Applied Mathematics for Physical Chemistry

by Barrante, James R

• ISBN13: 9780137417377
• ISBN10: 0137417373
• Edition: 2nd
• Format: Paperback
• Copyright: 1997-08-01
• Publisher: Prentice Hall

Summary

A "how to do it" review and learn book on advanced mathematics necessary to physical chemistry. Coordinate systems, functions and graphs, logarithms, differential calculus, integral calculus, infinite series, differential equations, scalars and vectors, matrices and determinants, operators, numerical methods and the use of the computer, and mathematical methods in the laboratory. Educators, Technicians, and other professionals using mathematics in physical chemistry.

Table of Contents

Preface	vii
1 Coordinate Systems	1	(10)
1.1 Introduction	1	(1)
1.2 Cartesian Coordinates	2	(2)
1.3 Plane Polar Coordinates	4	(1)
1.4 Spherical Polar Coordinates	5	(2)
1.5 The Complex Plane	7	(4)
2 Functions and Graphs	11	(13)
2.1 Functions	11	(1)
2.2 Graphical Representation of Functions	12	(8)
2.3 Roots to Polynomial Equations	20	(4)
3 Logarithms	24	(6)
3.1 Introduction	24	(1)
3.2 General Properties of Logarithms	24	(1)
3.3 Common Logarithms	25	(2)
3.4 Natural Logarithms	27	(3)
4 Differential Calculus	30	(24)
4-1 Introduction	30	(1)
4-2 Functions of Single Variables	31	(4)
4-3 Functions of Several Variables-Partial Derivatives	35	(2)
4-4 The Total Differential	37	(3)
4-5 Derivative as a Ratio of Infinitesimally Small Changes	40	(3)
4-6 Geometric Properties of Derivatives	43	(4)
4-7 Constrained Maxima and Minima	47	(7)
5 Integral Calculus	54	(15)
5-1 Introduction	54	(1)
5-2 Integral as an Antiderivative	55	(1)
5-3 General Methods of Integration	55	(2)
5-4 Special Methods of Integration	57	(2)
5-5 The Integral as a Summation of Infinitesimally Small Elements	59	(2)
5-6 Line Integrals	61	(2)
5-7 Double and Triple Integrals	63	(6)
6 Differential Equations	69	(25)
6-1 Introduction	69	(1)
6-2 Linear Combinations	70	(1)
6-3 First-Order Differential Equations	71	(3)
6-4 Second-Order Differential Equations with Constant Coefficients	74	(3)
6-5 General Series Method of Solution	77	(2)
6-6 Special Polynomial Solutions to Differential Equations	79	(5)
6-7 Exact and Inexact Differentials	84	(3)
6-8 Integrating Factors	87	(1)
6-9 Partial Differential Equations	88	(6)
7 Infinite Series	94	(16)
7-1 Introduction	94	(1)
7-2 Tests for Convergence and Divergence	95	(3)
7-3 Power Series Revisited	98	(1)
7-4 Maclaurin and Taylor Series	99	(2)
7-5 Fourier Series and Fourier Transforms	101	(9)
8 Scalars and Vectors	110	(10)
8.1 Scalars	110	(1)
8.2 Vectors and their Addition	111	(3)
8.3 Multiplication of Vectors	114	(3)
8.4 Applications	117	(3)
9 Matrices and Determinants	120	(15)
9.1 Introduction	120	(1)
9.2 Square Matrices and Determinants	121	(2)
9.3 Matrix Algebra	123	(3)
9.4 Solution of Systems of Linear Equations	126	(2)
9.5 Characteristic Equation of a Matrix	128	(7)
10 Operators	135	(15)
10.1 Introduction	135	(2)
10.2 Vector Operators	137	(1)
10.3 Eigenvalue Equations Revisited	138	(2)
10.4 Hermitian Operators	140	(2)
10.5 Rotational Operators	142	(3)
10.6 Transformation of XXX(2) to Plane Polar Coordinates	145	(5)
11 Numerical Methods and the Use of the Computer	150	(29)
11.1 Introduction	150	(2)
11.2 Programming a Computer	152	(11)
11.3 Programming Examples	163	(6)
11.4 Numerical Integration	169	(5)
11.5 Roots to Equations	174	(5)
12 Mathematical Methods in the Laboratory	179	(13)
12.1 Introduction	179	(1)
12.2 Probability	180	(2)
12.3 Experimental Errors	182	(3)
12.4 Propagation of Errors	185	(2)
12.5 Preparation of Graphs	187	(1)
12.6 Tongents and Areas	188	(4)
Appendices	192	(18)
I Table of Physical Constants	192	(1)
II Table of Integrals	192	(14)
III Transformation of XXX(2) to Spherical Polar Coordinates	206	(2)
IV Stirling's Approximation	208	(2)
Answers	210	(11)
Index	221