Contents -- Preface -- Numbers, Measurements, and Numerical Mathematics -- Numbers and Measurements -- Numerical Mathematical Operations -- Units of Measurement -- Numerical Calculations -- Symbolic Mathematics and Mathematical Functions -- Algebraic Operations on Real Scalar Variables -- Trigonometric Functions -- Inverse Trigonometric Functions -- Vectors and Coordinate Systems -- Imaginary and Complex Numbers -- Problem Solving and Symbolic Mathematics -- The Solution of Algebraic Equations -- Algebraic Methods for Solving One Equation with One Unknown -- Graphical Solution of Equations -- Numerical Solution of Algebraic Equations -- Simultaneous Equations: Two Equations with Two Unknowns -- Mathematical Functions and Differential Calculus -- Mathematical Functions -- The Tangent Line and the Derivative of a Function -- Differentials -- Some Useful Facts About Derivatives -- Higher-Order Derivatives -- Maximum-Minimum Problems -- Limiting Values of Functions: L'Hôpital's Rule -- Integral Calculus -- The Antiderivative of a Function -- The Process of Integration -- Indefinite Integrals: Tables of Integrals -- Improper Integrals -- Methods of Integration -- Numerical Integration -- Probability Distributions and Mean Values -- Mathematical Series and Transforms -- Constant Series -- Functional Series -- Fourier Series -- Mathematical Operations on Series -- Integral Transforms -- Calculus With Several Independent Variables -- Functions of Several Independent Variables -- Change of Variables -- Additional Useful Relations Between Partial Derivatives -- Exact and Inexact Differentials -- Line Integrals -- Multiple Integrals -- Vector Derivative Operators -- Maximum and Minimum Values of Functions of Several Variables -- Differential Equations -- Differential Equations and Newton's Laws of Motion.

The Harmonic Oscillator: Linear Differential Equations with Constant Coefficients -- Differential Equations with Separable Variables -- Exact Differential Equations -- Solution of Inexact Differential Equations by the Use of Integrating Factors -- Partial Differential Equations: Waves in a String -- Solution of Differential Equations with Laplace Transforms -- Numerical Solutions of Differential Equations -- Operators, Matrices, and Group Theory -- Operators and Operator Algebra -- Symmetry Operators -- Matrix Algebra -- Matrix Algebra with Mathematica -- An Elementary Introduction to Group Theory -- The Solution of Simultaneous Algebraic Equations -- Simultaneous Equations with More than Two Unknowns -- Cramer's Rule -- Solution by Matrix Inversion -- The Use of Mathematica to Solve Simultaneous Equations -- The Treatment of Experimental Data -- Experimental Errors in Measured Quantities -- Statistical Treatment of Random Errors -- Data Reduction and the Propagation of Errors -- Graphical and Numerical Data Reduction -- Numerical Curve Fitting: The Method of Least Squares (Regression) -- Appendixes -- Values of Physical Constants1 -- Some Mathematical Formulas and Identities -- Infinite Series -- Series with Constant Terms -- Power Series -- A Short Table of Derivatives -- A Short Table of Indefinite Integrals -- A Short Table of Definite Integrals -- Some Integrals with Exponentials in the Integrands: The Error Function -- Index.