Flanders / Price Calculus with Analytic Geometry

1. Auflage 2014
ISBN: 978-1-4832-6240-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 1054 Seiten, Web PDF

Calculus with Analytic Geometry presents the essentials of calculus with analytic geometry. The emphasis is on how to set up and solve calculus problems, that is, how to apply calculus. The initial approach to each topic is intuitive, numerical, and motivated by examples, with theory kept to a bare minimum. Later, after much experience in the use of the topic, an appropriate amount of theory is presented. Comprised of 18 chapters, this book begins with a review of some basic pre-calculus algebra and analytic geometry, paying particular attention to functions and graphs. The reader is then introduced to derivatives and applications of differentiation; exponential and trigonometric functions; and techniques and applications of integration. Subsequent chapters deal with inverse functions, plane analytic geometry, and approximation as well as convergence, and power series. In addition, the book considers space geometry and vectors; vector functions and curves; higher partials and applications; and double and multiple integrals. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

Autoren/Hrsg.

Flanders, Harley

Price, Justin J.

Inhaltsverzeichnis

1;Front Cover;1
2;Calculus with Analytic Geometry;4
3;Copyright Page;5
4;Table of Contents;10
5;Preface;6
6;Chapter 1. Functions and Graphs;16
6.1;1. INTRODUCTION;16
6.2;2. REAL NUMBERS;17
6.3;3. COORDINATES;22
6.4;4. FUNCTIONS AND GRAPHS;26
6.5;5. LINEAR FUNCTIONS;31
6.6;6. QUADRATIC FUNCTIONS;36
6.7;7. MORE ON GRAPHING;41
6.8;8. POLYNOMIALS AND RATIONAL FUNCTIONS;50
6.9;9. DISTANCE FORMULA AND APPLICATIONS;58
6.10;10. TANGENTS;64
6.11;11. MISCELLANEOUS EXERCISES;68
7;Chapter 2. Derivatives;70
7.1;1. THE SLOPE PROBLEM;70
7.2;2. LIMITS;74
7.3;3. THE DERIVATIVE;78
7.4;4. SUMS AND PRODUCTS;83
7.5;5. QUOTIENTS AND SQUARE ROOTS;88
7.6;6. THE CHAIN RULE;92
7.7;7. THE TANGENT LINE;97
7.8;8. ANTIDERIVATIVES;100
7.9;9. HIGHER DERIVATIVES;104
7.10;10. LIMITS AND CONTINUITY;109
7.11;11. DIFFERENTIABLE FUNCTIONS;117
7.12;12. MISCELLANEOUS EXERCISES;120
8;Chapter 3. Applications of Differentiation;122
8.1;1. CURVE SKETCHING;122
8.2;2. RECTILINEAR MOTION;128
8.3;3. RELATED RATES;133
8.4;4. MAXIMA AND MINIMA;138
8.5;5. APPLICATIONS OF MAX AND MIN;143
8.6;6. SECOND DERIVATIVE TEST;153
8.7;7. ON PROBLEM SOLVING;159
8.8;8. EXTREMA AND CONVEXITY;161
8.9;9. MISCELLANEOUS EXERCISES;168
9;Chapter 4. Exponential and Trigonometric Functions;170
9.1;1. THE EXPONENTIAL FUNCTION;170
9.2;2. PROPERTIES OF EXPONENTIAL FUNCTIONS;174
9.3;3. APPROXIMATION AND GROWTH RATES;180
