Smith R., Minton R. Calculus
Подождите немного. Документ загружается.
P1: OSO/OVY P2: OSO/OVY QC: OSO/OVY T1: OSO
MHDQ256-FM-MAIN MHDQ256-Smith-v1.cls January 8, 2011 12:17
LT (Late Transcendental)
CONFIRMING PAGES
Table of Contents ix
8.3 Direction Fields and Euler’s Method 510
8.4 Systems of First-Order Differential Equations 521
.
Predator-Prey Systems
CHAPTER 9
..
Infinite Series 531
9.1 Sequences of Real Numbers 532
9.2 Infinite Series 544
9.3 The Integral Test and Comparison Tests 554
.
Comparison Tests
9.4 Alternating Series 565
.
Estimating the Sum of an Alternating Series
9.5 Absolute Convergence and the Ratio Test 571
.
The Ratio Test
.
The Root Test
.
Summary of Convergence Tests
9.6 Power Series 579
9.7 Taylor Series 587
.
Representation of Functions as Power Series
.
Proof of Taylor’s Theorem
9.8 Applications of Taylor Series 599
.
The Binomial Series
9.9 Fourier Series 607
.
Functions of Period Other Than 2π
.
Fourier Series and Music Synthesizers
CHAPTER 10
..
Parametric Equations and
Polar Coordinates 625
10.1 Plane Curves and Parametric Equations 625
10.2 Calculus and Parametric Equations 634
10.3 Arc Length and Surface Area in Parametric Equations 641
10.4 Polar Coordinates 649
10.5 Calculus and Polar Coordinates 660
10.6 Conic Sections 668
.
Parabolas
.
Ellipses
.
Hyperbolas
10.7 Conic Sections in Polar Coordinates 677
CHAPTER 11
..
Vectors and the Geometry
of Space 687
11.1 Vectors in the Plane 688
11.2 Vectors in Space 697
.
Vectors in R
3
11.3 The Dot Product 704
.
Components and Projections
P1: OSO/OVY P2: OSO/OVY QC: OSO/OVY T1: OSO
MHDQ256-FM-MAIN MHDQ256-Smith-v1.cls January 8, 2011 12:17
LT (Late Transcendental)
CONFIRMING PAGES
x Table of Contents
11.4 The Cross Product 714
11.5 Lines and Planes in Space 726
.
Planes in R
3
11.6 Surfaces in Space 734
.
Cylindrical Surfaces
.
Quadric Surfaces
.
An Application
CHAPTER 12
..
Vector-Valued Functions 749
12.1 Vector-Valued Functions 750
.
Arc Length in R
3
12.2 The Calculus of Vector-Valued Functions 758
12.3 Motion in Space 769
.
Equations of Motion
12.4 Curvature 779
12.5 Tangent and Normal Vectors 786
.
Tangential and Normal Components of Acceleration
.
Kepler’s Laws
12.6 Parametric Surfaces 799
CHAPTER 13
..
Functions of Several Variables and
Partial Differentiation 809
13.1 Functions of Several Variables 809
13.2 Limits and Continuity 822
13.3 Partial Derivatives 833
13.4 Tangent Planes and Linear Approximations 844
.
Increments and Differentials
13.5 The Chain Rule 854
.
Implicit Differentiation
13.6 The Gradient and Directional Derivatives 864
13.7 Extrema of Functions of Several Variables 874
.
Proof of the Second Derivatives Test
13.8 Constrained Optimization and Lagrange Multipliers 887
A M.F. Mood Standard
Racket
Greater Than 3
THROAT
THROAT
Prince Racket
FIRST STRING
FIRST STRING
Greater Than 4
Greater Than 5
Greater Than 6
COEFFICENT OF RESTITUTION
RACKETS HELD BY VISE
BALL VELOCITY OF 385 M PA
FRAME
BALL HITS FRAME
IN THIS AREA
25
25
17
26
27
32
45
40
44
32
74
77
43
45
50
42
42
47
44
55
55
55
52
52
52
53
53
52
41
34
27
42
30
20
26
34
25
35
35
35
32
45
27
28
30
40
45
45
47
66
65
22
45
24
27
CHAPTER 14
..
Multiple Integrals 901
14.1 Double Integrals 901
.
Double Integrals over a Rectangle
.
Double Integrals over General Regions
14.2 Area, Volume and Center of Mass 916
.
Moments and Center of Mass
14.3 Double Integrals in Polar Coordinates 926
14.4 Surface Area 933
14.5 Triple Integrals 938
.
Mass and Center of Mass
P1: OSO/OVY P2: OSO/OVY QC: OSO/OVY T1: OSO
MHDQ256-FM-MAIN MHDQ256-Smith-v1.cls January 8, 2011 12:17
LT (Late Transcendental)
CONFIRMING PAGES
Table of Contents xi
14.6 Cylindrical Coordinates 948
14.7 Spherical Coordinates 956
.
Triple Integrals in Spherical Coordinates
14.8 Change of Variables in Multiple Integrals 962
CHAPTER 15
..
