Mathematics for physical chemistry/ Robert G Mortimer

Includes 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 Cartesian Coordinates; 3.3.2 Spherical Polar Coordinates; 3.3.3 Cylindrical Polar Coordinates; 3.4 Imaginary and Complex Numbers; 3.4.1 Mathematical Operations with Complex Numbers; 3.4.2 The Argand Diagram; 3.4.3 The Complex Conjugate; 3.4.4 The Magnitude of a Complex Quantity; 3.4.5 Roots of a Complex Number; 3.5 Problem Solving and Symbolic Mathematics; 4 Vectors and Vector Algebra; 4.1 Vectors in Two Dimensions; 4.1.1 The Sum and Difference of Two Vectors; 4.1.2 The Product of a Vector and a Scalar. 4.1.3 Unit Vectors4.1.4 The Scalar Product of Two Vectors; 4.1.5 The Magnitude of a Vector; 4.2 Vectors in Three Dimensions; 4.2.1 Unit Vectors in Three Dimensions; 4.2.2 The Magnitude of a Vector; 4.2.3 The Sum and Difference of Two Vectors; 4.2.4 The Product of a Scalar and a Vector; 4.2.5 The Scalar Product of Two Vectors; 4.2.6 The Vector Product of Two Vectors; 4.3 Physical Examples of Vector Products; 4.3.1 Magnetic Force; 4.3.2 Electrostatic Force; 4.3.3 Angular Momentum; 5 Problem Solving and the Solution of Algebraic Equations. 5.1 Algebraic Methods for Solving One Equation with One Unknown5.1.1 Polynomial Equations; 5.1.2 Approximate Solutions to Equations; 5.2 Numerical Solution of Algebraic Equations; 5.2.1 Graphical Solution of Algebraic Equations; 5.2.2 Trial and Error; 5.2.3 The Method of Bisection; 5.2.4 Solving Equations Numerically with Excel; 5.3 A Brief Introduction to Mathematica; 5.3.1 Numerical Calculations with Mathematica; 5.3.2 Symbolic Algebra with Mathematica; 5.3.3 Solving Equations with Mathematica; 5.3.4 Graphing with Mathematica; 5.4 Simultaneous Equations: Two Equations with Two Unknowns; 5.4.1 The Method of Substitution.

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