A Course of Mathematics for Engineers and Scientists
Volume 1
- 1st Edition - September 19, 2014
- Latest edition
- Authors: Brian H. Chirgwin, Charles Plumpton
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 1 - 6 8 3 6 - 4
- eBook 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
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
- Edition: 1
- Latest edition
- Published: September 19, 2014
- Language: English
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