Mathematics for Physical Chemistry

by Mortimer

• ISBN13: 9780125083478
• ISBN10: 0125083475
• Edition: 3rd
• Format: Paperback
• Copyright: 2005-06-10
• Publisher: Elsevier Science

Summary

Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data. * Numerous examples and problems interspersed throughout the presentations * Each extensive chapter contains a preview, objectives, and summary * Includes topics not found in similar books, such as a review of general algebra and an introduction to group theory * Provides chemistry specific instruction without the distraction of abstract concepts or theoretical issues in pure mathematics

Table of Contents

Preface	xi
Numbers, Measurements, and Numerical Mathematics	1	(20)
Numbers and Measurements	2	(3)
Numerical Mathematical Operations	5	(6)
Units of Measurement	11	(3)
Numerical Calculations	14	(7)
Symbolic Mathematics and Mathematical Functions	21	(36)
Algebraic Operations on Real Scalar Variables	22	(2)
Trigonometric Functions	24	(5)
Inverse Trigonometric Functions	29	(2)
Vectors and Coordinate Systems	31	(13)
Imaginary and Complex Numbers	44	(8)
Problem Solving and Symbolic Mathematics	52	(5)
The Solution of Algebraic Equations	57	(32)
Algebraic Methods for Solving One Equation with One Unknown	58	(6)
Graphical Solution of Equations	64	(6)
Numerical Solution of Algebraic Equations	70	(9)
Simultaneous Equations: Two Equations with Two Unknowns	79	(10)
Mathematical Functions and Differential Calculus	89	(32)
Mathematical Functions	90	(8)
The Tangent Line and the Derivative of a Function	98	(4)
Differentials	102	(2)
Some Useful Facts About Derivatives	104	(4)
Higher-Order Derivatives	108	(2)
Maximum-Minimum Problems	110	(3)
Limiting Values of Functions: L'Hopital's Rule	113	(8)
Integral Calculus	121	(37)
The Antiderivative of a Function	122	(2)
The Process of Integration	124	(8)
Indefinite Integrals: Tables of Integrals	132	(2)
Improper Integrals	134	(2)
Methods of Integration	136	(5)
Numerical Integration	141	(4)
Probability Distributions and Mean Values	145	(13)
Mathematical Series and Transforms	158	(31)
Constant Series	159	(6)
Functional Series	165	(7)
Fourier Series	172	(6)
Mathematical Operations on Series	178	(2)
Integral Transforms	180	(9)
Calculus With Several Independent Variables	189	(45)
Functions of Several Independent Variables	190	(6)
Change of Variables	196	(2)
Additional Useful Relations Between Partial Derivatives	198	(4)
Exact and Inexact Differentials	202	(3)
Line Integrals	205	(5)
Multiple Integrals	210	(7)
Vector Derivative Operators	217	(7)
Maximum and Minimum Values of Functions of Several Variables	224	(10)
Differential Equations	234	(34)
Differential Equations and Newton's Laws of Motion	235	(3)
The Harmonic Oscillator	238	(11)
Differential Equations with Separable Variables	249	(2)
Exact Differential Equations	251	(1)
Solution of Inexact Differential Equations by the Use of Integrating Factors	252	(1)
Partial Differential Equations: Waves in a String	253	(5)
Solution of Differential Equations with Laplace Transforms	258	(2)
Numerical Solutions of Differential Equations	260	(8)
Operators, Matrices, and Group Theory	268	(37)
Operators and Operator Algebra	269	(6)
Symmetry Operators	275	(7)
Matrix Algebra	282	(10)
Matrix Algebra with Mathematica	292	(2)
An Elementary Introduction to Group Theory	294	(11)
The Solution of Simultaneous Algebraic Equations	305	(13)
Simultaneous Equations with More than Two Unknowns	306	(1)
Cramer's Rule	306	(3)
Solution by Matrix Inversion	309	(4)
The Use of Mathematica to Solve Simultaneous Equations	313	(5)
The Treatment of Experimental Data	318	(46)
Experimental Errors in Measured Quantities	319	(3)
Statistical Treatment of Random Errors	322	(7)
Data Reduction and the Propagation of Errors	329	(4)
Graphical and Numerical Data Reduction	333	(6)
Numerical Curve Fitting: The Method of Least Squares (Regression)	339	(25)
Appendixes	364	(23)
A Values of Physical Constants	365	(2)
B Some Mathematical Formulas and Identities	367	(3)
C Infinite Series	370	(3)
Series with Constant Terms	370	(1)
Power Series	370	(3)
D A Short Table of Derivatives	373	(2)
E A Short Table of Indefinite Integrals	375	(4)
F A Short Table of Definite Integrals	379	(4)
G Some Integrals with Exponentials in the Integrands: The Error Function	383	(4)
Index	387