Mathematics for Physical ChemistryBy
- Robert Mortimer
Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data.
Published: June 2005
Imprint: Academic Press
"The text is a fairly easy read, well laid out, and laced with examples that serve to illustrate several concepts at once, thus obviating the necessity of hundreds more. The student will derive benefit from the clarity, and the professional from a concise compilation of techniques stressing application rather than theory. As such this book will be useful to a wide range of physical scientists and engineers, as well as the interested life scientist. My summary: Recommended." - John A. Wass, for SCIENTIFIC COMPUTING AND INSTRUMENTATION
- Preface1. Numbers, Measurements, and Numerical Mathematics Numbers and Measurements Numerical Mathematical OperationsUnits of Measurement Numerical Calculations2. Symbolic Mathematics and Mathematical FunctionsAlgebraic Operations on Real Scalar VariablesTrigonometric FunctionsInverse Trigonometric FunctionsVectors and Coordinate SystemsImaginary and Complex NumbersProblem Solving and Symbolic Mathematics3. The Solution of Algebraic EquationsAlgebraic Methods for Solving One Equation with One UnknownGraphical Solution of EquationsNumerical Solution of Algebraic EquationsSimultaneous Equations: Two Equations with Two Unknowns4. Mathematical Functions and Differential CalculusMathematical FunctionsThe Tangent Line and the Derivative of a Function Differentials Some Useful Facts about DerivativesHigher-Order DerivativesMaximum-Minimum ProblemsLimiting Values of Functions: LâHÃ´pitalâs Rule5. Integral CalculusThe Antiderivative of a FunctionThe Process of IntegrationIndefinite Integrals: Tables of IntegralsImproper IntegralsMethods of IntegrationNumerical IntegrationProbability Distributions and Mean Values6. Mathematical Series and TransformsConstant Series Functional SeriesFourier SeriesMathematical Operations on SeriesIntegral Transforms7. Calculus with Several Independent VariablesFunctions of Several Independent VariablesChange of VariablesAdditional Useful Relations Between Partial DerivativesExact and Inexact DifferentialsLine IntegralsMultiple IntegralsVector Derivative OperatorsMaximum and Minimum Values of Functions of Several Variables 8. Differential EquationsDifferential Equations and Newtonâs Laws of Motion The Harmonic OscillatorDifferential Equations with Separable VariablesExact Differential EquationsSolution of Inexact Differential Equations by the Use of Integrating FactorsPartial Differential Equations: Waves in a StringSolution of Differential Equations with Laplace TransformsNumerical Solutions of Differential Equations9. Operators, Matrices, and Group TheoryOperators and Operator Algebra Symmetry OperatorsMatrix AlgebraMatrix Algebra with MathematicaAn Elementary Introduction to Group Theory10. The Solution of Simultaneous Algebraic EquationsSimultaneous Equations with More than Two Unknowns Cramerâs RuleSolution by Matrix lnversionThe Use of Mathematica to Solve Simultaneous Equations11. The Treatment of Experimental DataExperimental Errors in Measured QuantitiesStatistical Treatment of Random ErrorsData Reduction and the Propagation of ErrorsGraphical and Numerical Data ReductionNumerical Curve Fitting: The Method of Least Squares (Regression)AppendixesA.Values of Physical ConstantsB. Some Mathematical Formulas and IdentitiesC. Infinite SeriesSeries with Constant TermsPower SeriesD. A Short Table of DerivativesE. A Short Table of Indefinite IntegralsF. A Short Table of Definite IntegralsG. Some Integrals with Exponentials in the Integrands: The Error FunctionIndex