Title overview
Support your students' development with this new edition of Thomas' time-tested text
Thomas' Calculus in SI Units, 14th edition, helps your students reach the level of proficiency needed to excel in their course. The text supports their development beyond memorising formulas through clear explanations, current applications, and generalised concepts.
This edition has been carefully revised to meet your students' needs, preserving everything great about Thomas' text while keeping it refreshingly modern.
With a host of learning features, this text is perfect for courses in Calculus, mathematics, engineering, or science.
This title has a Companion Website and is available with MyLab®
Hallmark features of this text
Teach your way at a level that challenges and encourages student development.
- Co-authors Chris Heil and Joel Hass continue Thomas' tradition ofdeveloping students' mathematical maturity and proficiency, going beyond memorizing formulas and routine procedures, and showing students how to generalize key concepts once they are introduced.
- Results are carefully stated and proved. The formal material is as carefully presented and explained as the informal development so you can downplay formality at any stage without impacting later developments in the text.
- Complete and precise multivariable coverage enhances the connections of multivariable ideas with their single-variable analogues studied earlier in the book.
Assess your students' understanding and skills through a range of exercises.
- Strong exercise sets feature a great breadth of progressive problems to encourage students to think about and practice the concepts until they achieve mastery.
- Writing exercises the text ask students to explore and explain calculus concepts and applications.
- Technology exercises ask students to use the calculator or computer when solving the problems.
New to this edition
Co-authors Hass and Heil have revised the text to encourage deeper geometric understanding.
- New types of homework exercises, including many geometric in nature, have been added, providing different perspectives and approaches to each topic.
- Short URLs have been added to the historical marginnotes, allowing students to navigate directly to online information.
- New annotations within examples (in blue type) guide the student through the problem solution and emphasize that each step in a mathematical argument is rigorously justified.
- All chapters have been revised for clarity, consistency, conciseness, and comprehension.
Table of contents
1. Functions
- 1.1 Functions and Their Graphs
- 1.2 Combining Functions; Shifting and Scaling Graphs
- 1.3 Trigonometric Functions
- 1.4 Exponential Functions
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
- 2.6 Continuity
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 Related Rates
- 3.9 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 Applied Optimization
- 4.6 Newton's Method
- 4.7 Antiderivatives
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
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 Centres of Mass
7. Transcendental Functions
- 7.1 Inverse Functions and Their Derivatives
- 7.2 Natural Logarithms
- 7.3 Exponential Functions
- 7.4 Exponential Change and Separable Differential Equations
- 7.5 Indeterminate Forms and L'Hôpital's Rule
- 7.6 Inverse Trigonometric Functions
- 7.7 Hyperbolic Functions
- 7.8 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
- 9.1 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
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
- 11.2 Vectors
- 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
Author bios
Joel Hass received his PhD from the University of California, Berkeley. He is currently a Professor of Mathematics at the University of California Davis. He has co-authored widely used calculus texts as well as calculus study guides. Hass's current areas of research include the geometry of proteins, three-dimensional manifolds, applied maths, and computational complexity.
Christopher Heil received his PhD from the University of Maryland. He is currently a Professor of Mathematics at the Georgia Institute of Technology. He is the author of a graduate text on analysis and a number of highly cited research survey articles. Heil's current areas of research include redundant representations, operator theory, and applied harmonic analysis.
Maurice D. Weir (late) of the the Naval Postgraduate School in Monterey, California, was Professor Emeritus as a member of the Department of Applied Mathematics. He held a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. He co-authored eight books, including University Calculus and Thomas' Calculus.
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