Calculator Calculus

✍ Scribed by George McCarty (auth.)

• Publisher: Springer US
• Year: 1982
• Tongue: English
• Leaves: 270
• Edition: 1
• Category: Library

✦ Synopsis

How THIS BOOK DIFFERS This book is about the calculus. What distinguishes it, however, from other books is that it uses the pocket calculator to illustrate the theory. A computation that requires hours of labor when done by hand with tables is quite inappropriate as an example or exercise in a beginning calculus course. But that same computation can become a delicate illustration of the theory when the student does it in seconds on his calculator. t Furthermore, the student's own personal involvement and easy accomplishment give hi~ reassurance and en­ couragement. The machine is like a microscope, and its magnification is a hundred millionfold. We shall be interested in limits, and no stage of numerical approximation proves anything about the limit. However, the derivative of fex) = 67.SgX, for instance, acquires real meaning when a student first appreciates its values as numbers, as limits of 10 100 1000 t A quick example is 1.1 , 1.01 , 1.001 , •••• Another example is t = 0.1, 0.01, in the function e/3t+9-3)/t. ix difference quotients of numbers, rather than as values of a function that is itself the result of abstract manipulation.

✦ Table of Contents

Front Matter....Pages N1-xiv
Squares, Square Roots, and the Quadratic Formula....Pages 1-13
More Functions and Graphs....Pages 14-26
Limits and Continuity....Pages 27-36
Differentiation, Derivatives, and Differentials....Pages 37-54
Maxima, Minima, and the Mean Value Theorem....Pages 55-63
Trigonometric Functions....Pages 64-80
Definite Integrals....Pages 81-99
Logarithms and Exponentials....Pages 100-116
Volumes....Pages 117-129
Curves and Polar Coordinates....Pages 130-144
Sequences and Series....Pages 145-167
Power Series....Pages 168-183
Taylor Series....Pages 184-201
Differential Equations....Pages 202-219
Back Matter....Pages 220-256

✦ Subjects

Analysis; Science, general