Integral and Differential Calculus: An Intuitive Approach

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Preface......Page 6
Acknowledgements......Page 10
Contents......Page 12
1. Representation of Functions by Tables,......Page 13
2. Representation of Functions by Graphs,......Page 16
3. Mathematical Representation of Functions,......Page 25
4. Straight Line,......Page 31
5. The General Line Equation,......Page 35
6. Intersection of Two Lines,......Page 39
7. Distance between Two Points,......Page 43
8. The Parabola,......Page 47
9. The Quadratic Equation,......Page 51
10. Tangent to a Parabola,......Page 57
11. Interval Notation,......Page 63
12. More Examples of Functions-Continuity,......Page 65
13. Uniform Continuity,......Page 72
Supplementary Problems I,......Page 81
1. Area of Rectangles,......Page 85
2. Area of Triangles,......Page 90
3. Series and Sequences,......Page 92
4. Manipulations with Limits,......Page 102
5. The Area of a Circle,......Page 109
6. Circumference of a Circle,......Page 116
7. Radian Measure,......Page 119
8. Area under a Curve,......Page 122
9. The Definite Integral,......Page 130
10. The Trapezoidal Rule,......Page 136
11. Integration by a Limit of a Sum Process,......Page 142
12. Finite Sums,......Page 147
13. AREA UNDER A PARABOLIC ARC......Page 149
14. SIMPSON'S RULE......Page 154
15. DEFINITE INTEGRAL WITH A VARIABLE UPPER LIMIT......Page 159
Supplementary Problems II......Page 166
1. THE DERIVATIVE......Page 173
2. DIFFERENTIATION RULES......Page 179
3. DIFFERENTIATION OF SOME SIMPLE FUNCTIONS......Page 184
4. THE CHAIN-RULE......Page 188
5. INTEGRATION BY ANTIDIFFERENTIATION......Page 192
6. THE INVERTED CHAIN-RULE......Page 197
7. THE DIFFERENTIAL......Page 199
8. NEWTON'S METHOD......Page 203
9. MAXIMA AND MINIMA......Page 207
10. MOTION......Page 216
11. FREELY FALLING BODIES......Page 225
12. SNELL'S LAW OF REFRACTION......Page 234
13. THE CYCLOID......Page 239
14. THE METHOD OF LEAST SQUARES......Page 245
15. MINIMUM OF FUNCTIONS OF TWO VARIABLES......Page 250
16. THE METHOD OF LEAST SQUARES (continued)......Page 253
Supplementary Problems III......Page 258
1. VOLUME OF A PRISM......Page 265
2. VOLUME OF A RIGHT CIRCULAR CYLINDER......Page 267
3. VOLUME OF A RIGHT CIRCULAR CONE......Page 270
4. THE LAW OF THE LEVER......Page 272
5. MASS CENTER OF REGIONS AND SOLIDS......Page 277
6. THE ARCHIMEDEAN SCALE......Page 283
7. VOLUME OF A SPHERE BY INTEGRATION......Page 289
8. VOLUME OF A TORUS......Page 293
9. SIMPSON'S RULE AND WINE BARRELS......Page 297
Supplementary Problems IV......Page 300
Al. POLYNOMIALS......Page 303
All. A UNIFORMLY CONTINUOUS FUNCTION THATDEFIES GRAPHICAL REPRESENTATION......Page 306
1. The Sine Function......Page 311
2. Some Values of the Sine Function......Page 313
3. Other Circular Functions......Page 317
4. Some Identity Relations Between Circular Functions......Page 321
5. Graphs of the Circular Functions*......Page 325
Supplementary Problems AIII......Page 329
ANSWERS TO EVENNUMBERED PROBLEMS......Page 331
Index......Page 337