AN INTRODUCTION TO PHYSICS FOR TECHNICAL STUDENTS

By D. MIERY

1 The Computer 1 11 The Operating System 2 111 Filesystem 3 112 Commands 10 113 Looking for Help 14 12 Text Processing Tools – Filters 16 13 Programming with Emacs 20 131 Calling Emacs 21 132 Interacting with Emacs 22 133 Basic Editing 25 134 Cut and Paste 27 135 Windows 28 136 Files and Buffers 29 137 Modes 30 138 Emacs Help 32 139 Emacs Customization 34 14 The C++ Programming Language 35 141 The Foundation 35 15 Gnuplot 47 16 Shell Scripting 52 2 Kinematics 63 21 Motion on the Plane 63 211 Plotting Data 72 212 More Examples 75 22 Motion in Space 87 23 Trapped in a Box 96 231 The One Dimensional Box 97 232 Errors 105 233 The Two Dimensional Box 109 24 Applications 112 25 Problems 132 3 Logistic Map 137 31 Introduction 137 32 Fixed Points and 2n Cycles 139 33 Bifurcation Diagrams 146 34 The Newton-Raphson Method 150 35 Calculation of the Bifurcation Points 156 36 Liapunov Exponents 160 37 Problems 174 4 Motion of a Particle 185 41 Numerical Integration of Newton’s Equations 185 42 Prelude: Euler Methods 186 43 Runge–Kutta Methods 198 431 A Program for the 4th Order Runge–Kutta 202 44 Comparison of the Methods 206 45 The Forced Damped Oscillator 209 46 The Forced Damped Pendulum 217 47 Appendix: On the Euler–Verlet Method 223 48 Appendix: 2nd order Runge–Kutta Method 227 49 Problems 230 5 Planar Motion 235 51 Runge–Kutta for Planar Motion 235 52 Projectile Motion 240 53 Planetary Motion 248 54 Scattering 252 541 Rutherford Scattering 255 542 More Scattering Potentials 263 55 More Particles 265 56 Problems 277 6 Motion in Space 281 61 Adaptive Stepsize Control for RK Methods 282 611 The rksuite Suite of RK Codes 282 612 Interfacing C++ Programs with Fortran 286 613 The rksuite Driver 292 62 Motion of a Particle in an EM Field 297 63 Relativistic Motion 298 64 Problems 310 7 Electrostatics 313 71 Electrostatic Field of Point Charges 313 72 The Program – Appetizer and Desert 316 73 The Program – Main Dish 325 74 The Program - Conclusion 331 75 Electrostatic Field in the Vacuum 336 76 Results 343 77 Poisson Equation 344 78 Problems 351 8 Diffusion Equation 355 81 Introduction 355 82 Heat Conduction in a Thin Rod 357 83 Discretization 358 84 The Program 360 85 Results 363 86 Diffusion on the Circle 365 87 Analysis 369 88 Problems 373 9 The Anharmonic Oscillator 375 91 Introduction 375 92 Calculation of the Eigenvalues of Hnm() 377 93 Results 387 94 The Double Well Potential 392 95 Problems 401 10 Time Independent Schrödinger Equation 405 101 Introduction 405 102 The Infinite Potential Well 408 103 Bound States 420 104 Measurements 430 105 The Anharmonic Oscillator - Again 436 106 The Lennard–Jones Potential 441 107 Problems 443