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. 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 enƯ 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 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
