Math Refresher for Scientists and Engineers, 2nd Edition

by John R. Fanchi

• ISBN13: 9780471384571
• ISBN10: 0471384577
• Edition: 2nd
• Format: Paperback
• Copyright: 2000-05-01
• Publisher: Wiley-IEEE Press

Summary

All of the basic math that scientists and engineers need-now expanded and revised! Whether you need to understand advances in modern technology, prepare for professional exams, or simply brush up on skills acquired long ago, John Fanchi's quick reference guide to applied math is for you. He has updated his 1997 book to include probability and statistics in new chapters with exercises and solutions. Fanchi explains all topics clearly and methodically, from the ground up. He begins with straightforward concepts in college math and gradually progresses to more advanced topics, using practical applications throughout to demonstrate relationships between different areas. The wealth of numerical methods and illustrative examples further enhances the utility of this truly indispensable book. Math Refresher for Scientists and Engineers, Second Edition reviews: * Algebra * Geometry, analytic geometry, trigonometry, and hyperbolic functions * Vectors, matrices, and linear algebra * Differential calculus, integral calculus, and special integrals * Partial derivatives * Ordinary differential equations and ODE solution techniques * Partial differential equations * Probability and statistics

Table of Contents

Prefaces	xi
Algebra	1	(19)
Algebraic Axioms	1	(5)
Algebraic Operations	6	(2)
Exponents and Roots	8	(2)
Quadratic Equations	10	(1)
Logarithms	11	(3)
Fractals	12	(2)
Factorials	14	(1)
Permutations and Combinations	14	(1)
Complex Numbers	15	(5)
Particle Lifetimes	18	(2)
Geometry, Trigonometry, and Hyperbolic Functions	20	(18)
Geometry	20	(5)
Trigonometry	25	(5)
Euler's Equation	30	(1)
Hyperbolic Functions	31	(3)
Burger's Equation	33	(1)
Series Representations	34	(4)
Taylor's Series	34	(2)
Radius of Convergence of Power Series	36	(2)
Analytic Geometry	38	(10)
Line	38	(4)
Least Squares Fit to a Straight Line	40	(2)
Conic Sections	42	(4)
Polar Coordinate Representation of Conic Sections	44	(2)
Polar Form of Complex Numbers	46	(2)
Linear Algebra I	48	(13)
Rotation of Axes	48	(2)
Matrices	50	(8)
Determinants	58	(3)
Cramer's Rule	59	(2)
Linear Algebra II	61	(15)
Vectors	61	(4)
Vector Spaces	65	(2)
Eigenvalues and Eigenvectors	67	(4)
Matrix Diagonalization	71	(5)
Diagonalizing a Square Matrix	72	(4)
Differential Calculus	76	(14)
Limits	76	(3)
Derivatives	79	(6)
Finite Difference Concept	85	(5)
Darcy's Law	86	(4)
Partial Derivatives	90	(14)
Partial Differentiation	91	(3)
Jacobian Transformation	93	(1)
Vector Analysis	94	(7)
Propagation of Seismic Waves	99	(2)
Analyticity and the Cauchy-Riemann Equations	101	(3)
Integral Calculus	104	(11)
Indefinite Integrals	104	(3)
Definite Integrals	107	(3)
Solving Integrals	110	(2)
Length of a Curve	111	(1)
Numerical Integration	112	(3)
Special Integrals	115	(11)
Line Integral	115	(2)
Double Integral	117	(2)
Fourier Analysis	119	(7)
Ordinary Differential Equations	126	(19)
First-Order ODE	126	(8)
Higher-Order ODE	134	(2)
Stability Analysis	136	(3)
Introduction to Nonlinear Dynamics and Chaos	139	(6)
Defining Chaos	141	(4)
ODE Solution Techniques	145	(17)
Higher-Order ODE with Constant Coefficients	145	(3)
Variation of Parameters	148	(4)
Cauchy Equation	152	(1)
Series Methods	153	(6)
Laplace Transforms	159	(3)
Partial Differential Equations	162	(15)
Boundary Conditions	163	(1)
PDE Classification Scheme	163	(1)
Analytical Solution Techniques	164	(6)
Numerical Solution Methods	170	(7)
Probability	177	(10)
Set Theory	177	(3)
Probability Defined	180	(1)
Properties of Probability	181	(4)
Dart Board	184	(1)
Probability Distribution Defined	185	(2)
Probability Distributions	187	(16)
Joint Probability Distribution	187	(4)
Expectation Values and Moments	191	(2)
Multivariate Distributions	193	(4)
Quantum Mechanics and Probability Theory	196	(1)
Example Probability Distributions	197	(6)
Statistics	203	(95)
Probability and Frequency	203	(3)
Ungrouped Data	206	(1)
Grouped Data	207	(2)
Statistical Coefficients	209	(2)
Curve Fitting, Regression, and Correlation	211	(8)
Trend Surface Analysis	214	(5)
SOLUTIONS TO EXERCISES
S1 Algebra	219	(5)
S2 Geometry, Trigonometry, and Hyperbolic Functions	224	(7)
S3 Analytic Geometry	231	(3)
S4 Linear Algebra I	234	(8)
S5 Linear Algebra II	242	(5)
S6 Differential Calculus	247	(9)
S7 Partial Derivatives	256	(5)
S8 Integral Calculus	261	(5)
S9 Special Integrals	266	(4)
S10 Ordinary Differential Equations	270	(7)
S11 ODE Solution Techniques	277	(7)
S12 Partial Differential Equations	284	(5)
S13 Probability	289	(3)
S14 Probability Distribution	292	(4)
S15 Statistics	296	(2)
References	298	(4)
Index	302