Calculus:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Fort Worth [u.a.]
Saunders College Publ.
1992
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| Edition: | 5. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | Getr. Zählung graph.Darst. |
| ISBN: | 0030964202 |
Staff View
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| 100 | 1 | |a Grossman, Stanley I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Calculus |
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Record in the Search Index
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| adam_text | CALCULUS
FIFTH EDITION
Stanley I Grossman
University of Montana and University College London
CONTENTS
0 REVIEW OF SOME TOPICS
IN ALGEBRA 1
0 1 Review of Real Numbers and Absolute
Value 1
0 2 The Cartesian Plane 10
0 3 Lines 16
0 4 Functions and Their Graphs 23
0 5 Shifting the Graphs of Function 38
1 LIMITS AND DERIVATIVES 49
1 1 Introduction and Some History 49
1 2 The Calculation of Limits 53
1 3 Some Limit Theorems 69
1 4 Infinite Limits and Limits at Infinity 74
1 5 Tangent Lines and Derivatives 83
1 6 The Derivative as a Rate of Change 97
1 7 Continuity 112
1 8 The Theory of Limits (Optional) 124
Problems Chapter 1 Review 131
Computer Exercises 132
2 MORE ABOUT DERIVATIVES 134
2 1 Some Differentiation Formulas 134
2 2 The Product and Quotient Rules 139
2 3 The Derivative of Composite Functions:
The Chain Rule 146
2 4 The Derivative of a Power Function 155
2 5 The Derivatives of the Trigonometric
Functions 161
2 6 Implicit Differentiation 168
2 7 Higher-Order Derivatives 174
Problems Chapter 2 Review 178
Computer Exercises 179
3 APPLICATIONS OF THE
DERIVATIVE 180
3 1 Related Rates of Change 180
3 2 Elementary Curve Sketching I: Increasing and
Decreasing Functions and the First-Derivative
Test 187
3 3 Elementary Curve Sketching II: Concavity
and the Second-Derivative Test 197
3 4 Elementary Curve Sketching III:
Asymptotes 205
3 5 Applications of Maxima and Minima 212
3 6 Newton s Method for Solving Equations 228
3 7 The Mean-Value Theorem 239
3 8 An Application of the Mean-Value Theorem:
The Linearization of a Function 248
3 9 Newton s Method and Chaos (Optional) 255
Problems Chapter 3 Review 261
Computer Exercises 263
4 THE INTEGRAL 265
4 1 Introduction 265
4 2 Antiderivatives 267
4 3 The X Notation 276
4 4 Approximations to Area 279
4 5 The Definite Integral 293
4 6 The Fundamental Theorem of Calculus 309
4 7 Integration by Substitution and
Differentials 320
xvfll
CONTENTS
4 8 Additional Integration Theory (Optional)
Problems Chapter 4 Review 332
Computer Exercises 333
5 APPLICATIONS OF THE DEFINITE
INTEGRAL 334
5 1 The Area Between Two Curves 334
5 2 Volumes 340
5 3 Arc Length 350
5 4 Work, Power, and Energy 356
5 5 Center of Mass and the First Moment 366
5 6 The Centroid of a Plane Region 369
5 7 Fluid Pressure (Optional) 377
Problems Chapter 5 Review 383
6 TRANSCENDENTAL FUNCTIONS AND
THEIR INVERSES 385
6 1 Inverse Functions 385
6 2 Review of Exponential and Logarithmic
Functions 396
6 3 The Natural Logarithm Function 408
6 4 The Exponential Function ex 419
6 5 The Functions ax and log/ 432
6 6 Differential Equations of Exponential
Growth and Decay 439
6 7 Integration of Trigonometric Functions 452
6 8 The Inverse Trigonometric Functions 456
6 9 The Hyperbolic Functions 466
6 10 The Inverse Hyperbolic Functions
(Optional) 471
Problems Chapter 6 Review 475
Computer Exercises 476
7 TECHNIQUES OF INTEGRATION 477
7 1 Review of the Basic Formulas of Integration
7 2 Integration by Parts 479
7 3 Integrals of Certain Trigonometric Functions
7 4 Trigonometric Substitutions 492
7 5 Other Substitutions (Optional) 503
7 6 The Integration of Rational Functions I:
Linear and Quadratic Denominators 506
7 7 The Integration of Rational Functions II:
The Method of Partial Functions 511
7 8 Using the Integral Tables 519
7 9 Numerical Integration 522
Problems Chapter 7 Review 535
Computer Exercises 537
8 CONIC SECTIONS AND POLAR
COORDINATES 539
8 1 The Ellipse and Translation of Axes 540
8 2 The Parabola 550
8 3 The Hyperbola 560
8 4 Second-Degree Equations and Rotation of
Axes 570
8 5 The Polar-Coordinate System 576
8 6 Graphing in Polar Coordinates 581
8 7 Areas in Polar Coordinates 590
Problems Chapter 8 Review 593
Computer Exercises 594
9 INDETERMINATE FORMS, IMPROPER
INTEGRALS, AND TAYLOR S
THEOREM 595
9 1 The Indeterminate Form 0/0 and L Hopital s
Rule 595
9 2 Other Indeterminate Forms 602
9 3 Improper Integrals 609
9 4 Taylor s Theorem and Taylor Polynomials
9 5 Approximation Using Taylor Polynomials
Problems Chapter 9 Review 634
Computer Exercises 636
CONTENTS
10 SEQUENCES AND SERIES 637
10 1 Sequences of Real Numbers 637
10 2 Bounded and Monotonic Sequences 645
10 3 Geometric Series 653
