|Thomas' Calculus: Early Transcendentals in SI Units||
Thomas' Calculus: Early Transcendentals in SI Units
|88.90||approx. 7-9 days|
For three-semester or four-quarter courses in Calculus for students majoring in mathematics, engineering, or science
Clarity and precision
Thomas' Calculus: Early Transcendentals helps students reach the level of mathematical proficiency and maturity you require, but with support for students who need it through its balance of clear and intuitive explanations, current applications, and generalized concepts. In the 14th SI Edition, new co-author Christopher Heil (Georgia Institute of Technology) partners with author Joel Hass to preserve what is best about Thomas' time-tested text while reconsidering every word and every piece of art with today's students in mind. The result is a text that goes beyond memorizing formulas and routine procedures to help students generalize key concepts and develop deeper understanding.
Also available with Pearson MyLab Math
Pearson MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. A full suite of Interactive Figures have been added to the accompanying Pearson MyLab Math course to further support teaching and learning. Enhanced Sample Assignments include just-in-time prerequisite review, help keep skills fresh with distributed practice of key concepts, and provide opportunities to work exercises without learning aids to help students develop confidence in their ability to solve problems independently.
About the Book
Teach calculus the way you want to teach it, and at a level that prepares students for their STEM majors
Assess student understanding of key concepts and skills through a wide range of time-tested exercises
Support a complete understanding of calculus for students at varying levels
Also available with Pearson MyLab Math
MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. A full suite of Interactive Figures have been added to the accompanying Pearson MyLab Math course to further support teaching and learning. Enhanced Sample Assignments include just-in-time prerequisite review, help keep skills fresh with distributed practice of key concepts, and provide opportunities to work exercises without learning aids to help students develop confidence in their ability to solve problems independently.
Engage students with the power of calculus through a variety of multimedia resources
Assess student understanding of concepts and skills through a wide range of exercises
New to the Book
Co-authors Joel Hass and Chris Heil reconsidered every word, symbol, and piece of art, motivating students to consider the content from different perspectives and compelling a deeper, geometric understanding.
Detailed content changes
Chapter 1• Clarified explanation of definition of exponential function in 1.4.• Replaced sin-1 notation for the inverse sine function with arcsin as default notation in 1.5, and similarly for other trig functions.• Added new Exercises: 1.1: 59–62, 1.2: 21–22; 1.3: 64–65,1.5: 61–64, 79cd; PE: 29–32.
Chapter 2• Added definition of average speed in 2.1.• Updated definition of limits to allow for arbitrary domains. The definition of limits is now consistent with the definition in multivariable domains later in the text and with more general mathematical usage.• Reworded limit and continuity definitions to remove implication symbols and improve comprehension.• Added new Example 7 in 2.4 to illustrate limits of ratios of trig functions.• Rewrote 2.6 Example 11 to solve the equation by finding a zero, consistent with previous discussion.• Added new Exercises: 2.1: 15–18; 2.2: 3h–k, 4f–I; 2.4: 19–20, 45–46; 2.5: 69–74; 2.6: 31–32; PE: 57–58; AAE: 35–38.
Chapter 3• Clarified relation of slope and rate of change.• Added new Figure 3.9 using the square root function to illustrate vertical tangent lines.• Added figure of x sin (1>x) in 3.2 to illustrate how oscillation can lead to non-existence of a derivative of a continuous function.• Revised product rule to make order of factors consistent throughout text, including later dot product and cross product formulas.• Added new Exercises: 3.2: 36, 43–44; 3.3: 65–66; 3.5: 43–44, 61bc; 3.6: 79–80, 111–113; 3.7: 27–28; 3.8: 97–100;3.9: 43–46; 3.10: 47; AAE: 14–15, 26–27.
Chapter 4• Added summary to 4.1.• Added new Example 12 with new Figure 4.35 to give basic and advanced examples of concavity.• Added new Exercises: 4.1: 53–56, 67–70; 4.3: 45–46, 67–68; 4.4: 107–112; 4.6: 37–42; 4.7: 7–10; 4.8: 115–118;PE: 1–16, 101–102; AAE: 19–20, 38–39. Moved Exercises 4.1: 53–68 to PE.
