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Calculus: Early Transcendental Functions: Multivariable


Calculus: Early Transcendental Functions: Multivariable Cover


Synopses & Reviews

Publisher Comments:

Students who have used Smith/Minton's Calculus say it was easier to read than any other math book they've used. That testimony underscores the success of the authors approach, which combines the best elements of reform with the most reliable aspects of mainstream calculus teaching, resulting in a motivating, challenging book. Smith/Minton also provide exceptional, reality-based applications that appeal to students interests and demonstrate the elegance of math in the world around us. New features include: • A new organization placing all transcendental functions early in the book and consolidating the introduction to L'Hôpital's Rule in a single section. • More concisely written explanations in every chapter. • Many new exercises (for a total of 7,000 throughout the book) that require additional rigor not found in the 2nd Edition. • New exploratory exercises in every section that challenge students to synthesize key concepts to solve intriguing projects. • New commentaries (“Beyond Formulas”) that encourage students to think mathematically beyond the procedures they learn. • New counterpoints to the historical notes, “Today in Mathematics,” that stress the contemporary dynamism of mathematical research and applications, connecting past contributions to the present. • An enhanced discussion of differential equations and additional applications of vector calculus.

Table of Contents

Chapter 0: Preliminaries

0.1 Polynomials and Rational Functions

0.2 Graphing Calculators and Computer Algebra Systems

0.3 Inverse Functions

0.4 Trigonometric and Inverse Trigonometric Functions

0.5 Exponential and Logarithmic Functions

Hyperbolic Functions
Fitting a Curve to Data

0.6 Transformations of Functions

Chapter 1: Limits and Continuity

1.1 A First Look at Calculus

1.2 The Concept of Limit

1.3 Computation of Limits

1.4 Continuity and its Consequences

The Method of Bisections

1.5 Limits Involving Infinity


1.6 Formal Definition of the Limit

Exploring the Definition of Limit Graphically

1.7 Limits and Loss-of-Significance Errors

Computer Representation of Real Numbers

Chapter 2: Differentiation

2.1 Tangent Lines and Velocity

2.2 The Derivative

Numerical Differentiation

2.3 Computation of Derivatives: The Power Rule

Higher Order Derivatives

2.4 The Product and Quotient Rules

2.5 The Chain Rule

2.6 Derivatives of the Trigonometric Functions

2.7 Derivatives of the Exponential and Logarithmic Functions

2.8 Implicit Differentiation and Inverse Trigonometric Functions

2.9 The Mean Value Theorem

Chapter 3: Applications of Differentiation

3.1 Linear Approximations and Newtons Method

3.2 Indeterminate Forms and LHopitals Rule

3.3 Maximum and Minimum Values

3.4 Increasing and Decreasing Functions

3.5 Concavity and the Second Derivative Test

3.6 Overview of Curve Sketching

3.7 Optimization

3.8 Related Rates

3.9 Rates of Change in Economics and the Sciences

Chapter 4: Integration

4.1 Antiderivatives

4.2 Sums and Sigma Notation

Principle of Mathematical Induction

4.3 Area

4.4 The Definite Integral

Average Value of a Function

4.5 The Fundamental Theorem of Calculus

4.6 Integration by Substitution

4.7 Numerical Integration

Error Bounds for Numerical Integration

4.8 The Natural Logarithm as an Integral

The Exponential Function as the Inverse of the Natural Logarithm

Chapter 5: Applications of the Definite Integral

5.1 Area Between Curves

5.2 Volume: Slicing, Disks, and Washers

5.3 Volumes by Cylindrical Shells

5.4 Arc Length and Surface Area

5.5 Projectile Motion

5.6 Applications of Integration to Economics and the Sciences

5.7 Probability

Chapter 6: Integration Techniques

6.1 Review of Formulas and Techniques

