Frontmatter Page v Monday, March 8, 2004 10:06 AM
Contents vDensity of Points 99
Functions 100
Variables 101
Limits 102
Continuity 103
Total Variation 105
Differentiation 106
Commonly Used Rules for Computing Derivatives 107
Higher Order Derivatives 111
Application to Bond Analysis 112
Taylor Series Expansion 121
Application to Bond Analysis 122
Integration 127
Riemann Integrals 127
Properties of Riemann Integrals 129
Lebesque-Stieltjes Integrals 130
Indefinite and Improper Integrals 131
The Fundamental Theorem of Calculus 132
Integral Transforms 134
Laplace Transform 134
Fourier Transforms 137
Calculus in More than One Variable 138
Summary 139
CHAPTER 5
Matrix Algebra 141
Vectors and Matrices Defined 141
Vectors 141
Matrices 144
Square Matrices 145
Diagonals and Antidiagonals 145
Identity Matrix 146
Diagonal Matrix 146
Upper and Lower Triangular Matrix 148
Determinants 148
Systems of Linear Equations 149
Linear Independence and Rank 151
Hankel Matrix 152
Vector and Matrix Operations 153
Vector Operations 153
Matrix Operations 156
Eigenvalues and Eigenvectors 160
Diagonalization and Similarity 161
Singular Value Decomposition 162
Summary 163
CHAPTER 6
Concepts of Probability 165
Representing Uncertainty with Mathematics 165
Probability in a Nutshell 167