Last edition Elsevier University Calculus, Early Transcendentals, Third Edition helps students generalize and apply the key ideas of calculus through clear and precise explanations, thoughtfully chosen examples, meticulously crafted figures, and superior exercise sets. This text offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This revision features more examples, more mid-level exercises, more figures, improved conceptual flow, and the best in technology for learning and teaching.
Last Edition
ISBN 13: 9781292104034
Imprint: Pearson Education
Language: English
Authors: Joel R. Hass
Pub Date: 02/2016
Pages: 1080
Illus: Illustrated
Weight: 2,040.000 grams
Size: h 218 X 276 mm
Product Type: Softcover
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- • The exercises are known for their breadth and quality, with carefully constructed exercise sets that progress from skills problems to applied and theoretical problems. The text contains more than 8,000 exercises in all. End-of-chapter exercises feature review questions, practice exercises covering the entire chapter, and a series of Additional and Advanced Exercises.
- • Figures are conceived and rendered to support conceptual reasoning and provide insight for students. They are also consistently captioned to aid understanding.
- • The use of theorems and proofs is essential to convey the methods and language of mathematics, and in this text results are both carefully stated and proved throughout. At the same time, ideas are introduced with examples and intuitive explanations that are then generalized so that students are not overwhelmed by abstraction.
- • Key topics, such as the definition of the derivative, are presented both informally and formally. The distinction between the two is clearly stated as each is developed, including an explanation as to why a formal definition is needed. Great care has been taken to point out when intuition is being developed and when ideas are formally stated.
- • Proofs of major theorems are given, but instructors in some cases may not cover the proofs and focus on content and applications instead. The book is designed so that instructors can choose how much formal mathematics their students can absorb. The text therefore provides options for the instructor to set the level of rigor for their class.
- • Within examples, the authors include explanatory notes that guide longer computations. The goal is to indicate to students the steps needed to get from one line of a computation to the next, so that students can focus on the main concept being explained rather than being hung up on why one step follows from another.
- Joel Hass is an American mathematician, a professor of mathematics and chair of the mathematics department at the University of California, Davis
- 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 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms
- 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 2.5 Continuity 2.6 Limits Involving Infinity; Asymptotes of Graphs
- 3. Differentiation
- 3.1 Tangents 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 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'H?pital's Rule 4.6 Applied Optimization 4.7 Newton's Method 4.8 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 Using Cross-Sections 6.2 Volumes Using Cylindrical Shells 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 6.5 Work 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
- 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 and Applications of Taylor Series
- 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 in Polar Coordinates 10.5 Areas and Lengths in Polar Coordinates 10.6 Conics in Polar Coordinates
- 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
- 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 12.6 Velocity and Acceleration in Polar Coordinates
- 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
- 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 Moments and Centers of Mass 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 14.8 Substitutions in Multiple Integrals
- 15. Integration in Vector Fields
- 15.1 Line Integrals 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
- 16. First-Order Differential Equations (Online)
- 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
- 17. Second-Order Differential Equations (Online)
- 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. Conic Sections 5. Proofs of Limit Theorems 6. Commonly Occurring Limits 7. Theory of the Real Numbers 8. Complex Numbers 9. The Distributive Law for Vector Cross Products 10. The Mixed Derivative Theorem and the Increment Theorem 11. Taylor's Formula for Two Variables
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