Difference between revisions of "Calculus (Book)"

Jump to navigation Jump to search

Calculus (Book) (view source)

Revision as of 16:11, 20 September 2021

2,694 bytes added ,  16:11, 20 September 2021
no edit summary
Line 159: Line 159:
| 1.27 || Proofs of the basic properties of the integral || 84
| 1.27 || Proofs of the basic properties of the integral || 84
|-
|-
! colspan="3" | PART II: INTUITIVE GEOMETRY
! colspan="3" | 2. SOME APPLICATIONS OF INTEGRATION
|-
|-
! colspan="3" | Chapter 5: Distance and Angles
| 2.1 || Introduction || 88
|-
|-
| 1 || Distance || 107
| 2.2 || The area of a region between two graphs expressed as an integral || 88
|-
|-
| 2 || Angles || 110
| 2.3 || Worked examples || 89
|-
|-
| 3 || The Pythagoras theorem || 120
| 2.4 || Exercises || 94
|-
|-
! colspan="3" | Chapter 6: Isometries
| 2.5 || The trigonometric functions || 94
|-
|-
| 1 || Some standard mappings of the plane || 133
| 2.6 || Integration formulas for the sine and cosine || 94
|-
|-
| 2 || Isometries || 143
| 2.7 || A geometric description of the sine and cosine functions || 94
|-
|-
| 3 || Composition of isometries || 150
| 2.8 || Exercises || 94
|-
|-
| 4 || Inverse of isometries || 155
| 2.9 || Polar coordinates || 94
|-
|-
| 5 || Characterization of isometries || 163
| 2.10 || The integral for area in polar coordinates || 94
|-
|-
| 6 || Congruences || 166
| 2.11 || Exercises || 94
|-
|-
! colspan="3" | Chapter 7: Area and Applications
| 2.12 || Application of integration to the calculation of volume || 94
|-
|-
| 1 || Area of a disc of radius ''r'' || 173
| 2.13 || Exercises || 94
|-
|-
| 2 || Circumference of a circle of radius ''r'' || 180
| 2.14 || Application of integration to the calculation of work || 94
|-
|-
! colspan="3" | PART III: COORDINATE GEOMETRY
| 2.15 || Exercises || 94
|-
|-
! colspan="3" | Chapter 8: Coordinates and Geometry
| 2.16 || Average value of a function || 94
|-
| 2.17 || Exercises || 94
|-
| 2.18 || The integral as a function of the upper limit. Indefinite integrals || 94
|-
| 2.19 || Exercises || 94
|-
! colspan="3" | 3. CONTINUOUS FUNCTIONS
|-
| 3.1 || Informal description of continuity || 126
|-
| 3.2 || The definition of the limit of a function || 127
|-
| 3.3 || The definition of continuity of a function || 130
|-
| 3.4 || The basic limit theorems. More examples of continuous functions || 131
|-
| 3.5 || Proofs of the basic limit theorems || 135
|-
| 3.6 || Exercises || 138
|-
| 3.7 || Composite functions and continuity || 140
|-
| 3.8 || Exercises || 142
|-
| 3.9 || Bolzano's theorem for continuous functions || 142
|-
| 3.10 || The intermediate-value theorem for continuous functions || 144
|-
| 3.11 || Exercises || 145
|-
| 3.12 || The process of inversion || 146
|-
| 3.13 || Properties of functions preserved by inversion || 147
|-
| 3.14 || Inverses of piecewise monotonic functions || 148
|-
| 3.15 || Exercises || 149
|-
| 3.16 || The extreme-value theorem for continuous functions || 150
|-
| 3.17 || The small-span theorem for continuous functions (uniform continuity) || 152
|-
| 3.18 || The integrability theorem for continuous functions || 152
|-
| 3.19 || Mean-value theorems for integrals of continuous functions || 154
|-
| 3.20 || Exercises || 155
|-
! colspan="3" | 4. DIFFERENTIAL CALCULUS
|-
| 4.1 || Historical introduction || 156
|-
| 4.2 || A problem involving velocity || 157
|-
| 4.3 || The derivative of a function || 159
|-
| 4.4 || Examples of derivatives || 161
|-
| 4.5 || The algebra of derivatives || 164
|-
| 4.6 || Exercises || 167
|-
| 4.7 || Geometric interpretation of the derivative as a slope || 169
|-
| 4.8 || Other notations for derivatives || 171
|-
| 4.9 || Exercises || 173
|-
| 4.10 || The chain rule for differentiating composite functions || 174
|-
| 4.11 || Applications of the chain rule. Related rates and implicit differentiation || 176
|-
| 4.12 || Exercises || 179
|-
| 4.13 || Applications of the differentiation to extreme values of cuntions|| 181
|-
| 4.14 || The mean-value theorem for derivatives || 183
|-
| 4.15 || Exercises || 186
|-
| 4.16 || Applications of the mean-value theorem to geometric properties of functions || 187
|-
| 4.17 || Second-derivative test for extrema || 188
|-
| 4.18 || Curve sketching || 189
|-
| 4.19 || Exercises || 191
|-
| 4.20 || Worked examples of extremum problems || 191
|-
| 4.21 || Exercises || 194
|-
| 4.22 || Partial derivatives || 196
|-
| 4.23 || Exercises || 201
|-
! colspan="3" | 5. THE RELATION BETWEEN INTEGRATION AND DIFFERENTIATION
|-
|-
| 1 || Coordinate systems || 191
| 1 || Coordinate systems || 191
Retrieved from ‘https://old.theportal.wiki/wiki/Special:MobileDiff/12258’

Navigation menu