Murphy Applied Mathematics

Made Simple
1. Auflage 2014
ISBN: 978-1-4831-4196-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 352 Seiten, Web PDF

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.

Autoren/Hrsg.

Murphy, Patrick

Inhaltsverzeichnis

1;Front Cover;1
2;Applied Mathematics: Made Simple;4
3;Copyright Page;5
4;Foreword;6
5;Table of Contents;7
6;CHAPTER ONE. MECHANICS;10
6.1;(1) Rigid Bodies;10
6.2;(2) Characteristics of a Force;11
6.3;(3) Measuring Force with a Spring;13
6.4;( 4 ) Mass and Weight;15
6.5;(5) The Unit of Force;17
6.6;(6) Newton's Third Law;18
6.7;(7) Simple Force Diagrams;19
7;CHAPTER TWO. PARALLEL FORCES AND RIGID BODIES;22
7.1;(1) Turning Effect of a Force;22
7.2;(2) The Beam Balance;27
7.3;( 3 ) Calculation of Moments;29
7.4;( 4 ) Resultant of Two Parallel Forces;31
7.5;(5) Centre of Gravity;37
7.6;(6) Composite Figures;40
7.7;( 7 ) Solid Figures;42
8;CHAPTER THREE. KINEMATICS;44
8.1;(1) Speed and Velocity;45
8.2;(2) Speed-Time Formulae;47
8.3;(3) Distance-Time Graphs;48
8.4;(4) Non-uniform Speeds;53
8.5;(5) Speed-Time Graphs;55
9;CHAPTER FOUR. MOTION WITH UNIFORM ACCELERATION IN ASTRAIGHT LINE;59
9.1;(1) Acceleration;59
9.2;(2) Equations of Motion;64
9.3;(3) Acceleration due to Gravity;68
10;CHAPTER FIVE. NEWTON'S LAWS OF MOTION;75
10.1;(1) Momentum;75
10.2;(2) The First Law;76
10.3;(3) The Second Law;77
10.4;(4) Impulse of a Force;81
10.5;(5) The Third Law;86
11;CHAPTER SIX. AN INTRODUCTION TO VECTORS;92
11.1;(1) Revision of Trigonometry;92
11.2;(2) Sine rule and Cosine rule;100
11.3;(3) Vector Quantities;105
11.4;(4) Vector Addition;110
11.5;(5) Resultant of Three Vectors;113
12;CHAPTER SEVEN. VECTOR ALGEBRA AND COPLANAR FORCES;116
12.1;(1) Addition and Subtraction;117
12.2;(2) Distributive Law and Associative Law;118
12.3;(3) Vectors in Elementary Geometry;122
12.4;(4) The Polygon of Forces;124
12.5;(5) Non-concurrent Vectors;127
12.6;(6) Resolution of Vectors;129
12.7;(7) Resolving Non-concurrent Vectors;135
12.8;(8) Locating the Line of Action;140
13;CHAPTER EIGHT. RELATIVE MOTION;144
13.1;(1) Latitude and Longitude;150
13.2;(2) Finding Latitude;152
13.3;(3) Finding Longitude;152
13.4;(4) Course Calculations;156
13.5;(5) Moving Reference Point;162
13.6;(6) Positions of Closest Approach;165
14;CHAPTER NINE. PROJECTILES;171
14.1;(1) Vector Components;172
14.2;(2) Acceleration;174
14.3;(3) Equations of Motion;175
14.4;(4) General Equations for Projectile Motion;178
14.5;(5) Motion Down an Inclined Plane;184
14.6;(6) Motion Down a Chord of a Circle;186
14.7;(7) Lines of Quickest Descent;187
15;CHAPTER TEN. FRICTION;188
15.1;(1) Force of Friction;189
15.2;(2) Experimental Investigation of Static Friction;192
15.3;(3) Motive Force at an Angle to the Slope;199
15.4;(4) Toppling before Sliding;202
15.5;(5) Stable and Unstable Equilibrium;204
15.6;(6) Freely Hanging Load;206
16;CHAPTER ELEVEN. RIGID BODIES IN EQUILIBRIUM UNDER THEACTION OF COPLANAR FORCES;210
16.1;(1) Point of Concurrency;210
16.2;(2) Force Normal to a Surface;215
16.3;(3) Frictional Force and Normal Reaction;218
16.4;(4) Equilibrium of a Body under the Action of More than Three Forces;221
17;CHAPTER TWELVE. WORK, ENERGY AND POWER;226
17.1;(1) Work;226
17.2;(2) Kinetic Energy;227
17.3;(3) Motion at an Angle to the Force Producing it;229
17.4;(4) Potential Energy;234
17.5;(5) Conservation of Energy;236
17.6;(6) Momentum;241
17.7;(7) Power;242
18;CHAPTER THIRTEEN. MACHINES;245
18.1;(1) Mechanical Advantage;245
18.2;(2) Levers;246
18.3;(3) Wheel and Axle;252
18.4;(4) Velocity Ratio;253
18.5;(5) Inclined Plane;258
18.6;(6) Pulleys;261
18.7;(7) The Law of the Machine;263
19;CHAPTER FOURTEEN. HYDROSTATICS I: DENSITY, RELATIVE DENSITY,AND BUOYANCY;266
19.1;(1) Density;267
19.2;(2) Mixtures;271
19.3;(3) The Relative-density Bottle;274
19.4;(4) Archimedes' Principle;276
19.5;(5) The Hydrometer;280
19.6;(6) Buoyancy and Equilibrium;282
20;CHAPTER FIFTEEN. HYDROSTATICS Ð: LIQUID PRESSURE;285
20.1;(1) Fundamental Principles;286
20.2;(2) Pascal's Law;287
20.3;(3) Pressure due to Weight of Liquid;288
20.4;(4) Hydraulic Machines;290
20.5;(5) Horizontal Thrust in a Liquid;293
21;CHAPTER SIXTEEN. HYDROSTATICS ÉÐ: BAROMETERS AND BOYLE'SLAW;296
21.1;(1) Atmospheric Pressure;296
21.2;(2) Pressure of a Gas;301
21.3;(3) Hare's Apparatus;301
21.4;( 4 ) Boyle's Law;303
21.5;(5) Pumps;306
21.6;(6) The Siphon;307
22;TABLES;310
22.1;Logarithms;311
22.2;Ântilogarithms;313
22.3;Natural Sines;315
22.4;Natural Cosines;317
22.5;Natural Tangents;319
22.6;Squares;321
22.7;Square Roots;323
22.8;Reciprocals;327
23;SI UNITS AND ABBREVIATIONS;329
24;ANSWERS;330
25;INDEX;352