Ames, W.F.; et. al. “Mathematics”
Mechanical Engineering Handbook
Ed. Frank Kreith
Boca Raton: CRC Press LLC, 1999
c©1999 by CRC Press LLC
Mathematics
19.1 Tables..............................................................................19-2
Greek Alphabet • International System of Units (SI) •
Conversion Constants and Multipliers • Physical Constants •
Symbols and Terminology for Physical and Chemical Qualities
• Elementary Algebra and Geometry • Table of Derivatives •
Integrals • The Fourier Transforms • Bessel Functions •
Legendre Functions • Table of Differential Equations
19.2 Linear Algebra and Matrices .......................................19-33
Basic Definitions • Algebra of Matrices • Systems of Equations
• Vector Spaces • Rank and Nullity • Orthogonality and Length
• Determinants • Eigenvalues and Eigenvectors
19.3 Vector Algebra and Calculus .......................................19-39
Basic Definitions • Coordinate Systems • Vector Functions •
Gradient, Curl, and Divergence • Integration • Integral
Theorems
19.4 Difference Equations....................................................19-44
First-Order Equations • Second-Order Equations • Linear
Equations with Constant Coefficients • Generating Function (z
Transform)
19.5 Differential Equations ..................................................19-47
Ordinary Differential Equations • Partial Differential Equations
19.6 Integral Equations ........................................................19-58
Classification and Notation • Relation to Differential Equations
• Methods of Solution
19.7 Approximation Methods ..............................................19-60
Perturbation • Iterative Methods
19.8 Integral Transforms ......................................................19-62
Laplace Transform • Convolution Integral • Fourier Transform
• Fourier Cosine Transform
19.9 Calculus of Variations ..................................................19-67
The Euler Equation • The Variation • Constrai