Much Ado About Calculus: A Modern Treatment with Applications Prepared for Use with the ComputerThe calculus has been one ofthe areas of mathematics with a large number of significant applications since its formal development in the seventeenth century. With the recent development of the digital computer, the range of applications of mathematics, including the calculus, has increased greatly and now includes many disciplines that were formerly thought to be non quantitative. Some of the more traditional applications have been altered, by the presence of a computer, to an extent such that many problems hitherto felt to be intractable are now solvable. This book has been written as a reaction to events that have altered the applications of the calculus. The use of the computer is made possible at an early point, although the extent to which the computer is used in the course is subject to the decision of the instructor. Some less traditional applications are included in order to provide some insight into the breadth of problems that are now susceptible to mathematical solution. The Stieltjes integral is introduced to provide for easier transition from the stated problem to its mathematical formulation, and also to permit the use of functions like step functions in later courses (such as statistics) with relative ease. The course is designed to include all the background material ordinarily associa ted with the first course in the calculus, but it is also designed with the user in mind. |
Contents
| 1 | |
| 2 | |
Integration | 85 |
Chapter III | 137 |
More About Integrals | 146 |
Chapter IV | 205 |
Chapter V | 245 |
Chapter II | 279 |
Chapter IX | 618 |
Infinite Series | 632 |
Chapter XII | 638 |
Appendix | 654 |
More Complicated Curves | 675 |
Rotation of Axes | 690 |
Appendix E BASIC Language | 728 |
Arithmetic Statements | 729 |
Chapter III | 325 |
Chapter VI | 330 |
Limits | 358 |
Chapter VIII | 394 |
Chapter VII | 399 |
Chapter VIII | 443 |
Chapter IX | 494 |
Chapter X | 563 |
Chapter XI | 601 |
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Much Ado About Calculus: A Modern Treatment with Applications Prepared for ... Robert Wilson No preview available - 2012 |
Common terms and phrases
absolute value algebra approximation Argand diagram chain rule complex numbers computation consider constant continuous function convergence Corollary correct cos² curve definition denominator derivative determine differential quotient domain dx² equation error evaluation set EXAMPLE Exercise exists expression fact Figure Find the area find the value formula give given graph hence identity function increasing indicated integral integrand interval inverse function involved l'Hôpital's rule limit lower bound lower sums mathematical induction mean value theorem method monotonic negative Newton's method notation Note obtain polynomial possible problem proof radius rate of change rational number real numbers refinement regular partition relation result Richardson extrapolation sec² Show Simpson's rule sin² Sketch slope Solution subinterval tangent tion trapezoidal rule trigonometric trigonometric functions upper and lower upper bound upper sum variable write x-axis x₁