10 4 Infinite Series 658
10 5 Series with Nonnegative Terms I: Two
Comparison Tests and the Integral Test
10 6 Series with Nonnegative Terms II: The
Ratio and Root Tests 676
10 7 Absolute and Conditional Convergence:
Alternating Series 681
10 8 Power Series 691
10 9 Differentiation and Integration of Power
Series 697
10 10 Taylor and Maclaurin Series 705
Problems Chapter 10 Review 716
Computer Exercises 717
11 VECTORS IN THE PLANE AND
IN SPACE 719
11 1 Vectors and Vector Operations 719
11 2 The Dot Product 729
11 3 The Rectangular Coordinate System in
Space 738
11 4 Vectors in IR3 __743
11 5 Lines in R3 750
11 6 The Cross Product of Two Vectors 757
11 7 Planes 767
11 8 Quadric Series 774
11 9 Cylindrical and Spherical Coordinates 781
Problems Chapter 11 Review 786
12 VECTOR FUNCTIONS, VECTOR
DIFFERENTIATION, AND PARAMETRIC
EQUATIONS 790
12 1 Vector Functions and Parametric Equations
12 2 The Equation of the Tangent Line to a
Plane Curve and Smoothness 795
12 3 The Differentiation and Integration of a
Vector Function 799
12 4 Some Differentiation Formulas 806
12 5 Arc Length Revisited 811
12 6 Curvature and the Acceleration Vector
(Optional) 819
Problems Chapter 12 Review 830
Computer Exercises 831
13 DIFFERENTIATION OF FUNCTIONS OF
TWO AND THREE VARIABLES 832
13 1 Functions of Two and Three Variables 833
13 2 Limits and Continuity 842
13 3 Partial Derivatives 852
13 4 Higher-Order Partial Derivatives 859
13 5 Differentiability and the Gradient 865
13 6 The Chain Rule 875
13 7 Tangent Planes, Normal Lines, and
Gradients 881
13 8 Directional Derivatives and the Gradient
13 9 The Total Differential and
Approximation 892
13 10 Maxima and Minima for a Function of
Two Variables 894
13 11 Constrained Maxima and Minima-
Lagrange Multipliers 903
13 12 Newton s Method for Functions of Two
Variables (Optional) 912
Problems Chapter 13 Review 917
Computer Exercises 919
14 MULTIPLE INTEGRATION 920
14 1 Volume Under a Surface and the Double
Integral 920
14 2 The Calculation of Double Integrals 928
14 3 Density, Mass, and Center of Mass
(Optional) 940
14 4 Double Integrals in Polar Coordinates 945
14 5 The Triple Integral 950
XX
CONTENTS
14 6 The Triple Integral in Cylindrical and
Spherical Coordinates 957
Problems Chapter 14 Review 962
Computer Exercises 963
15 INTRODUCTION TO VECTOR
ANALYSIS 964
15 1 Vector Fields 964
15 2 Work and Line Integrals 969
15 3 Exact Vector Fields and Independence of
Path 975
15 4 Green s Theorem in the Plane 984
15 5 The Parametric Representation of a Surface
and Surface Area 989
15 6 Surface Integrals 1001
15 7 Divergence and Curl 1009
15 8 Stokes s Theorem 1014
15 9 The Divergence Theorem 1020
15 10 Changing Variables in Multiple Integrals
and the Jacobian 1023
Problems Chapter 15 Review 1030
16 ORDINARY DIFFERENTIAL
EQUATIONS 1033
16 1 Introduction 1033
16 2 First-Order Differential Equations:
Separation of Variables 1033
16 3 First-Order Linear Differential Equations
16 4 Second-Order Linear, Homogeneous
Differential Equations with Constant
Coefficients 1050
16 5 Second-Order Nonhomogeneous Differential
Equations with Constant Coefficients: The
Method of Undetermined Coefficients 1057
16 6 Vibratory Motion (Optional) 1064
16 7 Numerical Solutions of Differential
Equations: Euler s Method 1071
Problems Chapter 16 Review 1076
APPENDICES:
A1 Review of Trigonometry A-l
A11 Angles and Radian Measure A-l
A12 The Trigonometric Functions and Basic
Identities A-3
A13 Other Trigonometric Functions A-7
A14 Triangles A-9
A2 Mathematical Induction A-12
A3 The Proofs of Some Theorems on Limits,
Continuity, and Differentiation A-16
A4 Determinants A-24
A5 Complex Numbers A-31
A6 Graphing Using a Calculator A-37
Table of Integrals A-64
Answers to Odd-Numbered Problems and
Review Exercises A-72
Credits A-154
Index 1 1
|
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| author | Grossman, Stanley I. |
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 5. ed. |
| format | Book |
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| spelling | Grossman, Stanley I. Verfasser aut Calculus 5. ed. Fort Worth [u.a.] Saunders College Publ. 1992 Getr. Zählung graph.Darst. txt rdacontent n rdamedia nc rdacarrier Kalkulus Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007752434&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grossman, Stanley I. Calculus Kalkulus Calculus Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 |
| title | Calculus |
| title_auth | Calculus |
| title_exact_search | Calculus |
| title_full | Calculus |
| title_fullStr | Calculus |
| title_full_unstemmed | Calculus |
| title_short | Calculus |
| title_sort | calculus |
| topic | Kalkulus Calculus Analysis (DE-588)4001865-9 gnd |
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