. The Dot Product
11.4. The Cross Product
11.5. Lines and Planes in Space
Practice Exercises

12. Vector-Valued Functions and Motion in Space
12.1. Curves in Space and Their Tangents
12.2. Integrals of Vector Functions: Projectile Motion
12.3. Arc Length in Space
12.4. Curvature and Normal Vectors of a Curve
12.5. Tangential and Normal Components of Acceleration
12.6. Velocity and Acceleration in Polar Coordinates
Practice Exercises

13. Partial Derivatives
13.1. Functions of Several Variables
13.2. Limits and Continuity in Higher Dimensions
13.3. Partial Derivatives
13.4. The Chain Rule
13.5. Directional Derivatives and Gradient Vectors
13.6. Tangent Planes and Differentials
13.7. Extreme Values and Saddle Points
13.8. Lagrange Multiplier
Practice Exercises

14. Multiple Integrals
14.1. Double and Iterated Integrals Over Rectangles
14.2. Double Integrals over General Regions
14.3. Area by Double Integration
14.4. Double Integrals in Polar Form
14.5. Triple Integrals in Rectangular Coordinates
14.6. Applications
14.7. Triple Integrals in Cylindrical and Spherical Coordinates
14.8. Substitutions in Multiple Integrals
Practice Exercises

15. Integrals and Vector Fields
15.1. Line Integrals of Scalar Functions
15.2. Vector Fields and Line Integrals: Work, Circulation, and Flux
15.3. Path Independence, Conservative Fields, and Potential Functions
15.4. Green′s Theorem in the Plane
15.5. Surfaces and Area
15.6. Surface Integrals
15.7. Stokes′ Theorem
15.8. The Divergence Theorem and a Unified Theory
Practice Exercises

16. First-Order Differential Equations (online at bit.ly/2pzYlEq)
16.1. Solutions, Slope Fields, and Euler′s Method
16.2. First-Order Linear Equations
16.3. Applications
16.4. Graphical Solutions of Autonomous Equations
16.5. Systems of Equations and Phase Planes

17. Second-Order Differential Equations (online at bit.ly/2IHCJyE)
17.1. Second-Order Linear Equations
17.2. Non-homogeneous Linear Equations
17.3. Applications
17.4. Euler Equations
17.5. Power-Series Solutions

Appendix
A.1. Real Numbers and the Real Line
A.2. Mathematical Induction AP-6
A.3. Lines and Circles AP-10
A.4. Conic Sections AP-16
A.5. Proofs of Limit Theorems
A.6. Commonly Occurring Limits
A.7. Theory of the Real Numbers
A.8. Complex Numbers
A.9. The Distributive Law for Vector Cross Products
A.10. The Mixed Derivative Theorem and the Increment Theorem

B.1. Relative Rates of Growth
B.2. Probability
B.3. Conics in Polar Coordinates
B.4. Taylor′s Formula for Two Variables
B.5. Partial Derivatives with Constrained Variables

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