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Einband grossThomas' Calculus: Early Transcendentals, eBook, SI Units
ISBN/GTIN

Thomas' Calculus: Early Transcendentals, eBook, SI Units

E-BookPDF1 - PDF WatermarkE-Book
Englisch
Pearson HigherEducationerschienen am26.04.202315. Auflage
For 3-semester or 4-quarter courses in Calculus for students majoring in mathematics, engineering, or science.
Clarity and precision
Thomas' Calculus: Early Transcendentals 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.
mehr
Verfügbare Formate
BuchKartoniert, Paperback
EUR90,94
E-BookPDF1 - PDF WatermarkE-Book
EUR59,49

Produkt

KlappentextFor 3-semester or 4-quarter courses in Calculus for students majoring in mathematics, engineering, or science.
Clarity and precision
Thomas' Calculus: Early Transcendentals 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.
Details
Weitere ISBN/GTIN9781292457628
ProduktartE-Book
EinbandartE-Book
FormatPDF
Format Hinweis1 - PDF Watermark
Erscheinungsjahr2023
Erscheinungsdatum26.04.2023
Auflage15. Auflage
SpracheEnglisch
Dateigrösse69542 Kbytes
Artikel-Nr.11611378
Rubriken
Genre9200

Inhalt/Kritik

Inhaltsverzeichnis
1. Functions 1.1 Functions and Their Graphs
1.2 Combining Functions; Shifting and Scaling Graphs
1.3 Trigonometric Functions
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms
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 Continuity
2.6 Limits Involving Infinity; Asymptotes of Graphs
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 Inverse Trigonometric Functions
3.10 Related Rates
3.11 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 Indeterminate Forms and L'Hôpital's Rule
4.6 Applied Optimization
4.7 Newton's Method
4.8 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. 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
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 Algebra Systems
8.7 Numerical Integration
8.8 Improper Integrals
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
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
13.6 Velocity and Acceleration in Polar Coordinates
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
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
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
16. First-Order Differential Equations 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
Questions to Guide Your Review
Practice Exercises
Technology Application Projects
17. Second-Order Differential Equations 17.1 Second-Order Linear Equations
17.2 Nonhomogeneous Linear Equations
17.3 Applications
17.4 Euler Equations
17.5 Power-Series Solutions
Questions to Guide Your Review
Practice Exercises
Additional and Advanced Exercises
Technology Application Projects
18. Complex Functions (online) 18.1 Complex Numbers
18.2 Limits and Continuity
18.3 Complex Derivatives
18.4 The Cauchy-Riemann Equations
18.5 Complex Series
18.6 Conformal Maps
19. Fourier Series and Wavelets (online) 19.1 Periodic Functions
19.2 Summing Sines and Cosines
19.3 Vectors and Approximation in Three and More Dimensions
19.4 Approximation of Functions
19.5 Advanced Topic: The Haar System and Wavelets
Appendix A A.1 Real Numbers and the Real Line
A.2 Graphing with Software
A.3 Mathematical Induction
A.4 Lines, Circles, and Parabolas
A.5 Proofs of Limit Theorems
A.6 Commonly Occurring Limits
A.7 Theory of the Real Numbers
A.8 The Distributive Law for Vector Cross Products
A.9 Probability
A.10 The Mixed Derivative Theorem and the Increment Theorem
Appendix B B.1 Determinants
B.2 Extreme Values and Saddle Points for Functions of More than Two Variables
B.3 The Method of Gradient Descent
Answers to Odd-Numbered Exercises Applications Index Subject Index A Brief Table of Integrals Creditsmehr

Autor

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.