Chapter 5• Improved discussion in 5.4 and added new Figure 5.18 to illustrate the Mean Value Theorem.• Added new Exercises: 5.2: 33–36; 5.4: 71–72; 5.6: 47–48; PE: 43–44, 75–76.
Chapter 6• Clarified cylindrical shell method.• Added introductory discussion of mass distribution along a line, with figure, in 6.6.• Added new Exercises: 6.1: 15; 6.2: 49–50; 6.3: 13–14; 6.5:1–2; 6.6: 1–6, 21–22; PE: 17–18, 23–24, 37–38.
Chapter 7• Clarified discussion of separable differential equations in 7.2.• Added new Exercises: 7.1: 61–62, 73; PE: 41–42.
Chapter 8• Updated 8.2 Integration by Parts discussion to emphasize u(x)v(x) dx form rather than u dv. Rewrote Examples 1–3 accordingly.• Removed discussion of tabular integration and associated exercises.• Updated discussion in 8.5 on how to find constants in Partial Fraction method.• Updated notation in 8.8 to align with standard usage in statistics.• Added new Exercises: 8.1: 41–44; 8.2: 53–56, 72–73; 8.3: 75–76; 8.4: 49–52; 8.5: 51–66, 73–74; 8.8: 35–38, 77–78;PE: 69–88.
Chapter 9• Clarified the different meaning of a sequence and a series.• Added new Figure 9.9 to illustrate sum of a series as area of a histogram.• Added to 9.3 a discussion on the importance of bounding errors in approximations.• Added new Figure 9.13 illustrating how to use integrals to bound remainder terms of partial sums.• Rewrote Theorem 10 in 9.4 to bring out similarity to the integral comparison test.• Added new Figure 9.16 to illustrate the differing behaviors of the harmonic and alternating harmonic series.• Renamed the nth term test the “nth term test for divergence” to emphasize that it says nothing about convergence.• Added new Figure 9.19 to illustrate polynomials converging to ln(1 + x), which illustrates convergence on the half-open interval (-1, 1].• Used red dots and intervals to indicate intervals and points where divergence occurs and blue to indicate convergence throughout Chapter 9.• Added new Figure 9.21 to show the six different possibilities for an interval of convergence.• Added new Exercises: 9.1: 27–30, 72–77; 9.2: 19–22, 73– 76, 105; 9.3: 11–12, 39–42; 9.4: 55–56; 9.5: 45–46, 65–66;9.6: 57–82; 9.7: 61–65; 9.8: 23–24, 39–40; 9.9: 11–12, 37–38; PE: 41–44, 97–102.
Chapter 10• Added new Example 1 and Figure 10.2 in 10.1 to give a straightforward first example of a parametrized curve.• Updated area formulas for polar coordinates to include conditions for positive r and non-overlapping u.• Added new Example 3 and Figure 10.37 in 10.4 to illustrate intersections of polar curves.• Added new Exercises: 10.1: 19–28; 10.2: 49–50; 10.4: 21–24.
Chapter 11• Added new Figure 11.13(b) to show the effect of scaling a vector.• Added new Example 7 and Figure 11.26 in 11.3 to illustrate projection of a vector.• Added discussion on general quadric surfaces in 11.6, with new Example 4 and new Figure 11.48 illustrating the description of an ellipsoid not centered at the origin via completing the square.• Added new Exercises: 11.1: 31–34, 59–60, 73–76; 11.2: 43–44; 11.3: 17–18; 11.4: 51–57; 11.5: 49–52.
Chapter 12• Added sidebars on how to pronounce Greek letters such as kappa, tau, etc.• Added new Exercises: 12.1: 1–4, 27–36; 12.2: 15–16, 19– 20; 12.4: 27–28; 12.6: 1–2.
Chapter 13• Elaborated on discussion of open and closed regions in 13.1.• Standardized notation for evaluating partial derivatives, gradients, and directional derivatives at a point, throughout the chapter.• Renamed “branch diagrams” as “dependency diagrams” which clarifies that they capture dependence of variables.• Added new Exercises: 13.2: 51–54; 13.3: 51–54, 59–60, 71–74, 103–104; 13.4: 20–30, 43–46, 57–58; 13.5: 41–44; 13.6: 9–10, 61; 13.7: 61–62.
