...I have assumed that the purpose of the
Differential Calculus is to inquire how natural phenomena
change from moment to moment. This change may be
uniform and simple (Chapter I.); or it may be associated
with certain so-called "singularities" (Chapter IlI.). The
Integral Calculus (Chapters IV. and VII.) attempts to deduce
the fundamental principle governing the whole course of
any natural process from the law regulating the momentary
states. Coordinate Geometry (Chapter II.) is concerned
with the study of natural processes by means of " pictures "
or geometrical figures. Infinite Series (Chapters V. and
VIII.) furnish approximate ideas about natural processes
when other attempts fail. From this, then, we proceed to
study the various methods - tools - to be employed in
Higher Mathematics.
This limitation of the scope of Higher Mathematics
enables us to dispense with many of the formal proofs of
rules and principles.
Author(s): J. W. Mellor
Edition: 4
Publisher: Longmans, Green & Co.
Year: 1922
Language: English
Pages: XX; 641
City: London
Title Page
Dedication
Preface to the Fourt and Second Edition
Preface to the First Edition
Contents
Introduction
Chapter I - The Differential Calculus
Chapter II - Coordinate or Analytical Geometry
Chapter III - Functions with Singular Properties
Chapter IV - The Integral Calculus
Chapter V - Infinite Series and Their Uses
Chapter VI - How to solve Numerical Equations
Chapter VII - How to solve Differential Equations
Chapter VIII - Fourier's Theorem
Chapter IX - Probability and the Theory of Errors
Chapter X - The Calculus of Variations
Chapter XI - Determinants
Appendix I - Collection of Formulae and Tables for Reference
Appendix II - Reference Tables
Index
