THE PRINCIPLES OF CHEMISTRY

By EMMA GONZALEZ

CONTENTS CHAPTER UNITS AND MEASUREMENTS INTRODUCTION BASIC ARITHMETIC OPERATIONS HIERARCHY OF OPERATIONS CLASSIFICATION OF UNIT SYSTEM METRIC SYSTEM OF UNITS CLASSIFICATION OF METRIC SYSTEM OF UNITS DEFINITION OF BASE UNITS INTERCONVERSION OF UNITS SIGNIFICANT FIGURES RULES FOR PERFORMING ARITHMETIC OPERATIONS ADDITION AND SUBTRACTION MULTIPLICATION AND DIVISION MIXED MATHEMATICAL OPERATIONS ROUNDING OFF SIGNIFICANT FIGURES PROBLEMS FOR PRACTICE CHAPTER UNCERTAINTIES AND ERRORS ABSOLUTE AND RELATIVE UNCERTAINTY PROPAGATION OF UNCERTAINTY ROUNDING OFF UNCERTAINTIES CLASSIFICATION OF ERRORS SOME MATHEMATICAL FUNCTIONS CLASSIFICATION OF FUNCTIONS LINEAR FUNCTION EXPONENTIAL LOGARITHMIC FUNCTION POLYNOMIALS POWER FUNCTION CIRCLE RATIONAL NUMBER PARTIAL FRACTIONS TRIGONOMETRIC FUNCTIONS INVERSE TRIGONOMETRIC FUNCTIONS HYPERBOLIC TRIGONOMETRIC FUNCTIONS TAYLOR’S SERIES MACLAURIN SERIES COORDINATE SYSTEMS NUMBER SYSTEM DESCRIPTIVE STATISTICS MEAN ARITHMETIC MEAN WEIGHTED MEAN GEOMETRIC MEAN HARMONIC MEAN MEDIAN MODE STANDARD DEVIATION VARIANCE COEFFICIENT OF VARIATION DATA ANALYSIS Q-TEST CONFIDENCE LIMIT T-TEST F-TEST DISTRIBUTION OF ERRORS GAUSSIAN DISTRIBUTION BINOMIAL DISTRIBUTION POISSON’S DISTRIBUTION STATISTICAL TOOLS USING SPREADSHEETS NUMERICAL CURVE FITTING CORRELATION PEARSON CORRELATION COEFFICIENT SPEARMAN’S RANK CORRELATION COEFFICIENT REGRESSION INTERPOLATION VERSUS CURVE FITTING LEAST SQUARE CURVE FITTING LINEAR REGRESSION MULTIVARIATE LINEAR REGRESSION POLYNOMIAL REGRESSION REGRESSION AND CORRELATION IN EXCEL EXERCISES FOR PRACTICE NUMERICAL INTEGRATION NEWTON–COTES FORMULA RIEMANN SUM TRAPEZOIDAL RULE ERROR OF TRAPEZOIDAL RULE SIMPSON’S 1/3RD RULE COMPOSITE INTEGRAL SIMPSON’S RULE SIMPSON’S 3/8 RULE BOOLE’S RULE DIFFERENTIAL EQUATIONS EULER’S METHOD RUNGE–KUTTA METHOD RK 2 OR PREDICTOR–CORRECTOR METHOD NUMERICAL DIFFERENTIATION DERIVATIVES USING NEWTON’S FORWARD INTERPOLATION POLYNOMIAL DERIVATIVES USING NEWTON’S BACKWARD INTERPOLATING POLYNOMIAL DERIVATIVES USING STIRLING INTERPOLATING POLYNOMIAL NEWTON’S DIVIDED DIFFERENCE POLYNOMIAL LAGRANGE’S POLYNOMIAL RICHARDSON’S EXTRAPOLATION NUMERICAL ROOT-FINDING METHODS NEWTON–RAPHSON METHOD ITERATION METHOD BINARY BISECTION METHOD SECANT METHOD REGULA-FALSI METHOD DIFFERENTIALS AND INTEGRALS PARTIAL DERIVATIVES RECIPROCAL IDENTITY SECOND PARTIAL DERIVATIVE MIXED SECOND PARTIAL DERIVATIVE EULER’S RECIPROCITY RELATIONSHIP CYCLIC RULE STATIONARY POINTS TOTAL DIFFERENTIALS EXACT AND INEXACT INTEGRALS LINE INTEGRALS MULTIPLE INTEGRAL DOUBLE INTEGRALS AS VOLUMES LINE INTEGRAL OF EXACT AND INEXACT DIFFERENTIALS LINE INTEGRALS IN THERMODYNAMICS