Vector Calculus 977
15.1 Vector Fields 977
15.2 Line Integrals 990
15.3 Independence of Path and Conservative Vector Fields 1003
15.4 Green’s Theorem 1014
15.5 Curl and Divergence 1022
15.6 Surface Integrals 1032
.
Parametric Representation of Surfaces
15.7 The Divergence Theorem 1044
15.8 Stokes’ Theorem 1053
15.9 Applications of Vector Calculus 1061
CHAPTER 16
..
Second-Order Differential
Equations 1073
16.1 Second-Order Equations with Constant Coefficients 1074
16.2 Nonhomogeneous Equations: Undetermined Coefficients 1082
16.3 Applications of Second-Order Equations 1090
16.4 Power Series Solutions of Differential Equations 1098
Appendix A: Proofs of Selected Theorems A-1
Appendix B: Answers to Odd-Numbered Exercises A-13
Credits C-1
Index I-1
Bibliography See www.mhhe.com/Smithminton
P1: OSO/OVY P2: OSO/OVY QC: OSO/OVY T1: OSO
MHDQ256-FM-MAIN MHDQ256-Smith-v1.cls January 8, 2011 12:17
LT (Late Transcendental)
CONFIRMING PAGES
McGraw-Hill Higher Education and Blackboard have teamed up.
Blackboard, the Web-based course-management system, has partnered with McGraw-
Hill to better allow students and faculty to use online materials and activitiesto complement
face-to-face teaching. Blackboard features exciting social learning and teaching tools that
foster more logical, visually impactful and active learning opportunities for students. You’ll
transform your closed-door classrooms into communities where students remain connected
to their educational experience 24 hours a day.
This partnership allows you and your students access to McGraw-Hill’s Connect
TM
and Create
TM
right from within your Blackboard course—all with one single sign-on.
Not only do you get single sign-on with Connect
TM
and Create
TM
, you also get deep
integration of McGraw-Hill content and content engines right in Blackboard. Whether
you’re choosing a book for your course or building Connect
TM
assignments, all the tools
you need are right where you want them—inside of Blackboard.
Gradebooks are now seamless. When a student completes an integrated Connect
TM
as-
signment,thegradeforthatassignmentautomatically (and instantly) feeds your Blackboard
grade center.
McGraw-Hill and Blackboard can now offer you easy access to industry leading tech-
nology and content, whether your campus hosts it, or we do. Be sure to ask your local
McGraw-Hill representative for details.
xii
P1: OSO/OVY P2: OSO/OVY QC: OSO/OVY T1: OSO
MHDQ256-FM-MAIN MHDQ256-Smith-v1.cls January 8, 2011 12:17
LT (Late Transcendental)
CONFIRMING PAGES
Seeing the Beauty and Power
of Mathematics
The calculus course is a critical course for science, technology, engineering, and math
majors. This course sets the stage for many majors and is where students see the beauty of
mathematics, encouraging them to take upper-level math courses.
In a calculus market-research study conducted in 2008, calculus faculty pointed out
three critical components to student success in the calculus.
The most critical is mastery of the prerequisite algebra and trigonometry skills. Our
market research study showed that 58 percent of faculty mentioned that students struggled
withcalculusbecauseofpooralgebraskillsand72percentsaidbecauseofpoortrigonometry
skills. This is the number one learning challenge preventing students from being successful
in the first calculus course.
The second critical component for student success is a text that presents calculus
concepts, especially the most challenging concepts, in a clear and elegant manner. This
helps students see and appreciate the beauty and power of mathematics.
Lastly, calculus faculty told us that it is critical for a calculus text to include all the
classic calculus problems.
Other calculus textbooks may reflect one or two of these critical components. However,
there is only ONE calculus textbook that includes all three: Smith/Minton, 4e.
ReadontounderstandhowSmith/Mintonhandlesallthreeissues,helpingyourstudents
to see the beauty and power of mathematics.
Mastery of Prerequisite Algebra and Trigonometry Skills
ALEKS Prep for Calculus
is a Web-based program that
focuses on prerequisite and
introductory material for
Calculus, and can be used
during the first six weeks of
the term to prepare students
for success in the course.
ALEKS uses artificial
intelligence and adaptive
questioning to assess
precisely a student’s preparedness and provide personalized instruction on the exact topics
the student is most ready to learn. By providing comprehensive explanations, practice and
feedback, ALEKS allows students to quickly fill in gaps in prerequisite knowledge on their
own time, while also allowing instructors to focus on core course concepts.
Use ALEKS Prep for Calculus during the first six weeks of the term to see improved
student confidence and performance, as well as fewer drops.
xiii
P1: OSO/OVY P2: OSO/OVY QC: OSO/OVY T1: OSO
MHDQ256-FM-MAIN MHDQ256-Smith-v1.cls January 8, 2011 12:17
LT (Late Transcendental)
CONFIRMING PAGES
xiv Seeing the Beauty and Power of Mathematics
ALEKS PREP FOR CALCULUS FEATURES:
r
Artificial Intelligence: Targets Gaps in Individual Student Knowledge
r
Adaptive, Open-Response Environment: Avoids Multiple-Choice Questions and
Ensures Student Mastery
r
Automated Reports: Monitor Student and Class Progress
For more information about ALEKS, please visit: www.aleks.com/highered/math
ALEKS is a registered trademark of ALEKS Corporation.
