Calculus and Its Applications, 15th Edition © 2023
Larry J. Goldstein | David C. Lay | David I. Schneider | Nakhle H. Asmar
Calculus and Its Applications builds intuition with key concepts before presenting analytical material, using a strategic and distinctive topic organization. Significant applications introduced early on make mathematics more accessible, and comprehensive exercise sets suit varying course needs.
The 15th edition introduces fresh insights from new co-author Edward Tavernetti of University of California - Davis. It improves and expands applications, updates example and exercise data, and provides new material on modeling with differential equations.
Hallmark features of this title
- Relevant, varied applications illustrate calculus in daily life and motivate students to be interested in mathematics wherever possible.
- Over 500 worked examples are provided. Computational details aid comprehension for students who need skills reinforcement.
- Exercises to meet all student needs: Now Try Exercises appear after select examples, as an instructor might stop in class to ask students to try a problem. Fundamental Concept Check exercises and Chapter Review exercises prepare students for exams.
- Check Your Understanding problems at the end of each section prepare students for the exercise sets.
- Integrating Technology features within sections incorporate technology including graphing calculators, spreadsheets, and Wolfram|Alpha®.
New and updated features of this title
- Greatly increased video coverage adds 25 new videos, bringing the total to 237. Videos were produced and incorporated for a modern and clear presentation of the examples; they are integrated into MyLab problems as learning aids and in the MyLab Video & Resource Library.
- Updated and improved exercises and applications, focusing on currency of data and topics, continue to draw students into the material and inspire learning. Hundreds of exercises have been improved and many exercises added to this revision.
- The scope of applications is expanded beyond typical offerings in a first applied calculus course. The new applications start in a rewritten section 5.4 (Applications of the Exponential and Natural Logarithmic Functions) and are revisited and expanded further in sections 6.5, 9.5, and 10.4.
This program offers:
- Review and enhancement of MyLab course by new co-author Edward Tavernetti. This includes overall accuracy and fidelity with the text, all exercises and solutions, video program, and more.
- New integrated review that bolsters prerequisite skills if needed. Skills Check assessment in each chapter pinpoints topics students need to review. Personalized homework asks them to practice only those topics requiring extra help. Integrated Review videos and worksheets offer more instruction on those topics.
- Expanded suite of interactive figures. Created in GeoGebra, these illustrate key concepts, can be manipulated by users, and can be used in lectures or independently by students.
- New mindset videos and assignable, open-ended exercises that encourage students to maintain a positive attitude and view mistakes as learning opportunities. New Personal Inventory assessments promote self-reflection and engagement with topics such as stress management, motivation and time management.
- New early alerts in Performance Analytics that identify struggling students. Instructors can email feedback to students individually or by group.
Prerequisite Skills Diagnostic Test
Introduction
0. FUNCTIONS
0.1 Functions and Their Graphs
0.2 Some Important Functions
0.3 The Algebra of Functions
0.4 Zeros of Functions - The Quadratic Formula and Factoring
0.5 Exponents and Power Functions
0.6 Functions and Graphs in Applications
Chapter Summary and Chapter Review Exercises
1. THE DERIVATIVE
1.1 The Slope of a Straight Line
1.2 The Slope of a Curve at a Point
1.3 The Derivative and Limits
*1.4 Limits and the Derivative
*1.5 Differentiability and Continuity
1.6 Some Rules for Differentiation
1.7 More About Derivatives
1.8 The Derivative as a Rate of Change
Chapter Summary and Chapter Review Exercises
2. APPLICATIONS OF THE DERIVATIVE
2.1 Describing Graphs of Functions
2.2 The First- and Second-Derivative Rules
2.3 The First- and Section-Derivative Tests and Curve Sketching
2.4 Curve Sketching (Conclusion)
2.5 Optimization Problems
*2.6 Further Optimization Problems
*2.7 Applications of Derivatives to Business and Economics
