Calculus with Differential Equations, 9th edition
Published by Pearson (April 10, 2006) © 2007
- Dale Varberg Hamline University , Macalester College
- Edwin Purcell
- Steve Rigdon Southern Illinois University, Edwardsville
- Hardcover, paperback or looseleaf edition
- Affordable rental option for select titles
- Free shipping on looseleafs and traditional textbooks
For freshman/sophomore-level courses treating calculus of both one and several variables with additional material on differential equations.
Clear and Concise!
Varberg focuses on the most critical concepts freeing you to teach the way you want!
This popular calculus text remains the shortest mainstream calculus book available — yet covers all the material needed by, and at an appropriate level for, students in engineering, science, and mathematics. It's conciseness and clarity helps students focus on, and understand, critical concepts in calculus without them getting bogged down and lost in excessive and unnecessary detail. It is accurate, without being excessively rigorous, up-to-date without being faddish. The authors make effective use of computing technology, graphics, and applications. Ideal for instructors who want a no-nonsense, concisely written treatment.
• Perfectly paced — The economical presentation enables instructors to move through the book at a reasonable pace, covering one section per lecture easily.
• Rigor is emphasized, while also developing conceptual understanding — Helps students to devise a mental picture before getting a formal definition.
• Student development of “number sense” is encouraged — Emphasizes estimation as a technique to learn number sense, which helps students to catch their numerical mistakes by recognizing answers that don’t make sense.
• Entire Chapter Devoted to Differential Equations —
• Moderate and reasonable integration of technology — Technology is carefully incorporated in exercises (and marked as such). Each chapter has 2 technology projects divided into 3 parts: (1) Preparation (think about the question before diving into technology) (2) Using Technology (3) Reflection (think a little deeper).
• Clear connections are drawn between algebra and geometry in the text and in figures — For example,geometric reasoning is used to understand a difficult concept in Figure 2 and Example on p.437 of the eighth edition.
• Huge number of high quality exercises that have benefited from years of development:
— Makes creating varied assignments easy.
— Every section exercise set begins with a Concepts Review, ensuring students get the big picture before sharpening his/her skills.
• Figures convey, not hide, mathematical ideas — Figures are intentionally drawn simply, to reflect a sketch a student might draw, unlike the overly elaborate figures in other books.
• New Chapter Openers now appear throughout the book:
— Each chapter begins with a set of “Review and Preview Problems” that serve as a necessary review of previous material or a preview of things to come.
• New Chapter on Differential Equations
• MyMathLab, the online course designed to accompany the text — Includes an online tutorial, assessment, text, videos, Student Solutions Manual, and access to Prentice Hall Tutor Center.
• Maple, Student Version Software
• Numerical methods rearranged to the appropriate chapters:
— Newton’s method in “Applications of the Derivative”
— numerical integration in “The Definite Integral”
— Taylor polynomial approximation in “Infinite Series”
— Euler’s method in “Transcendental Functions” or “Techniques of Integration and Differential Equations.”
• Single-chapter coverage of two- and three-dimensional vectors rather than in separate chapters.
• Streamlined material on conic sections — from five sections to three.
• New section on “Strategies for Integration” in the chapter on Techniques of Integration — Includes a summary of the methods of integration and a comparison of exact and numerical integration.
• New section on “Change of Variables in Multiple Integrals” in the chapter on Multiple Integration.
• New section on “Probability and Random Variables” in the chapter on Applications of the Integral.
Calculus with Differential Equations, 9/e
ISBN: 0-13-230633-6
Dale Varberg/Edwin J. Purcell/Steve E. Rigdon
0 PRELIMINARIES
0.1
Real Numbers, Estimation, and Logic
0.2
Inequalities and Absolute Values
0.3
The Rectangular Coordinate System
0.4
Graphs of Equations
0.5
Functions and Their Graphs
0.6
Operations on Functions
0.7
The Trigonometric Functions
0.8
Chapter Review
1 LIMITS
1.1
Introduction to Limits
1.2
Rigorous Study of Limits
1.3
Limit Theorems
1.4
Limits Involving Trigonometric Functions
1.5
Limits at Infinity; Infinite Limits
1.6
Continuity of Functions
1.7
Chapter Review
2 THE DERIVATIVE
2.1
Two Problems with One Theme
2.2
The Derivative
2.3
Rules for Finding Derivatives
2.4
