Thomas' Calculus: Early Transcendentals, Single Variable

For the single-variable component of three-semester or four-quarter courses in Calculus for students majoring in mathematics, engineering, or science Clarity and precision Thomas' Calculus: Early Transcendentals, Single Variable helps students reach the level of mathematical proficiency and maturity you require, but with support for students who need it through its balance of clear and intuitive explanations, current applications, and generalized concepts. In the 14th Edition, new co-author Christopher Heil (Georgia Institute of Technology) partners with author Joel Hass to preserve what is best about Thomas' time-tested text while reconsidering every word and every piece of art with today's students in mind. The result is a text that goes beyond memorizing formulas and routine procedures to help students generalize key concepts and develop deeper understanding. Also available with MyLab Math MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. A full suite of Interactive Figures have been added to the accompanying MyLab Math course to further support teaching and learning. Enhanced Sample Assignments include just-in-time prerequisite review, help keep skills fresh with distributed practice of key concepts, and provide opportunities to work exercises without learning aids to help students develop confidence in their ability to solve problems independently.   Note: You are purchasing a standalone product; MyLab does not come packaged with this content. Students, if interested in purchasing this title with MyLab, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.  If you would like to purchase both the physical text and MyLab, search for: 0134768515 / 9780134768519 Thomas' Calculus: Early Transcendentals, Single Variable plus MyLab Math with Pearson eText -- Title-Specific Access Card Package, 14/e   Package consists of:    0134439414 / 9780134439419 Thomas' Calculus: Early Transcendentals, Single Variable 0134764528 / 9780134764528 MyLab Math plus Pearson eText -- Standalone Access Card -- for Thomas' Calculus: Early Transcendentals

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 Software 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms   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   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   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    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 Centers of Mass   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      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 8.9 Probability   9. First-Order Differential Equations 9.1 Solutions, Slope Fields, and Euler's Method 9.2 First-Order Linear Equations 9.3 Applications 9.4 Graphical Solutions of Autonomous Equations 9.5 Systems of Equations and Phase Planes 10. Infinite Sequences and Series 10.1 Sequences 10.2 Infinite Series 10.3 The Integral Test 10.4 Comparison Tests 10.5 Absolute Convergence; The Ratio and Root Tests 10.6 Alternating Series and Conditional Convergence 10.7 Power Series 10.8 Taylor and Maclaurin Series 10.9 Convergence of Taylor Series 10.10 Applications of Taylor Series   11. Parametric Equations and Polar Coordinates 11.1 Parametrizations of Plane Curves 11.2 Calculus with Parametric Curves 11.3 Polar Coordinates 11.4 Graphing Polar Coordinate Equations 11.5 Areas and Lengths in Polar Coordinates 11.6 Conic Sections 11.7 Conics in Polar Coordinates   12. Vectors and the Geometry of Space 12.1 Three-Dimensional Coordinate Systems 12.2 Vectors 12.3 The Dot Product 12.4 The Cross Product 12.5 Lines and Planes in Space 12.6 Cylinders and Quadric Surfaces   13. Vector-Valued Functions and Motion in Space 13.1 Curves in Space and Their Tangents 13.2 Integrals of Vector Functions; Projectile Motion 13.3 Arc Length in Space 13.4 Curvature and Normal Vectors of a Curve 13.5 Tangential and Normal Components of Acceleration 13.6 Velocity and Acceleration in Polar Coordinates   14. Partial Derivatives 14.1 Functions of Several Variables 14.2 Limits and Continuity in Higher Dimensions 14.3 Partial Derivatives 14.4 The Chain Rule 14.5 Directional Derivatives and Gradient Vectors 14.6 Tangent Planes and Differentials 14.7 Extreme Values and Saddle Points 14.8 Lagrange Multipliers 14.9 Taylor's Formula for Two Variables 14.10 Partial Derivatives with Constrained Variables   15. Multiple Integrals 15.1 Double and Iterated Integrals over Rectangles 15.2 Double Integrals over General Regions 15.3 Area by Double Integration 15.4 Double Integrals in Polar Form 15.5 Triple Integrals in Rectangular Coordinates 15.6 Applications 15.7 Triple Integrals in Cylindrical and Spherical Coordinates 15.8 Substitutions in Multiple Integrals   16. Integrals and Vector Fields 16.1 Line Integrals of Scalar Functions 16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 16.3 Path Independence, Conservative Fields, and Potential Functions 16.4 Green's Theorem in the Plane 16.5 Surfaces and Area 16.6 Surface Integrals 16.7 Stokes' Theorem 16.8 The Divergence Theorem and a Unified Theory   17. Second-Order Differential Equations (Online at www.goo.gl/MgDXPY) 17.1 Second-Order Linear Equations 17.2 Nonhomogeneous Linear Equations 17.3 Applications 17.4 Euler Equations 17.5 Power-Series Solutions   Appendices 1. Real Numbers and the Real Line 2. Mathematical Induction 3. Lines, Circles, and Parabolas 4. Proofs of Limit Theorems 5. Commonly Occurring Limits 6. Theory of the Real Numbers 7. Complex Numbers 8. The Distributive Law for Vector Cross Products 9. The Mixed Derivative Theorem and the Increment Theorem