9.4;4. APPLICATIONS;186
9.5;5. TRIGONOMETRIC FUNCTIONS;193
9.6;6. ADDITIONAL TRIGONOMETRIC FUNCTIONS;199
9.7;7. DERIVATIVES;204
9.8;8. APPLICATIONS;209
9.9;9. MISCELLANEOUS EXERCISES;216
10;Chapter 5. Integration;219
10.1;1. THE AREA PROBLEM;219
10.2;2. EXAMPLES OF INTEGRALS;221
10.3;3. THE DEFINITE INTEGRAL AND THE FUNDAMENTAL THEOREM;228
10.4;4. APPLICATIONS;238
10.5;5. APPROXIMATE INTEGRATION;244
10.6;6. INTEGRATION OF PRODUCTS;251
10.7;7. SYMMETRY;256
10.8;8. INEQUALITIES AND ESTIMATES;262
10.9;9. INSIGHTS INTO INTEGRATION;266
10.10;10. MISCELLANEOUS EXERCISES;275
11;Chapter 6. Applications of Integration;277
11.1;1. INTRODUCTION;277
11.2;2. AREA;279
11.3;3. VOLUME;284
11.4;4. WORK;291
11.5;5. FLUID PRESSURE;296
11.6;6. MISCELLANEOUS APPLICATIONS;300
11.7;7. MISCELLANEOUS EXERCISES;311
12;Chapter 7. Inverse Functions;314
12.1;1 . INVERSE FUNCTIONS AND THEIR DERIVATIVES;314
12.2;2. THE LOGARITHM FUNCTION;322
12.3;3. FURTHER PROPERTIES OF LOGARITHMS;330
12.4;5. INVERSE TRIGONOMETRIC FUNCTIONS;342
12.5;6. DERIVATIVES AND APPLICATIONS;348
12.6;7. HYPERBOLIC FUNCTIONS;353
12.7;8. BASIC PROPERTIES;361
12.8;9. MISCELLANEOUS EXERCISES;369
13;Chapter 8. Techniques of Integration;372
13.1;1. INDEFINITE INTEGRALS;372
13.2;2. SUBSTITUTIONS AND DIFFERENTIALS;374
13.3;3. OTHER SUBSTITUTIONS;379
13.4;4. USE OF IDENTITIES;382
13.5;5. PARTIAL FRACTIONS;387
13.6;6. TRIGONOMETRIC SUBSTITUTIONS;392
13.7;7. INTEGRATION BY PARTS;395
13.8;8. REDUCTION FORMULAS;400
13.9;9. INTEGRAL TABLES;403
13.10;10. MISCELLANEOUS EXERCISES;405
14;Chapter 9. Plane Analytic Geometry;407
14.1;1. TRANSLATION AND CIRCLES;407
14.2;2. LOCUS;415
14.3;3. PARABOLA AND ELLIPSE;419
14.4;4. HYPERBOLA;428
14.5;5. POLAR COORDINATES;434
14.6;6. POLAR GRAPHS;440
14.7;7. ROTATION OF AXES;446
14.8;8. CALCULUS APPLIED TO CONICS;453
14.9;9. MISCELLANEOUS EXERCISES;460
15;Chapter 10. Approximation;462
15.1;1. INTRODUCTION;462
15.2;2. FIRST AND SECOND DEGREE APPROXIMATIONS;463
15.3;3. TAYLOR APPROXIMATIONS;469
15.4;4. TAYLOR'S FORMULA;474
15.5;5. ROLLE'S THEOREM;481
15.6;6. MEAN VALUE THEOREMS AND LHOSPITAL'S RULE;486
15.7;7. INTERPOLATION;496
15.8;9. APPROXIMATE INTEGRATION;509
15.9;10. ROOT APPROXIMATION AND HILL CLIMBING;521
15.10;11. ITERATION AND NEWTON'S METHOD;526
15.11;12. MISCELLANEOUS EXERCISES;538
16;Chapter 11. Convergence;540
16.1;1. SEQUENCES AND LIMITS;540
16.2;2. PROPERTIES OF LIMITS;548
16.3;3. INFINITE SERIES;554
16.4;4. SERIES WITH POSITIVE TERMS;560
16.5;6. IMPROPER INTEGRALS;568
16.6;7. CONVERGENCE AND DIVERGENCE TESTS;574
16.7;8. RELATION BETWEEN INTEGRALS AND SERIES;581
16.8;9. OTHER IMPROPER INTEGRALS;585
16.9;10. MISCELLANEOUS EXERCISES;590
