Finding Roots
Note: While inclusion of all components in this chapter would, in principle, be possible, selection of only a few of MACSYMA, MAPLE, Mathematica, IDL, MATLAB, FORTRAN (with or without Numerical Recipes), and C (with or without Numerical Recipes) would probably be more common.
| 12.1 | Sample Problems |
| 12.1.1 Classical Turning Points | |
| 12.1.2 A Max-Min Problem: Equilibrium Points | |
| 12.1.3 Natural Frequencies of Oscillating Systems | |
| 12.1.4 Range of Projectile in Viscous Medium | |
| 12.1.5 Energy Levels in a Quantum Well | |
| 12.2 | Symbolic Approaches |
| 12.3 | Finding Roots Symbolically with MACSYMA |
| 12.3.1 Classical Turning Points | |
| 12.3.2 Equilibrium Points | |
| 12.3.3 Natural Frequencies | |
| 12.3.4 Range of Projectile in Viscous Medium | |
| 12.4 | Finding Roots Symbolically with MAPLE |
| 12.4.1 Classical Turning Points | |
| 12.4.2 Equilibrium Points | |
| 12.4.3 Natural Frequencies | |
| 12.4.4 Range of Projectile in Viscous Medium | |
| 12.5 | Finding Roots Symbolically with Mathematica |
| 12.5.1 Classical Turning Points | |
| 12.5.2 Equilibrium Points | |
| 12.5.3 Natural Frequencies | |
| 12.5.4 Range of Projectile in Viscous Medium | |
| 12.6 | Algorithms for Finding Roots Numerically |
| 12.6.1 The Method of Bisection | |
| 12.6.2 Newton's Method | |
| 12.6.3 Other Methods | |
| 12.6.4 Assessing Accuracy | |
| 12.7 | Finding Roots Numerically with IDL |
| 12.7.1 Classical Turning Points | |
| 12.7.2 Natural Frequencies | |
| 12.7.3 Range of Projectile | |
| 12.7.4 Energy Levels in Quantum Well | |
| 12.8 | Finding Roots Numerically with MATLAB |
| 12.8.1 Classical Turning Points | |
| 12.8.2 Natural Frequencies | |
| 12.8.3 Range of Projectile | |
| 12.8.4 Energy Levels in Quantum Well | |
| 12.9 | Finding Roots Numerically with MACSYMA |
| 12.9.1 Classical Turning Points | |
| 12.9.2 Range of Projectile | |
| 12.9.3 Energy Levels in Quantum Well | |
| 12.10 | Finding Roots Numerically with MAPLE |
| 12.10.1 Classical Turning Points | |
| 12.10.2 Range of Projectile | |
| 12.10.3 Energy Levels in Quantum Well | |
| 12.11 | Finding Roots Numerically with Mathematica |
| 12.11.1 Classical Turning Points | |
| 12.11.2 Range of Projectile | |
| 12.11.3 Energy Levels in Quantum Well | |
| 12.12 | Finding Roots Numerically with FORTRAN |
| 12.12.1 FORTRAN Programs from Scratch | |
| 12.12.2 Using Numerical Recipes | |
| 12.13 | Finding Roots Numerically with C |
| 12.13.1 C Programs from Scratch | |
| 12.13.2 Using Numerical Recipes | |
| 12.14 | Solving Simultaneous Equations |
| 12.14.1 Systems of Linear Equations | |
| 12.14.2 Systems of Nonlinear Equations | |
| 12.15 | Exercises |
| 12.15.1 ... using Symbolic Methods | |
| 12.15.2 ... using Numerical Methods | |
| 12.15.3 ... using Numerical Recipes | |
| 12.15.4 Finding More than One Unknown | |
| 12.A | Listing of bisect.f |
| 12.B | Listing of tt bisect.c |