Chapter 12

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.

12.1Sample 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
12.2Symbolic Approaches
12.3Finding 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
12.4Finding 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
12.5Finding 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
12.6Algorithms 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
12.7Finding 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
12.8Finding 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
12.9Finding Roots Numerically with MACSYMA
12.9.1 Classical Turning Points
12.9.2 Range of Projectile
12.9.3 Energy Levels in Quantum Well
12.10Finding Roots Numerically with MAPLE
12.10.1 Classical Turning Points
12.10.2 Range of Projectile
12.10.3 Energy Levels in Quantum Well
12.11Finding Roots Numerically with Mathematica
12.11.1 Classical Turning Points
12.11.2 Range of Projectile
12.11.3 Energy Levels in Quantum Well
12.12Finding Roots Numerically with FORTRAN
12.12.1 FORTRAN Programs from Scratch
12.12.2 Using Numerical Recipes
12.13Finding Roots Numerically with C
12.13.1 C Programs from Scratch
12.13.2 Using Numerical Recipes
12.14Solving Simultaneous Equations
12.14.1 Systems of Linear Equations
12.14.2 Systems of Nonlinear Equations
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.AListing of bisect.f
12.BListing of tt bisect.c

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