Calculus: An Intuitive and Physical ApproachCourier Corporation, 1998/06/19 - 943 ページ Application-oriented introduction relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x, and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, numerous drills, illustrative examples. 1967 edition. Solution guide available upon request. |
目次
WHY CALCULUS? | 1 |
THE DERIVATIVE | 7 |
THE ANTIDERIVED FUNCTION OR THE INTEGRAL | 39 |
THE GEOMETRICAL SIGNIFICANCE OF THE DERIVATIVE | 75 |
THE DIFFERENTIATION AND INTEGRATION OF POWERS OF x | 99 |
SOME THEOREMS ON DIFFERENTIATION AND ANTIDIFFERENTIATION | 114 |
THE CHAIN RULE | 142 |
MAXIMA AND MINIMA | 197 |
FURTHER TECHNIQUES OF INTEGRATION | 404 |
SOME GEOMETRIC USES OF THE DEFINITE INTEGRAL | 430 |
SOME PHYSICAL APPLICATIONS OF THE DEFINITE INTEGRAL | 468 |
POLAR COORDINATES | 506 |
RECTANGULAR PARAMETRIC EQUATIONS AND CURVILINEAR MOTION | 541 |
POLAR PARAMETRIC EQUATIONS AND CURVILINEAR MOTION | 597 |
TAYLORS THEOREM AND INFINITE SERIES | 625 |
FUNCTIONS OF TWO OR MORE VARIABLES AND THEIR GEOMETRIC REPRESENTATION | 676 |
THE DEFINITE INTEGRAL | 229 |
THE TRIGONOMETRIC FUNCTIONS | 261 |
THE INVERSE TRIGONOMETRIC FUNCTIONS | 296 |
LOGARITHMIC AND EXPONENTIAL FUNCTIONS | 326 |
DIFFERENTIALS AND THE LAW OF THE MEAN | 380 |
PARTIAL DIFFERENTIATION | 721 |
MULTIPLE INTEGRALS | 769 |
AN INTRODUCTION TO DIFFERENTIAL EQUATIONS | 834 |
A RECONSIDERATION OF THE FOUNDATIONS | 852 |
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多く使われている語句
acceleration angle antiderivative antidifferentiation apply approximation arc length becomes infinite calculate chain rule Chapter circle constant converges cos² curve cycloid cylinder definite integral denote derived function determine differential direction directrix distance double integral dy dx dy/dx earth ellipse evaluate example EXERCISES Figure force formula ft/sec geometrical given graph gravity height Hence horizontal hyperbola initial velocity interval inverse function length Let us consider limit logarithm mass mathematical maxima and minima maximum motion negative object obtain parabola parametric equations particle perpendicular plane Polar axis polar coordinates positive problem quantity quotient radius rate of change represents result rotation Section semimajor axis sequence shell Show sin² slope sphere subinterval Suppose surface tangent theorem vector volume x-axis x₁ y-values y₁