Applied Mathematics

Applied Mathematics: Made Simple provides an elementary study of the three main branches of classical applied mathematics: statics, hydrostatics, and dynamics. The book begins with discussion of the concepts of mechanics, parallel forces and rigid bodies, kinematics, motion with uniform acceleration in a straight line, and Newton's law of motion. Separate chapters cover vector algebra and coplanar motion, relative motion, projectiles, friction, and rigid bodies in equilibrium under the action of coplanar forces. The final chapters deal with machines and hydrostatics. The standard and content of the book covers C.S.E. and 'O' level G.C.E. examinations in Applied Mathematics and Mechanics as well as the relevant parts of the syllabuses for Physics and General Science courses related to Engineering, Building, and Agriculture. The book is also written for the home study reader who is interested in widening his mathematical appreciation or simply reviving forgotten ideas. The author hopes that the style of presentation will be found sufficiently attractive to recapture those who may at one time have lost interest.

Foreword

1 Mechanics

(1) Rigid Bodies

(2) Characteristics of a Force

(3) Measuring Force with a Spring

(4) Mass and Weight

(5) The Unit of Force

(6) Newton's Third Law

(7) Simple Force Diagrams

(8) Bodies in Equilibrium

2 Parallel Forces and Rigid Bodies

(1) Turning Effect of a Force

(2) The Beam Balance

(3) Calculation of Moments

(4) Resultant of Two Parallel Forces

(5) Center of Gravity

(6) Composite Figures

(7) Solid Figures

3 Kinematics

(1) Speed and Velocity

(2) Speed-Time Formula

(3) Distance-Time Graphs

(4) Non-uniform Speeds

(5) Speed-Time Graphs

4 Motion with Uniform Acceleration in a Straight Line

(1) Acceleration

(2) Equations of Motion

(3) Acceleration due to Gravity

(4) Falling Bodies and Equations of Motion

5 Newton's Laws of Motion

(1) Momentum

(2) The First Law

(3) The Second Law

(4) Impulse of a Force

(5) The Third Law

6 An Introduction to Vectors

(1) Revision of Trigonometry

(2) Sine rule and Cosine rule

(3) Vector Quantities

(4) Vector Addition

(5) Resultant of Three Vectors

7 Vector Algebra and Coplanar Forces

(1) Addition and Subtraction

(2) Distributive Law and Associative Law

(3) Vectors in Elementary Geometry

(4) The Polygon of Forces

(5) Non-concurrent Vectors

(6) Resolution of Vectors

(7) Resolving Non-concurrent Vectors

(8) Locating the Line of Action

8 Relative Motion

(1) Latitude and Longitude

(2) Finding Latitude

(3) Finding Longitude

(4) Course Calculations

(5) Moving Reference Point

(6) Positions of Closest Approach

9 Projectiles

(1) Vector Components

(2) Acceleration

(3) Equations of Motion

(4) General Equations for Projectile Motion

(5) Motion Down an Inclined Plane

(6) Motion Down a Chord of a Circle

(7) Lines of Quickest Descent

10 Friction

(1) Force of Friction

(2) Experimental Investigation of Static Friction

(3) Motive Force at an Angle to the Slope

(4) Toppling before Sliding

(5) Stable and Unstable Equilibrium

(6) Freely Hanging Load

11 Rigid Bodies in Equilibrium under the Action of Coplanar Forces

(1) Point of Concurrency

(2) Force Normal to a Surface

(3) Frictional Force and Normal Reaction

(4) Equilibrium of a Body under the Action of More than Three Forces

12 Work, Energy, and Power

(1) Work

(2) Kinetic Energy

(3) Motion at an Angle to the Force Producing it

(4) Potential Energy

(5) Conservation of Energy

(6) Momentum

(7) Power

13 Machines

(1) Mechanical Advantage

(2) Levers

(3) Wheel and Axle

(4) Velocity Ratio

(5) Inclined Plane

(6) Pulleys

(7) The Law of the Machine

14 Hydrostatics I: Density, Relative Density, and Buoyancy

(1) Density

(2) Mixtures

(3) The Relative-density Bottle

(4) Archimedes' Principle

(5) The Hydrometer

(6) Buoyancy and Equilibrium

15 Hydrostatics II: Liquid Pressure

(1) Fundamental Principles

(2) Pascal's Law

(3) Pressure due to Weight of Liquid

(4) Hydraulic Machines

(5) Horizontal Thrust in a Liquid

16 Hydrostatics III: Barometers and Boyles' Law

(1) Atmospheric Pressure

(2) Pressure of a Gas

(3) Hare's Apparatus

(4) Boyle's Law

(5) Pumps

(6) The Siphon

Tables

Logarithms

Antilogarithms

Natural Sines

Natural Cosines

Natural Tangents

Squares

Square Roots

Reciprocals

SI Units and Abbreviations

Answers

Index