Elegant Presentation of Calculus Concepts
Calculus reviewers and focus groups worked with the authors to provide a more concise,
streamlined presentation that maintains the clarity of past editions. New examples and
exercises illustrate the physical meaning of the derivative and give real counterexamples.
The proofs of basic differentiation rules in sections 2.4–2.6 have been revised, making
them more elegant and easy for students to follow, as were the theorems and proofs of basic
integration and integration rules. Further, an extensive revision of multivariable calculus
chapters includes a revision of the definition and proof of the derivative of a vector-valued
function, the normal vector, the gradiant and both path and surface integration.
“More than any other text, I
believe Smith/Minton approaches
deep concepts from a thoughtful
perspective in a very friendly
style.”—Louis Rossi,
University of Delaware
“[Smith-Minton is] sufficiently
rigorous without being
considered to too ‘mathy’. It is
a very readable book with
excellent graphics and
outstanding applications
sections.”—Todd King,
Michigan Technological
University
“Rigorous, more interesting to
read than Stewart. Full of great
application examples.”—Fred
Bourgoin, Laney College
“The material is very well
presented in a rigorous
manner . . . very readable,
numerous examples for students
with a wide variety of
interests.”—John Heublein,
Kansas State University–Salina
P1: OSO/OVY P2: OSO/OVY QC: OSO/OVY T1: OSO
MHDQ256-FM-MAIN MHDQ256-Smith-v1.cls January 8, 2011 12:17
LT (Late Transcendental)
CONFIRMING PAGES
Seeing the Beauty and Power of Mathematics xv
Classic Calculus Problems
Many new classic calculus exercises have been added. From basic derivative problems to
related rates applications involving flow, and multivariable applications to electricity and
magnetism, these exercisesgive students the opportunity to challenge themselves and allow
instructors flexibility when choosing assignments. The authors have also reorganized the
exercises to move consistently from the simplest to most difficultproblems, making it easier
for instructors to choose exercises of the appropriate level for their students. They moved
the applications to a separate section within the exercise sets and were careful to include
many examples from the common calculus majors such as engineering, physical sciences,
computer science and biology.
“Thought provoking, clearly organized,
challenging, excellent problem sets, guarantee
that students will actually read the book and
ask questions about concepts and topics.”—
Donna Latham, Sierra College
“[Smith-Minton is] a traditional calculus book
that is easy to read and has excellent
applications.”—Hong Liu, Embry-Riddle
Aeronautical University—Daytona Beach
“The rigorous treatment of calculus with an
easy conversational style that has a wealth of
examples and problems. The topics are nicely
arranged so that theoretical topics are
segregated from applications.”—Jayakumar
Ramanatan, Eastern Michigan University
P1: OSO/OVY P2: OSO/OVY QC: OSO/OVY T1: OSO
MHDQ256-FM-MAIN MHDQ256-Smith-v1.cls January 8, 2011 12:17
LT (Late Transcendental)
CONFIRMING PAGES
xvi
P1: OSO/OVY P2: OSO/OVY QC: OSO/OVY T1: OSO
MHDQ256-FM-MAIN MHDQ256-Smith-v1.cls January 8, 2011 12:17
LT (Late Transcendental)
CONFIRMING PAGES
xvii
P1: OSO/OVY P2: OSO/OVY QC: OSO/OVY T1: OSO
MHDQ256-FM-MAIN MHDQ256-Smith-v1.cls January 8, 2011 12:17
LT (Late Transcendental)
CONFIRMING PAGES
the future of custom
publishing is here.
Introducing McGraw-Hill Create™ –a new, self-
service website that allows you to create custom
course materials by drawing upon McGraw-Hill’s
comprehensive, cross-disciplinary content and other
third party resources. Select, then arrange the content
in a way that makes the most sense for your course.
Even personalize your book with your course
information and choose the best format for your
students–color print, black-and-white print, or eBook.
•
Build custom print and eBooks easily
•
Combine material from different sources
and even upload your own content
•
Receive a PDF review copy in minutes
begin creating now:
www.mcgrawhillcreate.com
Start by registering for a free Create account.
If you already have a McGraw-Hill account with one
of our other products, you will not need to register
on Create. Simply Sign In and enter your username
and password to begin using the site.
w
s you to create custom
i
ng upon McGraw-Hi
ll
’s
cip
l
inary content an
d
ot
h
er
e
ct, t
h
en arrange t
h
e conten
t
m
ost sense
f
or your course.
o
k
wit
h
your course
t
he best format for your
c
k-
a
n
d
-
w
hite print, or
e
B
oo
k
.
nd
eBoo
k
s easi
l
y
o
m
d
ifferent s
ou
rces
u
r own content
w
copy in minutes
If you already have a McGraw-Hill account with on
e
o
f our other products, you will not need to register
o
n Create. Simp
l
y Sign In an
d
enter your username
a
n
d
passwor
d
to
b
egin using t
h
e site.
xviii