Synopses & Reviews
University Calculus: Alternate Edition Part One, Single Variable answers the demand for a more streamlined, less expensive version of the highly acclaimed
Thomas' Calculus, Eleventh Edition. The text retains the same quality and quantity of exercises as the eleventh edition while using a faster-paced presentation. This text focuses on the thinking behind calculus and uses the same precise, accurate exposition for which the Thomas series is well known. The elegant art program helps today’s readers visualize important concepts.
KEY TOPICS: Functions; Limits and Continuity; Differentiation; Applications of Derivatives; Integration; Applications of Definite Integrals; Transcendental Functions; Techniques of Integration; Infinite Sequences and Series; Polar Coordinates and Conics. MARKET: For all readers interested in Calculus.
About the Author
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 coauthored six widely used calculus texts as well as two calculus study guides. He is currently on the editorial board of Geometriae Dedicata and Media-Enhanced Mathematics. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass’s current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking.
Maurice D. Weir holds a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. He is a Professor Emeritus of the Department of Applied Mathematics at the Naval Postgraduate School in Monterey, California. Weir enjoys teaching Mathematical Modeling and Differential Equations. His current areas of research include modeling and simulation as well as mathematics education. Weir has been awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He has coauthored eight books, including the University Calculus series and the twelfth edition of Thomas’ Calculus.
George B. Thomas, Jr. (late) of the Massachusetts Institute of Technology, was a professor of mathematics for thirty-eight years; he served as the executive officer of the department for ten years and as graduate registration officer for five years. Thomas held a spot on the board of governors of the Mathematical Association of America and on the executive committee of the mathematics division of the American Society for Engineering Education. His book, Calculus and Analytic Geometry, was first published in 1951 and has since gone through multiple revisions. The text is now in its twelfth edition and continues to guide students through their calculus courses. He also co-authored monographs on mathematics, including the text Probability and Statistics.
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 Graphing with Calculators and Computers
2. Limits and Continuity
2.1 Rates of Change and Tangents to Curves
2.2 Limit of a Function and Limit Laws
2.3 The Precise Definition of a Limit
2.4 One-Sided Limits and Limits at Infinity
2.5 Infinite Limits and Vertical Asymptotes
2.6 Continuity
2.7 Tangents and Derivatives at a Point
3. Differentiation
3.1 The Derivative as a Function
3.2 Differentiation Rules
3.3 The Derivative as a Rate of Change
3.4 Derivatives of Trigonometric Functions
3.5 The Chain Rule
3.6 Implicit Differentiation
3.7 Related Rates
3.8 Linearization and Differentials
3.9 Parametrizations of Plane Curves
4. Applications of Derivatives
4.1 Extreme Values of Functions
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. Integration
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 Rule
5.6 Substitution and Area Between Curves
6. Applications of Definite Integrals
6.1 Volumes by Slicing and Rotation About an Axis
6.2 Volumes by Cylindrical Shells
6.3 Lengths of Plane Curves
6.4 Areas of Surfaces of Revolution
6.5 Work
6.6 Moments and Centers of Mass
6.7 Fluid Pressures and Forces
7. Transcendental Functions
7.1 Inverse Functions and Their Derivatives
7.2 Natural Logarithms
7.3 Exponential Functions
7.4 Inverse Trigonometric Functions
7.5 Exponential Change and Separable Differential Equations
7.6 Indeterminate Forms and L'Hopital's Rule
7.7 Hyperbolic Functions
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
9. Infinite Sequences and Series
9.1 Sequences
9.2 Infinite Series
9.3 The Integral Test
9.4 Comparison Tests
9.5 The Ratio and Root Tests
9.6 Alternating Series, Absolute and Conditional Convergence
9.7 Power Series
9.8 Taylor and Maclaurin Series
9.9 Convergence of Taylor Series
9.10 The Binomial Series
10. Polar Coordinates and Conics
10.1 Polar Coordinates
10.2 Graphing in Polar Coordinates
10.3 Areas and Lengths in Polar Coordinates
10.4 Conic Sections
10.5 Conics in Polar Coordinates 10.6 Conics and Parametric Equations; The Cycloid