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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

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1st Edition - January 1, 1961

Authors: Brian H. Chirgwin, Charles Plumpton

Language: EnglisheBook ISBN:

9 7 8 - 1 - 4 8 3 1 - 8 4 1 7 - 3

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… Read more

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Immediately download your ebook while waiting for your print delivery. No promo code is needed.

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.

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

- No. of pages: 334
- Language: English
- Edition: 1
- Published: January 1, 1961
- Imprint: Pergamon
- eBook ISBN: 9781483184173

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