A Course of Mathematics for Engineers and Scientists

A Course of Mathematics for Engineers and Scientists

Volume 1

1st Edition - January 1, 1961

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  • Authors: Brian H. Chirgwin, Charles Plumpton
  • eBook ISBN: 9781483184173

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Description

A Course of Mathematics for Engineers and Scientists, Volume 1 studies the various concepts in pure and applied mathematics, specifically the technique and applications of differentiation and integration of one variable, geometry of two dimensions, and complex numbers. The book is divided into seven chapters, wherein the first of which presents the introductory concepts, such as the functional notation and fundamental definitions; the roots of equations; and limits and continuity. The text then tackles the techniques and applications of differentiation and integration. Geometry of two dimensions and complex numbers are also encompassed in the book. The text will be very invaluable to students of pure and applied mathematics and engineering, as well as those mathematicians and engineers who need a refresher on the topic.

Table of Contents


  • Chapter I. Introductory Concepts

    Functional Notation and Fundamental Definitions

    The Roots of Equations

    Elementary Two-Dimensional Coordinate Geometry

    Limits and Continuity

    Orders of Magnitude

    Chapter II. The Technique of Differentiation

    Differentiation from First Principles

    The Rules of Differentiation

    Repeated Differentiation

    Exponentials, Logarithms and Hyperbolic Functions

    Inverse Functions

    Differentiation of Equations

    Leibniz's Theorem on Repeated Differentiations

    Elementary Partial Differentiation

    Differentials

    Chapter III. The Technique of Integration

    Definitions and Standard Forms

    The Definite Integral as the Limit of a Sum

    Elementary Rules and Examples

    Integration by Substitution

    Integration by Parts

    Partial Fractions

    Integration of Rational Functions

    Miscellaneous Methods

    Reduction Formula

    Chapter IV. Geometry of Two Dimensions

    Introduction

    Gradient, Tangent and Normal

    Points of Inflexion

    The Arc Length of a Curve

    Curvature

    Envelopes

    The Loaded Cable

    Polar Coordinates

    Curve Sketching

    Translation and Rotation of Axes

    The Area of a Triangle

    The General Equation of the Second Degree

    The Properties of the Ellipse

    The Properties of the Hyperbola

    The Properties of the Parabola

    The Polar Equation of a Conic

    Chapter V. Applications of Differentiation

    Convergence of Series

    Inequalities

    The Mean Value Theorem and Linear Approximations

    Taylor's and Maclaurin's Theorems

    Expansions in Power Series

    Maxima and Minima

    Small Increments and Proportional Errors

    Approximate Solution of Equations

    Kinematics

    Chapter VI. Applications of Integration

    Introduction-The Area Bounded by a Plane Curve

    Volumes and Surfaces of Revolution

    Polar Coordinates

    First Moments

    The Theorems of Pappus

    Mean Values-Root Mean Square

    Second Moments-Moments of Inertia

    Applications to Hydrostatics

    Numerical Integration

    Chapter VII. Complex Numbers

    Introduction-The Argand Diagram

    De Moivre's Theorem

    Multiplication and Division on the Argand Diagram

    The Roots of Complex Numbers

    Trigonometric Expansions

    Functions of x + iy

    Answers to Exercises

    Index


Product details

  • No. of pages: 334
  • Language: English
  • Copyright: © Pergamon 1961
  • Published: January 1, 1961
  • Imprint: Pergamon
  • eBook ISBN: 9781483184173

About the Authors

Brian H. Chirgwin

Charles Plumpton

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