Thomas' Calculus - SI Units

Auteur

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 widely used calculus texts as well as calculus study guides. He is currently on the editorial board of several publications, including the Notices of the American Mathematical Society. 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.

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. He serves on the editorial boards of Applied and Computational Harmonic Analysis and The Journal of Fourier Analysis and Its Applications. Heil's current areas of research include redundant representations, operator theory, and applied harmonic analysis. In his spare time, Heil pursues his hobby of astronomy.

The late Maurice D. Weir 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. Weir was awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He co-authored eight books, including University Calculus and Thomas' Calculus.

Przemyslaw Bogacki is an Associate Professor of Mathematics and Statistics and a University Professor at Old Dominion University. He received his PhD in 1990 from Southern Methodist University. He is also the author of a text on linear algebra, which appeared in 2019. He is actively involved in applications of technology in collegiate mathematics. His areas of research include computer aided geometric design and numerical solution of initial value problems for ordinary differential equations.

Texte du rabat

For 3-semester or 4-quarter courses in Calculus for students majoring in mathematics, engineering or science. Clarity and precision Thomas' Calculus goes beyond memorizing formulas and routine procedures to help students develop deeper understanding. It guides students to a level of mathematical proficiency and maturity needed for the course, with support for those who require it through its balance of clear and intuitive explanations, current applications and generalized concepts. The 15th Edition meets the needs of students with increasingly varied levels of readiness for the calculus sequence. This revision also adds exercises, revises figures and narrative for clarity, and updates many applications with modern topics. Hallmark features of this title

• Key topics are presented both informally and formally.
• Results are carefully stated and proved throughout, and proofs are clearly explained and motivated.
• Strong exercise sets feature a wide range from skills problems to applied and theoretical problems.
• Writing exercises ask students to explore and explain various concepts and applications. A list of questions at the end of each chapter asks them to review and summarize what they have learned.
• Technology exercises in each section ask students to use the calculator or computer when solving the problems. Computer Explorations offer exercises requiring a computer algebra system such as Maple or Mathematica.

• Annotations within examples guide students through the problem solution and emphasize that each step in a mathematical argument is justified.New and updated features of this title

• Many narrative clarifications and revisions have been made throughout the text.
• A new appendix on Determinants and Gradient Descent has been added, covering many topics relevant to students interested in Machine Learning and Neural Networks.
• Many updated graphics and figures have been enhanced to bring out clear visualization and mathematical correctness.
• Many exercise instructions have been clarified, such as suggesting where the use of a calculator may be needed.
• Notation of inverse trig functions has been changed throughout the text to favor arcsin notation over sin^{-1}, etc.

Contenu

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
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

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
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

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 Related Rates
• 3.10 Linearization and Differentials
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

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
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

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
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

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
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises
• Technology Application Projects

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
• Questions to Guide Your Review
• Practice Exercises
• Additional and Advanced Exercises

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 …