Chapter Summary and Chapter Review Exercises
3. TECHNIQUES OF DIFFERENTIATION
3.1 The Product and Quotient Rules
3.2 The Chain Rule
*3.3 Implicit Differentiation and Related Rates
Chapter Summary and Chapter Review Exercises
4. THE EXPONENTIAL AND NATURAL LOGARITHM FUNCTIONS
4.1 Exponential Functions
4.2 The Exponential Function ex
4.3 Differentiation of Exponential Functions
4.4 The Natural Logarithm Function
4.5 The Derivative of ln x
4.6 Properties of the Natural Logarithm Function
Chapter Summary and Chapter Review Exercises
5. APPLICATIONS OF THE EXPONENTIAL AND NATURAL LOGARITHM FUNCTIONS
5.1 Exponential Growth and Decay
5.2 Compound Interest
*5.3 Applications of the Natural Logarithm Function to Economics
*5.4 Further Applications in Business and Economics
Chapter Summary and Chapter Review Exercises
6. THE DEFINITE INTEGRAL
6.1 Antidifferentiation
6.2 The Definite Integral and Net Change of a Function
6.3 The Definite Integral and Area Under a Graph
6.4 Areas in the xy-Plane
6.5 Applications of the Definite Integral
Chapter Summary and Chapter Review Exercises
7. FUNCTIONS OF SEVERAL VARIABLES
7.1 Examples of Functions of Several Variables
7.2 Partial Derivatives
7.3 Maxima and Minima of Functions of Several Variables
7.4 Lagrange Multipliers and Constrained Optimization
*7.5 The Method of Least Squares
*7.6 Double Integrals
Chapter Summary and Chapter Review Exercises
8. THE TRIGONOMETRIC FUNCTIONS
8.1 Radian Measure of Angles
8.2 The Sine and the Cosine
8.3 Differentiation and Integration of sin t and cos t
8.4 The Tangent and Other Trigonometric Functions
Chapter Summary and Chapter Review Exercises
9. TECHNIQUES OF INTEGRATION
9.1 Integration by Substitution
9.2 Integration by Parts
9.3 Evaluation of Definite Integrals
*9.4 Approximation of Definite Integrals
*9.5 Applications in Business and Economics
9.6 Improper Integrals
Chapter Summary and Chapter Review Exercises
10. DIFFERENTIAL EQUATIONS
10.1 Solutions of Differential Equations
10.2 Separation of Variables
*10.3 First-Order Linear Differential Equations
*10.4 Applications of First-Order Linear Differential Equations
10.5 Graphing Solutions of Differential Equations
10.6 Applications of Differential Equations
*10.7 Numerical Solution of Differential Equations
Chapter Summary and Chapter Review Exercises
11. TAYLOR POLYNOMIALS AND INFINITE SERIES
11.1 Taylor Polynomials
*11.2 The Newton–Raphson Algorithm
11.3 Infinite Series
11.4 Series with Positive Terms
11.5 Taylor Series
Chapter Summary and Chapter Review Exercises
12. PROBABILITY AND CALCULUS
12.1 Discrete Random Variables
12.2 Continuous Random Variables
12.3 Expected Value and Variance
12.4 Exponential and Normal Random Variables
12.5 Poisson and Geometric Random Variables
Chapter Summary and Chapter Review Exercises
*These sections are optional in the sense that they are not prerequisites for later material.
Appendix: Areas under the Standard Normal Curve
LEARNING OBJECTIVES
SOURCES
SELECTED ANSWERS
INDEX OF APPLICATIONS
INDEX
Larry J. Goldstein
Goldstein Educational Technologies
Larry Goldstein has received several distinguished teaching awards, given more than 50 Conference and Colloquium talks & addresses, and written more than 50 books in math and computer programming. He received his PhD at Princeton and his BA and MA at the University of Pennsylvania. He also teaches part time at Drexel University.
David I. Schneider
University of Maryland
David Schneider, who is known widely for his tutorial software, holds a BA degree from Oberlin College and a PhD from MIT. He is currently an emeritus professor of mathematics at the University of Maryland. He has authored 8 widely used math texts, 14 highly acclaimed computer books, and 3 widely used mathematical software packages. He has also produced instructional videotapes at both the University of Maryland and the BBC.
This program is available in a variety of formats. You can review the individual prices for each ISBN in our catalog. All access codes are for use by 1 student, for 1 course, for up to 1 year, and are non-transferable.
| Format | ISBN-13 |
|---|---|
| MyMathLab for School with eTextbook (1-year access) | 100% digital solution. Access code is delivered via email. |
9780132962377 |
| MyMathLab for School with eTextbook (6-year access) | 100% digital solution. Access code is delivered via email. |
9780132962391 |
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