## Differential and Integral Calculus for Technical Schools and Colleges |

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### Contents

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### Common terms and phrases

abscissa algebraic angle approaches zero arbitrary constants axis becomes indefinitely large becomes indefinitely small called center of mass changes sign chord circle circular circular sector continuous function coordinates corresponding cos2 curvature cycloid decreases Denoting determine differential equation distance dx dx dx dx dx dx dy dx Writing dxdy dy _ dy dx dz dx ellipse Example exponential function factor Find area bounded Find the area Find the center Find the length Find the volume finite formula fraction Hence higher order hypothesis inertia infinitesimal intersection lamina limit Ax linear logarithms maximum minimum ordinate parabola y2 parallelopiped partial differential partial differential equation partial fractions power series PROBLEMS quantity radius rate of change ratio region of convergence revolution solution Solve Substituting subtangent tion true value uniformly convergent variable velocity whence X-axis

### Popular passages

Page 250 - Elementary Trigonometry" etc Edited and Arranged for American Schools By CHARLOTTE ANGAS SCOTT, D.SC., Head of Math. Dept., Bryn Ma-wr College, Pa. 1 6mo. Cloth. 75 cents. " Evidently the work of a thoroughly; good teacher. The elementary truth, that arithmetic is common sense, is the principle which pervades the whole book, and no process, however simple, is deemed unworthy of clear explanation. Where it seems advantageous, a rule is given after the explanation. . . . Mr. Lock's admirable Trigonometry...

Page 205 - ... equation. The order of a differential equation is the order of the highest derivative which occurs.

Page 70 - The stiffness of a rectangular beam varies as the product of the breadth and the cube of the depth. Find the dimensions of the stiffest rectangular beam that can be cut from a circular cylindrical log of radius a in.

Page 69 - The strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from a circular cylindrical log of radius r.

Page 250 - SUITABLE FOR USE IN PREPARATORY SCHOOLS. SELECTED FROM THE LISTS OF THE MACMILLAN COMPANY, Publishers. ARITHMETIC FOR SCHOOLS. By JB LOCK, Author of " Trigonometry for Beginners" "Elementary Trigonometry" etc Edited and Arranged for American Schools By CHARLOTTE ANGAS SCOTT, D.SC., Head of Math.

Page 247 - ... Institute, Chicago, 111.: — We have used the English Edition for the past two years in our Scientific Academy. The new edition is superior to the old, and we shall certainly use it. In my opinion it is the best of all the elementary algebras. AMERICAN EDITION OF ALGEBRA FOR BEGINNERS. By HS HALL, MA, and SR KNIGHT. REVISED BY FRANK L. SEVENOAK, AM, Assistant Principal of the Academic Department, Stevens Institute of Technology. 16mo. Cloth. 6O cents. An edition of this book containing additional...

Page 69 - A person being in a boat 3 miles from the nearest point of the beach, wishes to reach in the shortest time a place 5 miles from that point along the shore : supposing he can walk 5 miles an hour, but row only at the rate of 4 miles an hour, required the place where he must land.

Page 247 - By HS HALL, MA, and SR KNIGHT, BA Revised and Enlarged for the Use of American Schools and Colleges By FRANK L. SEVENOAK, AM, Assistant Principal of the Academic Department, Stevens Institute of Technology. THE MACMILLAN COMPANY, HENRY DALLAS THOMPSON, D.Sc., Ph.D., Professor of Mathematics in Princeton University.

Page 154 - The ordinary notation of the differential calculus has been retained, because it answers to the system of the infinitely small, adopted in this treatise. When one has well comprehended the spirit of this system and has convinced himself of the exactitude of its results by the geometrical method of prime and ultimate ratios, or by the analytical method of derived functions, one may employ the infinitely little as an instrument that is safe and convenient for abbreviating and simplifying demonstrations....

Page 165 - ... is called the moment of inertia of the body with respect to the fixed line or axis.