1 online resource (xi, 247 pages) : illustrations
"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"-- Provided by publisher.
Includes bibliographical references and index.
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.
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Print version record.
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.
eBooks on EBSCOhost EBSCO eBook Subscription Science Reference Center Collection
Print version: Mortimer, Robert G. Mathematics for physical chemistry. 4th ed. Amsterdam : Amsterdam Press, Elsevier, 2013 9780124158092 (DLC) 2012047249 (OCoLC)828774811
9780123978455 (electronic bk.)
0123978459 (electronic bk.)