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Cover image for The language of physics : a foundation for university study
Title:
The language of physics : a foundation for university study
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Publication Information:
New York : Oxford University Press, 2008
Physical Description:
xiv, 225 p. : ill. ; 26 cm.
ISBN:
9780199533794
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30000010204709 QC20 C84 2008 Open Access Book Book
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Summary

Summary

This book introduces physics to a first year undergraduate in the language of mathematics. As such it aims to give a mathematical foundation to the physics taught at school as well as extending it to the skills and disciplines approached during a first degree course in physical science or engineering. It bridges two gaps in modern education - between the level of difficulty between A-level and undergraduate study, and between mathematics and physics. Many of the concepts are revised or introduced in the course of 'workshop' questions which are an integral part of the text. Fully explained solutions to these workshops are given as a substantial appendix to the book. The student will be enabled to study classical mechanics in terms of vector calculus, fields in terms of line and surface integrals, oscillations and waves in terms of complex exponentials and so on. As far as we are aware, this book is unique in its aim, its content, and its approach.


Author Notes

John P. CullerneHead of Physics Winchester CollegeAnton MachacekHead of PhysicsRoyal Grammar SchoolHigh Wycombe


Reviews 1

Choice Review

The Language of Physics aims to fill the perceived gap in education between pre-university and university studies in the British educational system. Physicists Cullerne (Winchester College, UK) and Machacek (Royal Grammar School, High Wycombe, UK) argue that their university engineering and physics students are unprepared for the level of mathematics required to properly study physics. It is clear that the authors' expectations for university preparation are higher than those in the US. The mathematical techniques they stress are typically taught in an introductory three-semester calculus sequence. That said, the book does contain many very good problems that stress mathematical application, making the work useful as a review or secondary source for US students. This reviewer found many of the discussions terse and at a mathematical level that only his better first-year students would be able to follow. Chapters include "Linear Mechanics," "Fields," "Rotation, Oscillation and Waves," "Circuits," and "Thermal Physics." Worked solution sets are available at the end of the book. Because of its brevity (200 pages including solutions), the volume would not serve well as a lone introductory resource. Summing Up: Recommended. Lower-division undergraduates. E. Kincanon Gonzaga University


