| Preface |
|
vii | |
| 1 Symbolic Mathematics and Math Tools |
|
1 | (22) |
|
|
|
1 | (1) |
|
1.2 Symbolic Differentiation |
|
|
2 | (1) |
|
|
|
3 | (2) |
|
|
|
5 | (2) |
|
|
|
7 | (1) |
|
1.6 Polynomial Factorization |
|
|
7 | (1) |
|
|
|
7 | (2) |
|
|
|
9 | (1) |
|
|
|
10 | (1) |
|
|
|
10 | (1) |
|
1.11 Ordinary Differential Equations |
|
|
10 | (2) |
|
|
|
12 | (4) |
|
|
|
16 | (5) |
|
|
|
21 | (2) |
| 2 Classical Mechanics |
|
23 | (40) |
|
2.1 Simple Harmonic Oscillator |
|
|
23 | (5) |
|
|
|
28 | (2) |
|
|
|
30 | (1) |
|
2.4 Scattering Angle and Force Laws |
|
|
31 | (5) |
|
2.5 Classical Hard Sphere Scattering |
|
|
36 | (3) |
|
2.6 Ballistics and Air Resistance |
|
|
39 | (1) |
|
2.7 Rocket Motion - Symbolic and Numerical |
|
|
39 | (6) |
|
2.8 Taking the Free Subway |
|
|
45 | (1) |
|
2.9 Large Angle Oscillations - Pendulum |
|
|
46 | (2) |
|
|
|
48 | (2) |
|
|
|
50 | (1) |
|
2.12 Kepler Orbits - Numerical |
|
|
51 | (2) |
|
2.13 Analytic Kepler Orbits - Energy Considerations |
|
|
53 | (6) |
|
2.14 Stable Orbits and Perihelion Advance |
|
|
59 | (4) |
| 3 Electromagnetism |
|
63 | (27) |
|
3.1 Electric Potential for Point Charges |
|
|
63 | (2) |
|
3.2 Image Charge for a Grounded Sphere |
|
|
65 | (2) |
|
3.3 Magnetic Current Loop |
|
|
67 | (2) |
|
|
|
69 | (2) |
|
|
|
71 | (1) |
|
3.6 Potentials and Complex Variables |
|
|
72 | (2) |
|
3.7 Numerical Solution - Laplace Equation |
|
|
74 | (3) |
|
3.8 Numerical Solution - Poisson Equation |
|
|
77 | (2) |
|
3.9 Light Pressure and Solar Sailing |
|
|
79 | (4) |
|
3.10 Motion in Electric and Magnetic Fields |
|
|
83 | (2) |
|
|
|
85 | (2) |
|
|
|
87 | (3) |
| 4 Waves and Optics |
|
90 | (26) |
|
|
|
90 | (1) |
|
4.2 Damped and Driven Oscillations |
|
|
91 | (3) |
|
|
|
94 | (2) |
|
|
|
96 | (1) |
|
4.5 Diffraction by Slits and Apertures |
|
|
97 | (3) |
|
|
|
100 | (3) |
|
4.7 Doppler Shift and Cerenkov Radiation |
|
|
103 | (2) |
|
4.8 Reflection and Transmission at an Interface |
|
|
105 | (2) |
|
|
|
107 | (2) |
|
|
|
109 | (1) |
|
4.11 A Magnetic Quadrupole Lens System |
|
|
110 | (6) |
| 5 Gases and Fluid Flow |
|
116 | (29) |
|
|
|
116 | (3) |
|
5.2 An Ideal Gas Model in Two Dimensions |
|
|
119 | (1) |
|
5.3 Maxwell-Boltzmann Distributions |
|
|
120 | (3) |
|
5.4 Fermi-Dirac and Bose-Einstein Distributions |
|
|
123 | (2) |
|
5.5 Chemical Potential, Bosons |
|
|
125 | (2) |
|
5.6 Chemical Potential, Fermions |
|
|
127 | (1) |
|
5.7 Critical Temperature for He |
|
|
128 | (2) |
|
5.8 Exact Fermion Chemical Potential |
|
|
130 | (2) |
|
5.9 Complex Variables and Flow |
|
|
132 | (1) |
|
5.10 Complex Variables and Airfoils |
|
|
133 | (2) |
|
5.11 Complex Variables and Sources of Flow |
|
|
135 | (2) |
|
|
|
137 | (2) |
|
5.13 Transport and Viscosity |
|
|
139 | (1) |
|
5.14 Fluid Flow in a Pipe |
|
