An Elementary Treatise on the Calculus: With Illustrations from Geometry, Mechanics and Physics (Classic Reprint) Book

THE rapid growth in recent years of all branches of applied science and the consequent increasing claims on the time of students have given rise in various quarters to the demand for a change in the character of mathematical text-books. To meet this demand several works have been published, addressed to particular classes of students and designed to supply them with the special kind and quantity of mathematics they are supposed to need. With many of the arguments urged in favour of the change I am in hearty sympathy, but it is as true now as it was of old that there is no royal road to mathematics, and that no really useful knowledge can be gained except by strenuous effort. It is sometimes alleged that a thorough knowledge of the derivatives and integrals of the simpler powers, of the exponential and the logarithmic functions, and perhaps of the sine and the cosine, is quite sufficient preparation in the Calculus for the engineer. This contentionTable of Contents CHAPTER 1; COORDINATES FUNCTIONS; · Directed Segments or Steps,; ~ Addition of Steps,; 3' Symmetric Steps and Subtraction of Steps,; i ~bscissa of a Point Fundamental Axiom,; 'J Measure of a Step,; 6 Axes of Coordinates Squared Paper,; 7 Distance between two Points,; 8 'Polar Coordinates,; 9 Variable Continuity,; 10 � · Geometrical Representatiou of Magnitudes,; 11 F~ction Dependent and Independent Variables,; 12 Notation for Functions, ; 13' Explicit end Implicit Functions,; 14 Multiplevalued and Inverse Functions,; Exercises I,; CHAPTER II; GRAPHS RATIONAL FUNCTIONS,; 15 Object of the Calculus Graphs,; 16 Grapb of x2, '; 17 Equation of a Curve Symmetry Turning Values,; 18 Graph of cx2,; "19 Scale Units,; 20 Coordinate Geometry,; Exercise" II, �; PAGE; 1; 2; 3; 4; 5; 6; 9; 10; 12; 13; 13; 16; 16; 17; 19; 20; _20; 23; 24; 26; 27; 29; xii AN ~LEMENTARY TREATISE ON THE CALCULus; ART l',OE; 21 The Linear Function Intercepts,; 22 Gradient, ; 23; 24; RaRead More