Table of Contents

1 Linear mechanicsp. 1
1.1 Kinematicsp. 1
1.1.1 The law of falling bodiesp. 1
1.1.2 The kinematics of falling bodiesp. 4
1.1.3 Workshop: Simple differential equationsp. 9
1.1.4 The kinematics of a projectilep. 11
1.1.5 Workshop: Motion on the surface of a smooth inclined planep. 14
1.1.6 Adding and subtracting vectorsp. 15
1.2 Dynamicsp. 17
1.2.1 Newton's lawsp. 17
1.2.2 The principle of relativityp. 21
1.2.3 Impulse and impulsive forcesp. 22
1.2.4 Workshop: The conservation of linear momentump. 23
1.2.5 The law of falling bodiesp. 25
1.2.6 Workshop: Newton and the applep. 26
1.3 Conclusionp. 27
2 Fieldsp. 29
2.1 Introduction and field strengthp. 29
2.2 Workshop: Motion in a uniform field in one dimensionp. 30
2.3 Workshop: Scalar product of vectorsp. 32
2.4 Workshop: Motion in a uniform field in three dimensionsp. 34
2.5 Non-uniform fieldsp. 36
2.6 Workshop: Evaluating line integralsp. 37
2.7 Potential gradientsp. 39
2.8 Setting up a fieldp. 44
2.8.1 Workshop: The electrostatic field surrounding a charged wirep. 47
2.8.2 Electrostatic charge in a parallel plate capacitorp. 48
2.8.3 Gravitational fields inside planetsp. 50
2.8.4 Formalizing the notationp. 51
2.9 Conclusionp. 53
3 Rotationp. 54
3.1 Rotational kinematics and dynamicsp. 54
3.1.1 Kinematics on a circular pathp. 54
3.1.2 Workshop: Rotated coordinate systems and matricesp. 56
3.1.3 Workshop: Rotating vectors and the vector productp. 58
3.1.4 Angular velocityp. 59
3.1.5 Workshop: Vector triple productp. 61
3.1.6 Acceleration vectors in rotating framesp. 62
3.1.7 'Fictitious force': Centrifugal and Coriolis forcesp. 64
3.2 Orbitsp. 66
3.2.1 The Kepler problemp. 66
3.2.2 Kepler's first law and properties of (d[superscript 2]/dt[superscript 2])rp. 70
3.2.3 Workshop: Kepler's second lawp. 74
3.2.4 Workshop: Kepler's third lawp. 75
3.3 Conclusionp. 77
4 Oscillations and wavesp. 78
4.1 Describing an oscillationp. 78
4.1.1 Workshop: Simple harmonic motionp. 80
4.2 Workshop: Introducing complex numbersp. 81
4.3 Describing an oscillation using complex numbersp. 84
4.4 Workshop: Damped oscillatorsp. 85
4.5 Describing a wave in one dimensionp. 86
4.6 Interference - a brief introductionp. 87
4.7 Workshop: The wave equationp. 89
4.8 A wave on a stringp. 89
4.9 Energy content of a wavep. 91
4.10 Impedance matchingp. 92
4.11 Describing waves in three dimensionsp. 94
4.11.1 Plane wavesp. 94
4.11.2 Spherical wavesp. 95
4.11.3 Workshop: Stellar magnitudesp. 96
4.12 Conclusionp. 97
5 Circuitsp. 98
5.1 Fundamentalsp. 98
5.1.1 Electric currentp. 99
5.1.2 Electric potentialp. 100
5.1.3 Workshop: Using voltage to solve simple circuit problemsp. 101
5.1.4 Ohm's law and resistancep. 101
5.2 Direct current circuit analysisp. 102
5.2.1 Analysis using fundamental principlesp. 103
5.2.2 Method of loop currentsp. 104
5.3 Introducing alternating currentp. 105
5.3.1 Resistorsp. 106
5.3.2 Power in a.c. circuits and rms valuesp. 106
5.3.3 Capacitorsp. 108
5.3.4 Inductorsp. 109
5.3.5 Sign conventionsp. 109
5.3.6 Phasor methods in a.c. analysisp. 109
5.4 Alternating current circuit analysisp. 111
5.4.1 Analysis using impedancesp. 112
5.4.2 Analysis using a phasorp. 114
5.5 Conclusionp. 115
6 Thermal physicsp. 116
6.1 The conservation of energy: The first lawp. 116
6.2 The second lawp. 117
6.3 Carnot's theoremp. 118
6.3.1 Heat engines and fridgesp. 118
6.3.2 Thermodynamic temperaturep. 121
6.3.3 Efficiency of a heat enginep. 122
6.4 Entropyp. 123
6.4.1 Reversible processesp. 123
6.4.2 Irreversible processes and the second lawp. 124
6.4.3 Restatement of first lawp. 125
6.5 The Boltzmann lawp. 125
6.5.1 Workshop: Atmospheric pressurep. 125
6.5.2 Velocity distribution of molecules in a gasp. 126
6.5.3 Workshop: Justification of Boltzmann lawp. 127
6.6 Perfect gasesp. 129
6.6.1 Heat capacity of a perfect gasp. 130
6.6.2 Pumping heatp. 131
6.7 Conclusionp. 135
7 Miscellanyp. 136
7.1 Workshop: Setting up integralsp. 136
7.2 Workshop: Logarithmsp. 138
7.3 Workshop: Rockets and stagesp. 140
7.4 Workshop: Unit conversionp. 143
7.5 Workshop: Dimensional analysisp. 144
7.6 Workshop: Error analysisp. 147
7.7 Workshop: Centres of massp. 150
7.8 Workshop: Rigid body dynamicsp. 152
7.9 Workshop: Parallel axes theoremp. 155
7.10 Workshop: Perpendicular axes theoremp. 157
7.11 Workshop: Orbital energy and orbit classificationp. 159
8 Summary of equationsp. 162
8.1 Linear mechanicsp. 162
8.2 Fieldsp. 163
8.3 Rotationp. 165
8.4 Wavesp. 167
8.5 Circuitsp. 169
8.6 Thermal physicsp. 170
Workshop solutionsp. 172
Chapter 1

p. 172

Chapter 2

p. 178

Chapter 3

p. 181

Chapter 4

p. 188

Chapter 5

p. 197

Chapter 6

p. 198

Chapter 7

p. 203

Indexp. 223
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