Mathematics for physical chemistry

"Principal Facts and Ideas. Problem solving is the principal tool for learning physical chemistry. Problem solving can be approached in a systematic way. Many problems involve numerical calculations involving measurable quantities. A measured quantity consists of a number and a unit of measurement. The SI units have been officially adopted by international organizations of physicists and chemists. Consistent units must be used in any calculation. The factor-label method can be used to convert from one unit of measurement to another. Reported values of all quantities should be rounded so that insignifi- cant digits are not reported. Objectives After you have studied the chapter, you should be able to: analyze a problem and design a procedure for solving the problem; 4 1. Problem Solving and Numerical Mathematics carry out the numerical procedures use in solving a simple problem; use numbers and units correctly to express measured quantities; understand the relationship of uncertainties in measurements to the use of significant digits; use consistent units, especially the SI units, in equations and formulas; use the factor-label method to convert from one unit of measurement to another. 1.1 Problem Solving Techniques of problem solving are applicable to many intellectual areas. There is a useful little book on problem solving by G. Polya, 1 and much of our discussion of problem solving is based on this book. Most physical chemistry problems are stated verbally, like the so-called 'word problems' of elementary school. The information contained in the statement of the problem generally includes a statement of the physical system involved, some information about the state of the system, and a statement of the desired outcome"--

Machine generated contents note: Preface 1. Problem Solving and Numerical Mathematics 2. Mathematical Functions 3. Problem Solving and Symbolic Mathematics: Algebra 4. Vectors and Vector Algebra 5. Problem Solving and the Solution of Algebraic Equations 6. Differential Calculus 7. Integral Calculus 8. Differential Calculus With Several Independent Variables 9. Integral Calculus With Several Independent Variables 10. Mathematical Series 11. Functional Series and Integral Transforms 12. Differential Equations 13. Operators, Matrices, and Group Theory 14. The Solution of Simultaneous Algebraic Equations with More than Two Unknowns 15. Probability, Statistics, and Experimental Errors 16. Data Reduction and the Propagation of Errors Index.

1 Problem Solving and Numerical Mathematics; 1.1 Problem Solving; 1.2 Numbers and Measurements; 1.3 Numerical Mathematical Operations; 1.3.1 Binary Arithmetic Operations; 1.3.2 Additional Numerical Operations; 1.4 Units of Measurement; 1.5 The Factor-Label Method; 1.6 Measurements, Accuracy, and Significant Digits; 1.6.1 Scientific Notation; 1.6.2 Rounding; 1.6.3 Significant Digits in a Calculated Quantity; 2 Mathematical Functions; 2.1 Mathematical Functions in Physical Chemistry; 2.1.1 Functions in Thermodynamics.

2.1.2 Functions in Quantum Mechanics2.1.3 Function Notation; 2.1.4 Continuity; 2.1.5 Graphs of Functions; 2.2 Important Families of Functions; 2.2.1 Linear Functions; 2.2.2 Quadratic Functions; 2.2.3 Cubic Functions; 2.2.4 Logarithms; 2.2.5 Exponentials; 2.2.6 Trigonometric Functions; 2.2.7 Inverse Trigonometric Functions; 2.2.8 Hyperbolic Trigonometric Functions; 2.2.9 Significant Digits in Logarithms, Exponentials, and Trigonometric Functions; 2.3 Generating Approximate Graphs; 3 Problem Solving and Symbolic Mathematics: Algebra; 3.1 The Algebra of Real Scalar Variables.

3.2 Coordinate Systems in Two Dimensions3.3 Coordinate Systems in Three Dimensions; 3.3.1 Carte…