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好书大家分享Mathematics for Physical Chemistry（3nd)
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1 Numbers,Measurements, andNumerical Mathematics 1 NumbersandMeasurements ....................... 2 NumericalMathematicalOperations................... 5 UnitsofMeasurement........................... 11 NumericalCalculations.......................... 14 2 Symbolic Mathematicsand Mathematical Functions 21 AlgebraicOperationsonRealScalarVariables.............. 22 Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . 24 InverseTrigonometric Functions . . . . . . . . . . . . . . . . . . . . . 29 VectorsandCoordinateSystems ..................... 31 ImaginaryandComplexNumbers .................... 44 Problem Solving and Symbolic Mathematics . . . . . . . . . . . . . . . 52 3 TheSolution of Algebraic Equations 57 Algebraic Methods for Solving OneEquation withOne Unknown . . . 58 GraphicalSolutionofEquations ..................... 64 NumericalSolutionofAlgebraicEquations ............... 70 Simultaneous Equations: TwoEquations with TwoUnknowns . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4 Mathematical Functionsand Differential Calculus 89 MathematicalFunctions.......................... 90 The Tangent Line and the Derivative of aFunction . . . . . . . . . . . . 98 Differentials................................ 102 SomeUsefulFactsAbout Derivatives . . . . . . . . . . . . . . . . . . 104 Higher-OrderDerivatives......................... 108 Maximum-MinimumProblems...................... 110 Limiting Values of Functions: L’Hopital’sRule . . . . . . . . . . . . . 113 5 Integral Calculus 121 TheAntiderivativeofaFunction..................... 122 TheProcessofIntegration ........................ 124 IndefiniteIntegrals:TablesofIntegrals.................. 132 ImproperIntegrals............................. 134 Methods of Integration . . . . . . . . . . . . . . . . . . . . . . . . . . 136 NumericalIntegration........................... 141 Probability Distributions and Mean Values . . . . . . . . . . . . . . . . 145 6 Mathematical Series and Transforms 158 ConstantSeries .............................. 159 FunctionalSeries ............................. 165 FourierSeries............................... 172 MathematicalOperationsonSeries.................... 178 IntegralTransforms............................ 180 7 CalculusWithSeveral IndependentVariables 189 Functions of Several Independent Variables . . . . . . . . . . . . . . . 190 ChangeofVariables............................ 196 Additional Useful Relations Between PartialDerivatives.......................... 198 ExactandInexactDifferentials...................... 202 LineIntegrals ............................... 205 Multiple Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 VectorDerivativeOperators........................ 217 Maximum and Minimum Values of Functions of Several Variables . . . 224 8 DifferentialEquations 234 Differential Equations and Newton’sLaws ofMotion.............................. 235 The Harmonic Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . 238 Differential Equations with Separable Variables . . . . . . . . . . . . . 249 ExactDifferentialEquations ....................... 251 Solution of Inexact Differential Equations by the Useof Integrating Factors................................ 252 PartialDifferential Equations: Waves ina String . . . . . . . . . . . . . 253 Solution of Differential Equations with Laplace Transforms . . . . . . . 258 Numerical Solutions of Differential Equations . . . . . . . . . . . . . . 260 9 Operators, Matrices, and GroupTheory 268 OperatorsandOperatorAlgebra ..................... 269 SymmetryOperators ........................... 275 MatrixAlgebra .............................. 282 MatrixAlgebrawithMathematica .................... 292 AnElementary Introduction to Group Theory . . . . . . . . . . . . . . 294 10 TheSolution of SimultaneousAlgebraic Equations 305 Simultaneous Equations with More than TwoUnknowns . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 Cramer’sRule............................... 306 SolutionbyMatrixInversion....................... 309 The Useof Mathematica to Solve Simultaneous Equations . . . . . . . 313 11 TheTreatment of Experimental Data 318Experimental Errorsin Measured Quantities . . . . . . . . . . . . . . . 319 Statistical Treatment of Random Errors . . . . . . . . . . . . . . . . . . 322 DataReductionandthePropagationofErrors.............. 329 GraphicalandNumericalDataReduction ................ 333 Numerical Curve Fitting: The Method of Least Squares(Regression) . . 339 |
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