Derivatives of Trigonometric Functions
2.5
The Chain Rule
2.6
Higher-Order Derivatives
2.7
Implicit Differentiation
2.8
Related Rates
2.9
Differentials and Approximations
2.10
Chapter Review
3 APPLICATIONS OF THE DERIVATIVE
3.1
Maxima and Minima
3.2
Monotonicity and Concavity
3.3
Local Extrema and Extrema on Open Intervals
3.4
Practical Problems
3.5
Graphing Functions Using Calculus
3.6
The Mean Value Theorem for Derivatives
3.7
Solving Equations Numerically
3.8
Antiderivatives
3.9
Introduction to Differential Equations
3.10
Chapter Review
4 THE DEFINITE INTEGRAL
4.1
Introduction to Area
4.2
The Definite Integral
4.3
The 1st Fundamental Theorem of Calculus
4.4
The 2nd Fundamental Theorem of Calculus and the Method of Substitution
4.5
The Mean Value Theorem for Integrals & the Use of Symmetry
4.6
Numerical Integration
4.7
Chapter Review
5 APPLICATIONS OF THE INTEGRAL
5.1
The Area of a Plane Region
5.2
Volumes of Solids: Slabs, Disks, Washers
5.3
Volumes of Solids of Revolution: Shells
5.4
Length of a Plane Curve
5.5
Work and Fluid Pressure
5.6
Moments, Center of Mass
5.7
Probability and Random Variables
5.8
Chapter Review
6 TRANSCENDENTAL FUNCTIONS
6.1
The Natural Logarithm Function
6.2
Inverse Functions and Their Derivatives
6.3
The Natural Exponential Function
6.4
General Exponential & Logarithmic Functions
6.5
Exponential Growth and Decay
6.6
First-Order Linear Differential Equations
6.7
Approximations for Differential Equations
6.8
The Inverse Trig Functions & Their Derivatives
6.9
The Hyperbolic Functions & Their Inverses
6.10
Chapter Review
7 TECHNIQUES OF INTEGRATION
7.1
Basic Integration Rules
7.2
Integration by Parts
7.3
Some Trigonometric Integrals
7.4
Rationalizing Substitutions
7.5
Integration of Rational Functions Using Partial Fractions
7.6
Strategies for Integration
7.7
Chapter Review
8 INDETERMINATE FORMS & IMPROPER INTEGRALS
8.1
Indeterminate Forms of Type 0/0
8.2
Other Indeterminate Forms
8.3
Improper Integrals: Infinite Limits of Integration
8.4
Improper Integrals: Infinite Integrands
8.5
Chapter Review
9 INFINITE SERIES
9.1
Infinite Sequences
9.2
Infinite Series
9.3
Positive Series: The Integral Test
9.4
Positive Series: Other Tests
9.5
Alternating Series, Absolute Convergence, and Conditional Convergence
9.6
Power Series
9.7
Operations on Power Series
9.8
Taylor and Maclaurin Series
9.9
The Taylor Approximation to a Function
9.10
Chapter Review
10 CONICS AND POLAR COORDINATES
10.1
The Parabola
10.2
Ellipses and Hyperbolas
10.3
Translation and Rotation of Axes
10.4
Parametric Representation of Curves in the Plane
10.5
The Polar Coordinate System
10.6
Graphs of Polar Equations
10.7
Calculus in Polar Coordinates
10.8
Chapter Review
11 GEOMETRY IN SPACE AND VECTORS
11.1
Cartesian Coordinates in Three-Space
11.2
Vectors
11.3
The Dot Product
11.4
The Cross Product
11.5
Vector Valued Functions & Curvilinear Motion
11.6
Lines in Three-Space
11.7
Curvature and Components of Acceleration
11.8
Surfaces in Three Space
11.9
Cylindrical and Spherical Coordinates
11.10
Chapter Review
12 DERIVATIVES OF FUNCTIONS OF TWO OR MORE VARIABLES
12.1
Functions of Two or More Variables
12.2
Partial Derivatives
12.3
Limits and Continuity
12.4
Differentiability
12.5
Directional Derivatives and Gradients
12.6
The Chain Rule
12.7
Tangent Planes and Approximations
12.8
Maxima and Minima
12.9
The Method of Lagrange Multipliers
12.10
Chapter Review
13 MULTIPLE INTEGRATION
13.1
Double Integrals over Rectangles
13.2
Iterated Integrals
13.3
Double Integrals over Nonrectangular Regions
13.4
Double Integrals in Polar Coordinates
13.5
Applications of Double Integrals
13.6
Surface Area
13.7
Triple Integrals in Cartesian Coordinates
13.8
Triple Integrals in Cylindrical & Spherical Coordinates
13.9
Change of Variables in Multiple Integrals
13.1
Chapter Review
14 VECTOR CALCULUS
14.1
Vector Fields
14.2
Line Integrals
14.3
Independence of Path
14.4
Green's Theorem in the Plane
14.5
Surface Integrals
14.6
Gauss's Divergence Theorem
14.7
Stokes's Theorem
14.8
Chapter Review
15 DIFFERENTIAL EQUATIONS
15.1
Linear Homogeneous Equations
15.2
Nonhomogeneous Equations
15.3
Applications of Second-Order Equations
APPENDIX
A.1
Mathematical Induction
A.2
Proofs of Several Theorems
Need help? Get in touch
Play
Pearson eTextbook: What’s on the inside just might surprise you
They say you can’t judge a book by its cover. It’s the same with your students. Meet each one right where they are with an engaging, interactive, personalized learning experience that goes beyond the textbook to fit any schedule, any budget, and any lifestyle.
Digital Learning NOW
Extend your professional development and meet your students where they are with free weekly Digital Learning NOW webinars. Attend live, watch on-demand, or listen at your leisure to expand your teaching strategies. Earn digital professional development badges for attending a live session.