|
140 | (2) |
|
|
|
142 | (3) |
| 6 Quantum Mechanics |
|
145 | (36) |
|
6.1 Preliminaries - Planck Distribution |
|
|
145 | (2) |
|
6.2 Bound States - Oscillating or Damped |
|
|
147 | (1) |
|
|
|
148 | (3) |
|
6.4 Periodic Table - Ionization Potential and Atomic Radius |
|
|
151 | (3) |
|
6.5 Simple Harmonic Oscillator |
|
|
154 | (2) |
|
|
|
156 | (1) |
|
|
|
156 | (2) |
|
|
|
158 | (1) |
|
|
|
159 | (3) |
|
6.10 Numerical Solution for Bound States |
|
|
162 | (2) |
|
6.11 Scattering off a Potential Step |
|
|
164 | (3) |
|
6.12 Scattering Off a Potential Well or Barrier |
|
|
167 | (2) |
|
6.13 Wave Packet Scattering on a Well or Barrier |
|
|
169 | (2) |
|
6.14 Born Approximation - Scattering and Force Laws |
|
|
171 | (3) |
|
6.15 Spherical Harmonics - 3D |
|
|
174 | (2) |
|
|
|
176 | (2) |
|
6.17 Radioactive Decay - Fitting |
|
|
178 | (3) |
| 7 Special and General Relativity |
|
181 | (35) |
|
|
|
181 | (1) |
|
|
|
182 | (3) |
|
7.3 The Relativistic Rocket |
|
|
185 | (2) |
|
7.4 Charge in an Electric Field |
|
|
187 | (1) |
|
7.5 Charge in Electric and Magnetic Fields |
|
|
188 | (3) |
|
7.6 Relativistic Scattering and Decay |
|
|
191 | (3) |
|
7.7 Electric Field of a Moving Charge |
|
|
194 | (1) |
|
7.8 Minimum Ionizing Particle |
|
|
194 | (3) |
|
7.9 Range and Energy Loss |
|
|
197 | (1) |
|
7.10 Relativistic Radiation |
|
|
198 | (1) |
|
|
|
199 | (3) |
|
7.12 Photoelectric Effect |
|
|
202 | (1) |
|
7.13 Electrons and Muons in Materials |
|
|
203 | (2) |
|
|
|
205 | (5) |
|
7.15 Inspiraling Binary Stars |
|
|
210 | (1) |
|
7.16 Gravity Wave Detector |
|
|
211 | (5) |
| 8 Astrophysics and Cosmology |
|
216 | (24) |
|
8.1 Gravity and Clustering |
|
|
216 | (1) |
|
8.2 Fermi Pressure and Stars |
|
|
217 | (5) |
|
|
|
222 | (1) |
|
8.4 Stellar Differential Equations |
|
|
222 | (2) |
|
8.5 Radiation and Matter in the Universe |
|
|
224 | (6) |
|
8.6 Element Abundance and Entropy |
|
|
230 | (3) |
|
|
|
233 | (3) |
|
|
|
236 | (4) |
| Appendix Script for Classical Mechanics |
|
240 | (49) |
|
2.1 Simple Harmonic Oscillator |
|
|
240 | (4) |
|
|
|
244 | (3) |
|
|
|
247 | (3) |
|
2.4 Scattering Angle and Force Laws |
|
|
250 | (3) |
|
2.5 Classical Hard Sphere Scattering |
|
|
253 | (3) |
|
2.6 Ballistics and Air Resistance |
|
|
256 | (4) |
|
2.7 Rocket Motion - Symbolic |
|
|
260 | (3) |
|
2.8 Rocket Motion - Numerical |
|
|
263 | (4) |
|
2.9 Taking the Free Subway |
|
|
267 | (2) |
|
2.10 Large Angle Oscillations - Pendulum |
|
|
269 | (3) |
|
|
|
272 | (2) |
|
|
|
274 | (2) |
|
2.13 Kepler Orbits - Numerical |
|
|
276 | (4) |
|
2.14 Analytic Kepler Orbits Energy Considerations |
|
|
280 | (5) |
|
2.15 Stable Orbits and Perihelion Advance |
|
|
285 | (4) |
| References |
|
289 | (2) |
| Index |
|
291 | |
Rohkem infot World Scientific e-raamatute kohta