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Preface | |

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List of Examples | |

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Greek Alphabet | |

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Calculus | |

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Functions: General Properties | |

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Mappings | |

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Differentials and Derivatives | |

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Partial Derivatives | |

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Integrals | |

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Critical Points | |

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Functions: Examples | |

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Algebraic Functions | |

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Transcendental Functions | |

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Logarithm and Exponential | |

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Circular Functions | |

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Gamma and Beta Functions | |

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Functionals | |

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Coordinate Systems | |

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Points in Space | |

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Coordinate Systems for Molecules | |

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Abstract Coordinates | |

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Constraints | |

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Degrees of Freedom | |

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Constrained Extrema* | |

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Differential Operators in Polar Coordinates | |

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Integration | |

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Change of Variables in Integrands | |

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Change of Variable: Examples | |

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Jacobian Determinant | |

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Gaussian Integrals | |

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Improper Integrals | |

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Dirac Delta Function | |

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Line Integrals | |

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Numerical Methods | |

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Interpolation | |

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Numerical Differentiation | |

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Numerical Integration | |

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Random Numbers | |

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Root Finding | |

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Minimization* | |

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Complex Numbers | |

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Complex Arithmetic | |

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Fundamental Theorem of Algebra | |

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The Argand Diagram | |

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Functions of a Complex Variable* | |

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Branch Cuts* | |

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Extrapolation | |

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Taylor Series | |

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Partial Sums | |

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Applications of Taylor Series | |

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Convergence | |

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Summation Approximants* | |

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Statistics | |

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Estimation | |

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Error and Estimation | |

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Probability Distributions | |

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Probability Distribution Functions | |

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The Normal Distribution | |

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The Poisson Distribution | |

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The Binomial Distribution* | |

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The Boltzmann Distribution* | |

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Outliers | |

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Robust Estimation | |

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Analysis of Significance | |

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Confidence Intervals | |

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Propagation of Error | |

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Monte Carlo Simulation of Error | |

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Significance of Difference | |

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Distribution Testing* | |

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Fitting | |

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Method of Least Squares | |

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Polynomial Fitting | |

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Weighted Least Squares | |

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Generalizations of the Least-Squares Method* | |

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Fitting with Error in Both Variables | |

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Uncontrolled Error in x | |

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Controlled Error in x | |

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Nonlinear Fitting | |

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Quality of Fit | |

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Confidence Intervals for Parameters | |

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Confidence Band for a Calibration Line | |

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Outliers and Leverage Points | |

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Robust Fitting* | |

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Model Testing | |

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Experiment Design | |

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Risk Assessment | |

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Randomization | |

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Multiple Comparisons | |

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ANOVA* | |

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Post-Hoc Tests* | |

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Optimization* | |

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Differential Equations | |

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Examples of Differential Equations | |

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Chemical Reaction Rates | |

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Classical Mechanics | |

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Newtonian Mechanics | |

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Lagrangian and Hamiltonian Mechanics | |

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Angular Momentum | |

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Differentials in Thermodynamics | |

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Transport Equations | |

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Solving Differential Equations, I | |

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Basic Concepts | |

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The Superposition Principle | |

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First-Order ODE's | |

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Higher-Order ODE's | |

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Partial Differential Equations | |

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Solving Differential Equations, II | |

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Numerical Solution | |

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Basic Algorithms | |

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The Leapfrog Method* | |

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Systems of Differential Equations | |

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Chemical Reaction Mechanisms | |

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Approximation Methods | |

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Taylor Series* | |

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Perturbation Theory* | |

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Linear Algebra | |

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Vector Spaces | |

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Cartesian Coordinate Vectors | |

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Sets | |

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Groups | |

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Vector Spaces | |

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Functions as Vectors | |

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Hilbert Spaces | |

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Basis Sets | |

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Spaces of Functions | |

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Orthogonal Polynomials | |

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Function Resolution | |

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Fourier Series | |

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Spherical Harmonics | |

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Matrices | |

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Matrix Representation of Operators | |

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Matrix Algebra | |

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Matrix Operations | |

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Pseudoinverse* | |

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Determinants | |

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Orthogonal and Unitary Matrices | |

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Simultaneous Linear Equations | |

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Eigenvalue Equations | |

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Matrix Eigenvalue Equations | |

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Matrix Diagonalization | |

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Differential Eigenvalue Equations | |

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Hermitian Operators | |

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The Variational Principle* | |

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Schrï¿½dinger's Equation | |

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Quantum Mechanics | |

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Quantum Mechanical Operators | |

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The Wavefunction | |

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The Basic Postulates* | |

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Atoms and Molecules | |

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The One-Electron Atom | |

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Orbitals | |

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The Radial Equation* | |

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Hybrid Orbitals | |

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Antisymmetry* | |

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Molecular Orbitals* | |

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Fourier Analysis | |

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The Fourier Transform | |

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Spectral Line Shapes* | |

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Discrete Fourier Transform* | |

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Signal Processing | |

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Noise Filtering* | |

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Convolution* | |

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Computer Programs | |

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Robust Estimators | |

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FREML | |

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Nelder-Mead Simplex Optimization | |

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Answers to Selected Exercises | |

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Bibliography | |

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Index | |