Chapter 14• Added new Figure 14.21b to illustrate setting up limits of a double integral.• Added new 14.5 Example 1, modified Examples 2 and 3, and added new Figures 14.31, 14.32, and 14.33 to give basic examples of setting up limits of integration for a triple integral.• Added new material on joint probability distributions as an application of multivariable integration.• Added new Examples 5, 6 and 7 to Section 14.6.• Added new Exercises: 14.1: 15–16, 27–28; 14.6: 39–44; 14.7: 1–22.
Chapter 15• Added new Figure 15.4 to illustrate a line integral of a function.• Added new Figure 15.17 to illustrate a gradient field.• Added new Figure 15.19 to illustrate a line integral of a vector field.• Clarified notation for line integrals in 15.2.• Added discussion of the sign of potential energy in 15.3.• Rewrote solution of Example 3 in 15.4 to clarify connection to Green’s Theorem.• Updated discussion of surface orientation in 15.6 along with Figure 15.52.• Added new Exercises: 15.2: 37–38, 41–46; 15.4: 1–6; 15.6: 49–50; 15.7: 1–6; 15.8: 1–4.
Chapter 16• Added new Example 3 with Figure 16.3 to illustrate how to construct a slope field.• Added new Exercises: 16.1: 11–14; PE: 17–22, 43–44.
Appendices: Rewrote Appendix 8 on complex numbers. Shortened
Appendix 2 to focus on issues arising in use of mathematical software and potential pitfalls.
Also available with Pearson MyLab Math
MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. A full suite of Interactive Figures have been added to the accompanying MyLab Math course to further support teaching and learning. Enhanced Sample Assignments include just-in-time prerequisite review, help keep skills fresh with distributed practice of key concepts, and provide opportunities to work exercises without learning aids to help students develop confidence in their ability to solve problems independently.
New to Pearson MyLab Math:
1.1 Functions and Their Graphs
1.2 Combining Functions; Shifting and Scaling Graphs
1.3 Trigonometric Functions
1.4 Exponential Functions
1.5 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 Limits Involving Infinity; Asymptotes of Graphs
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
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
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
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 and Fluid Forces
6.6 Moments and Centers of Mass
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
7.4 Relative Rates of Growth
8. Techniques of Integration
8.1 Using Basic Integration Formulas
8.2 Integration by Parts
8.3 Trigonometric Integrals
8.4 Trigonometric Substitutions
8.5 Integration of Rational Functions by Partial Fractions
8.6 Integral Tables and Computer Algebra Systems
8.7 Numerical Integration
8.8 Improper Integrals
9. Infinite Sequences and Series
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
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
10.6 Conic Sections
10.7 Conics in Polar Coordinates
11. Vectors and the Geometry of Space
11.1 Three-Dimensional Coordinate Systems
11.3 The Dot Product
11.4 The Cross Product
11.5 Lines and Planes in Space
11.6 Cylinders and Quadric Surfaces
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
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 Multipliers
13.9 Taylor’s Formula for Two Variables
13.10 Partial Derivatives with Constrained Variables
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
14.7 Triple Integrals in Cylindrical and Spherical Coordinates
14.8 Substitutions in Multiple Integrals
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
16. First-Order Differential Equations
16.1 Solutions, Slope Fields, and Euler’s Method
16.2 First-Order Linear Equations
16.4 Graphical Solutions of Autonomous Equations
16.5 Systems of Equations and Phase Planes
Second-Order Differential Equations (Online)
17.1 Second-Order Linear Equations
17.2 Nonhomogeneous Linear Equations
17.4 Euler Equations
17.5 Power-Series Solutions
1. Real Numbers and the Real Line AP-1
2 Graphing with Software
3. Mathematical Induction AP-6
4 Lines, Circles, and Parabolas AP-9
5 Proofs of Limit Theorems AP-19
6 Commonly Occurring Limits AP-22
7 Theory of the Real Numbers AP-23
8 Complex Numbers AP-26
10. The Distributive Law for Vector Cross Products AP-34
11. The Mixed Derivative Theorem and the Increment Theorem