Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version

Larry Goldstein, David Lay, David Schneider, Nakhle Asmar, William Tavernetti (Autoren)

Software / Digital Media

15. Available via MyLab
Pearson Education (US) (Hersteller)
978-0-13-759107-7 (ISBN)

Infos

Calculus & Its Applications builds intuition with key concepts before presenting analytical material, using a strategic and distinctive topic organization to make learning calculus more accessible. Significant applications introduced early on make the mathematics more digestible, and comprehensive exercise sets suit different types of courses. 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.

Autor

About our authors 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 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. Martha Siegel holds a BA from Russell Sage College, attended Rensselaer Polytechnic Institute as a special student, and received her PhD at the University of Rochester. From 1966 until 1971 she taught at Goucher University in Baltimore. Since 1971 she has been a professor at Towson State University, also in Maryland. Professor Siegel has been on the writing team of this book since the 5th Edition and is also the co-author of a precalculus reform book. William Tavernetti holds a PhD in Applied Mathematics from University of California - Davis and currently is a continuing lecturer there in the department of Mathematics. He earned a BS in Mathematical Science and a BA in Philosophy of Ethics and Public Policy from University of California - Santa Barbara. He also worked on the NASA Altair Lunar Lander as a risk analyst. He was the 2018 winner of the UC Davis University Honors Program Outstanding Teaching Award, the Thomas Salle Teaching Award (twice), the Henry Adler Prize for excellence in teaching, and also has a TEDx talk on the "Beauty and Power of Mathematics." He also works as an instructor for the California State Summer School for Mathematics and Science (COSMOS).

Inhalt

Prerequisite Skills Diagnostic Test Introduction

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


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


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


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


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


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


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


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


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


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


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


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


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

Produkt-Details

• Verlagsort: Upper Saddle River
• Sprache: englisch
• ISBN-10: 0-13-759107-1 / 0137591071
• ISBN-13: 978-0-13-759107-7 / 9780137591077
• Zustand: Neuware