17;Chapter 12. Power Series;593
17.1;1. BASIC PROPERTIES;593
17.2;2. TAYLOR SERIES;599
17.3;3. EXPANSION OF FUNCTIONS;605
17.4;4. FURTHER TECHNIQUES;613
17.5;5. BINOMIAL SERIES;620
17.6;6. NUMERICAL APPLICATIONS;625
17.7;7. SEQUENCES AND SERIES OF FUNCTIONS;634
17.8;8. MISCELLANEOUS EXERCISES;641
18;Chapter 13. Space Geometry and Vectors;643
18.1;1. RECTANGULAR COORDINATES;643
18.2;2. VECTOR ALGEBRA;646
18.3;3. LENGTH AND INNER PRODUCT;650
18.4;4. LINES AND PLANES;657
18.5;5. LINEAR SYSTEMS;664
18.6;6. CROSS PRODUCT;672
18.7;7. APPLICATIONS OF THE CROSS PRODUCT;679
18.8;8. MISCELLANEOUS EXERCISES;688
19;Chapter 14. Vector Functions and Curves;690
19.1;1. DIFFERENTIATION;690
19.2;2. ARC LENGTH;695
19.3;3. PLANE CURVES;702
19.4;4. TANGENT, NORMAL AND CURVATURE;711
19.5;5. VELOCITY AND ACCELERATION;719
19.6;6. CURVES IN POLAR COORDINATES;724
19.7;7. MISCELLANEOUS EXERCISES;730
20;Chapter 15. Functions of Several Variables;733
20.1;1. FUNCTIONS AND GRAPHS;733
20.2;2. PARTIAL DERIVATIVES;741
20.3;3. GRADIENTS AND DIRECTIONAL DERIVATIVES;747
20.4;4. SURFACES;754
20.5;5. PARAMETRIC SURFACES AND SURFACE OF REVOLUTION;761
20.6;6. QUADRIC SURFACES;766
20.7;7. OPTIMIZATION;775
20.8;8. FURTHER OPTIMIZATION PROBLEMS;781
20.9;9. IMPLICIT FUNCTIONS;789
20.10;10. DIFFERENTIALS AND APPROXIMATION;795
20.11;11. DIFFERENTIABLE FUNCTIONS;801
20.12;12. MISCELLANEOUS EXERCISES;806
21;Chapter 16. Higher Partials and Applications;809
21.1;1. MIXED PARTIALS;809
21.2;2. TAYLOR APPROXIMATION;815
21.3;3. STABILITY;819
21.4;4. CONSTRAINED OPTIMIZATION;825
21.5;5. FURTHER CONSTRAINT PROBLEMS;831
21.6;6. ADDITIONAL TOPICS;837
21.7;7. MISCELLANEOUS EXERCISES;843
22;Chapter 17. Double Integrals;846
22.1;1. INTRODUCTION;846
22.2;2. RECTANGULAR DOMAINS;851
22.3;3. DOMAIN BETWEEN GRAPHS;859
22.4;4. ARBITRARY DOMAINS;868
22.5;5. POLAR COORDINATES;873
22.6;6. APPLICATIONS;883
22.7;7. PHYSICAL APPLICATIONS;889
22.8;8. APPROXIMATE INTEGRATION;898
22.9;9. MISCELLANEOUS EXERCISES;903
23;Chapter 18. Multiple Integrals;906
23.1;1. TRIPLE INTEGRALS;906
23.2;2. CYLINDRICAL COORDINATES;914
23.3;3. SPHERICAL COORDINATES;920
23.4;4. CENTER OF GRAVITY;930
23.5;5. MOMENTS OF INERTIA;934
23.6;6. LINE INTEGRALS;939
23.7;7. GREEN'S THEOREM;946
23.8;8. SURFACE INTEGRALS;952
23.9;9. MISCELLANEOUS EXERCISES;964
24;Numerical Tables;968
24.1;Three-Place Mantissas for Common Logarithms;969
24.2;Exponential Functions;971
24.3;Natural Logarithms;973
24.4;Trigonometric Functions of Degrees;974
24.5;Trigonometric Functions of Radians;975
24.6;Inverse Trigonometric Functions to Radians;976
24.7;Trigonometric Functions of a = p · x Radians;977
25;Answers to Odd-Numbered Exercises;978
26;Index;1050