| Autore |
Thomas G. B (George B.)
|
| Edizione | [Thirteenth edition, global edition.] |
| Pubbl/distr/stampa |
Boston : , : Pearson, , [2016]
|
| Descrizione fisica |
1 online resource (137 pages) : illustrations (some color), photographs
|
| Disciplina |
515
|
| Collana |
Always learning
|
| Soggetto topico |
Calculus
Calculus - Data processing
|
| Formato |
Materiale a stampa  |
| Livello bibliografico |
Monografia |
| Lingua di pubblicazione |
eng
|
| Nota di contenuto |
Cover -- Thomas' Calculus: Thirteenth Edition in SI Units -- Copyright -- Contents -- Preface -- Chapter 1: Functions -- Functions and Their Graphs -- Combining Functions -- Shifting and Scaling Graphs -- Trigonometric Functions -- Graphing with Software -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 2: Limits and Continuity -- Rates of Change and Tangents to Curves -- Limit of a Function and Limit Laws -- The Precise Definition of a Limit -- One-Sided Limits -- Continuity -- Limits Involving Infinity -- Asymptotes of Graphs -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 3: Derivatives -- Tangents and the Derivative at a Point -- The Derivative as a Function -- Differentiation Rules -- The Derivative as a Rate of Change -- Derivatives of Trigonometric Functions -- The Chain Rule -- Implicit Differentiation -- Related Rates -- Linearization and Differentials -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 4: Applications of Derivatives -- Extreme Values of Functions -- The Mean Value Theorem -- Monotonic Functions and the First Derivative Test -- Concavity and Curve Sketching -- Applied Optimization -- Newton's Method -- Antiderivatives -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 5: Integrals -- Area and Estimating with Finite Sums -- Sigma Notation and Limits of Finite Sums -- The Definite Integral -- The Fundamental Theorem of Calculus -- Indefinite Integrals and the Substitution Method -- Definite Integral Substitutions and the Area Between Curves -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 6: Applications of Definite Integrals -- Volumes Using Cross-Sections.
Volumes Using Cylindrical Shells -- Arc Length -- Areas of Surfaces of Revolution -- Work and Fluid Forces -- Moments and Centers of Mass -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 7: Transcendental Functions -- Inverse Functions and Their Derivatives -- Natural Logarithms -- Exponential Functions -- Exponential Change and Separable Differential Equations -- Indeterminate Forms and L'Hôpital's Rule -- Inverse Trigonometric Functions -- Hyperbolic Functions -- Relative Rates of Growth -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 8: Techniques of Integration -- Using Basic Integration Formulas -- Integration by Parts -- Trigonometric Integrals -- Trigonometric Substitutions -- Integration of Rational Functions by Partial Fractions -- Integral Tables and Computer Algebra Systems -- Numerical Integration -- Improper Integrals -- Probability -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 9: First-Order Differential Equations -- Solutions, Slope Fields, and Euler's Method -- First-Order Linear Equations -- Applications -- Graphical Solutions of Autonomous Equations -- Systems of Equations and Phase Planes -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 10: Infinite Sequences and Series -- Sequences -- Infinite Series -- The Integral Test -- Comparison Tests -- Absolute Convergence -- The Ratio and Root Tests -- Alternating Series and Conditional Convergence -- Power Series -- Taylor and Maclaurin Series -- Convergence of Taylor Series -- The Binomial Series and Applications of Taylor Series -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises.
Chapter 11: Parametric Equations and Polar Coordinates -- Parametrizations of Plane Curves -- Calculus with Parametric Curves -- Polar Coordinates -- Graphing Polar Coordinate Equations -- Areas and Lengths in Polar Coordinates -- Conic Sections -- Conics in Polar Coordinates -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 12: Vectors and the Geometry of Space -- Three-Dimensional Coordinate Systems -- Vectors -- The Dot Product -- The Cross Product -- Lines and Planes in Space -- Cylinders and Quadric Surfaces -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 13: Vector-Valued Functions and Motion in Space -- Curves in Space and Their Tangents -- Integrals of Vector Functions -- Projectile Motion -- Arc Length in Space -- Curvature and Normal Vectors of a Curve -- Tangential and Normal Components of Acceleration -- Velocity and Acceleration in Polar Coordinates -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 14: Partial Derivatives -- Functions of Several Variables -- Limits and Continuity in Higher Dimensions -- Partial Derivatives -- The Chain Rule -- Directional Derivatives and Gradient Vectors -- Tangent Planes and Differentials -- Extreme Values and Saddle Points -- Lagrange Multipliers -- Taylor's Formula for Two Variables -- Partial Derivatives with Constrained Variables -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 15: Multiple Integrals -- Double and Iterated Integrals over Rectangles -- Double Integrals over General Regions -- Area by Double Integration -- Double Integrals in Polar Form -- Triple Integrals in Rectangular Coordinates -- Moments and Centers of Mass.
Triple Integrals in Cylindrical and Spherical Coordinates -- Substitutions in Multiple Integrals -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 16: Integrals and Vector Fields -- Line Integrals -- Vector Fields and Line Integrals: Work, Circulation, and Flux -- Path Independence, Conservative Fields, and Potential Functions -- Green's Theorem in the Plane -- Surfaces and Area -- Surface Integrals -- Stokes' Theorem -- The Divergence Theorem and a Unified Theory -- Questions to Guide Your Review -- Practice Exercises -- Additional and Advanced Exercises -- Chapter 17: Second-Order Differential Equations -- Second-Order Linear Equations -- Nonhomogeneous Linear Equations -- Applications -- Euler Equations -- Power Series Solutions -- Appendices -- Real Numbers and the Real Line -- Mathematical Induction -- Lines, Circles, and Parabolas -- Proofs of Limit Theorems -- Commonly Occurring Limits -- Theory of the Real Numbers -- Complex Numbers -- The Distributive Law for Vector Cross Products -- The Mixed Derivative Theorem and the Increment Theorem -- Answers to Odd-Numbered Exercises -- Credits -- Index -- A Brief Table of Integrals -- Basic Formulas and Rules.
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| Record Nr. | UNINA-9910154942003321 |
Info
Calculus and differential equations with mathematica / / Pramote Dechaumphai