6.2 Integration by Parts

6.3 Trigonometric Techniques of Integration

Integrals Involving Powers of Trigonometric Functions
Trigonometric Substitution

6.4 Integration of Rational Functions Using Partial Fractions

General Strategies for Integration Techniques

6.5 Integration Tables and Computer Algebra Systems

6.6 Improper Integrals

A Comparison Test

Chapter 7: First Order Differential Equations

7.1 Growth and Decay Problems

Compound Interest
Modeling with Differential Equations

7.2 Separable Differential Equations

Logistic Growth

7.3 Direction Fields and Euler's Method

7.4 Systems of First Order Differential Equations

Predator-Prey Systems

Chapter 8: Infinite Series

8.1 Sequences of Real Numbers

8.2 Infinite Series

8.3 The Integral Test and Comparison Tests

8.4 Alternating Series

Estimating the Sum of an Alternating Series

8.5 Absolute Convergence and the Ratio Test

The Root Test
Summary of Convergence Tests

8.6 Power Series

8.7 Taylor Series

Representations of Functions as Series
Proof of Taylors Theorem

8.8 Applications of Taylor Series

The Binomial Series

8.9 Fourier Series

Chapter 9: Parametric Equations and Polar Coordinates

9.1 Plane Curves and Parametric Equations

9.2 Calculus and Parametric Equations

9.3 Arc Length and Surface Area in Parametric Equations

9.4 Polar Coordinates

9.5 Calculus and Polar Coordinates

9.6 Conic Sections

9.7 Conic Sections in Polar Coordinates

Chapter 10: Vectors and the Geometry of Space

10.1 Vectors in the Plane

10.2 Vectors in Space

10.3 The Dot Product

Components and Projections

10.4 The Cross Product

10.5 Lines and Planes in Space

10.6 Surfaces in Space

Chapter 11: Vector-Valued Functions

11.1 Vector-Valued Functions

11.2 The Calculus of Vector-Valued Functions

11.3 Motion in Space

11.4 Curvature

11.5 Tangent and Normal Vectors

Tangential and Normal Components of Acceleration
Keplers Laws

11.6 Parametric Surfaces

Chapter 12: Functions of Several Variables and Differentiation

12.1 Functions of Several Variables

12.2 Limits and Continuity

12.3 Partial Derivatives

12.4 Tangent Planes and Linear Approximations

Increments and Differentials

12.5 The Chain Rule

12.6 The Gradient and Directional Derivatives

12.7 Extrema of Functions of Several Variables

12.8 Constrained Optimization and Lagrange Multipliers

Chapter 13: Multiple Integrals

13.1 Double Integrals

13.2 Area, Volume, and Center of Mass

13.3 Double Integrals in Polar Coordinates

13.4 Surface Area

13.5 Triple Integrals

Mass and Center of Mass

13.6 Cylindrical Coordinates

13.7 Spherical Coordinates

13.8 Change of Variables in Multiple Integrals

Chapter 14: Vector Calculus

14.1 Vector Fields

14.2 Line Integrals

14.3 Independence of Path and Conservative Vector Fields

14.4 Green's Theorem

14.5 Curl and Divergence

14.6 Surface Integrals

14.7 The Divergence Theorem

14.8 Stokes' Theorem

14.9 Applications of Vector Calculus

Chapter 15: Second Order Differential Equations

15.1 Second-Order Equations with Constant Coefficients

15.2 Nonhomogeneous Equations: Undetermined Coefficients

15.3 Applications of Second Order Equations

15.4 Power Series Solutions of Differential Equations

Appendix A: Proofs of Selected Theorems

Appendix B: Answers to Odd-Numbered Exercises

Product Details

McGraw-Hill Higher Education
Smith, Robert T.
Minton, Roland
Cram101 Textbook Reviews
Smith, Robert
Minton, Roland B.
Edition Number:
Publication Date:
September 2006
Grade Level:
College/higher education:
10.30x8.72x.97 in. 2.84 lbs.

Related Subjects

Science and Mathematics » Mathematics » Calculus » General
Textbooks » General

Calculus: Early Transcendental Functions: Multivariable
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Product details 476 pages McGraw-Hill Higher Education - English 9780073309378 Reviews:
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