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| Preface | |
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| Numbers, Measurements, and Numerical Mathematics | |
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| Numbers and Measurements | |
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| Numerical Mathematical Operations | |
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| Units of Measurement | |
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| Numerical Calculations | |
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| Symbolic Mathematics and Mathematical Functions | |
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| Algebraic Operations on Real Scalar Variables | |
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| Trigonometric Functions | |
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| Inverse Trigonometric Functions | |
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| Vectors and Coordinate Systems | |
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| Imaginary and Complex Numbers | |
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| Problem Solving and Symbolic Mathematics | |
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| The Solution of Algebraic Equations | |
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| Algebraic Methods for Solving One Equation with One Unknown | |
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| Graphical Solution of Equations | |
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| Numerical Solution of Algebraic Equations | |
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| Simultaneous Equations: Two Equations with Two Unknowns | |
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| Mathematical Functions and Differential Calculus | |
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| Mathematical Functions | |
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| The Tangent Line and the Derivative of a Function | |
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| Differentials | |
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| Some Useful Facts About Derivatives | |
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| Higher-Order Derivatives | |
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| Maximum-Minimum Problems | |
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| Limiting Values of Functions: L'Hopital's Rule | |
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| Integral Calculus | |
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| The Antiderivative of a Function | |
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| The Process of Integration | |
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| Indefinite Integrals: Tables of Integrals | |
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| Improper Integrals | |
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| Methods of Integration | |
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| Numerical Integration | |
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| Probability Distributions and Mean Values | |
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| Mathematical Series and Transforms | |
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| Constant Series | |
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| Functional Series | |
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| Fourier Series | |
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| Mathematical Operations on Series | |
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| Integral Transforms | |
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| Calculus With Several Independent Variables | |
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| Functions of Several Independent Variables | |
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| Change of Variables | |
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| Additional Useful Relations Between Partial Derivatives | |
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| Exact and Inexact Differentials | |
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| Line Integrals | |
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| Multiple Integrals | |
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| Vector Derivative Operators | |
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| Maximum and Minimum Values of Functions of Several Variables | |
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| Differential Equations | |
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| Differential Equations and Newton's Laws of Motion | |
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| The Harmonic Oscillator | |
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| Differential Equations with Separable Variables | |
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| Exact Differential Equations | |
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| Solution of Inexact Differential Equations by the Use of Integrating Factors | |
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| Partial Differential Equations: Waves in a String | |
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| Solution of Differential Equations with Laplace Transforms | |
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| Numerical Solutions of Differential Equations | |
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| Operators, Matrices, and Group Theory | |
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| Operators and Operator Algebra | |
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| Symmetry Operators | |
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| Matrix Algebra | |
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| Matrix Algebra with Mathematica | |
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| An Elementary Introduction to Group Theory | |
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| The Solution of Simultaneous Algebraic Equations | |
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| Simultaneous Equations with More than Two Unknowns | |
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| Cramer's Rule | |
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| Solution by Matrix Inversion | |
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| The Use of Mathematica to Solve Simultaneous Equations | |
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| The Treatment of Experimental Data | |
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| Experimental Errors in Measured Quantities | |
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| Statistical Treatment of Random Errors | |
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| Data Reduction and the Propagation of Errors | |
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| Graphical and Numerical Data Reduction | |
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| Numerical Curve Fitting: The Method of Least Squares (Regression) | |
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| Appendixes | |
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| Values of Physical Constants | |
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| Some Mathematical Formulas and Identities | |
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| Infinite Series | |
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| Series with Constant Terms | |
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| Power Series | |
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| A Short Table of Derivatives | |
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| A Short Table of Indefinite Integrals | |
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| A Short Table of Definite Integrals | |
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| Some Integrals with Exponentials in the Integrands: The Error Function | |
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| Index | |