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課程概述與目標
This course aims to establish the mathematical ability of undergraduates in mechanical engineering. Fundamental concepts and examples are introduced in the course.
課程章節
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章節
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章節名稱
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第一章
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Ordinary Differential Equations (ODE)
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Exact 1st order equations
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Separable 1st order equations
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Homogeneous 1st order equations
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Linear 1st order equations
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Nonohomogeous equations
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Variation of parameters
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2nd order equations
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Differential equations with constant coefficients
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Applications
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第二章
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Linear Algebra
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System of linear equations
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Determinants
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Vector spaces
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Linear transformation
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Eigenvalue problems
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Quadratic forms
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Applications
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第三章
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Laplace Transform
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Convergence of Laplace transform
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Special functions
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Properties
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Convolution theorem
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Application to system theory
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第四章
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Fourier Series and Transform
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Fourier series
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Half-range expansion
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Applications of Fourier series
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Fourier transform
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Properties
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Applications
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課程書目
Wylie, C. R. and Barrett, L. C., Advanced Engineering Mathematics, 6th ed., McGraw-Hill, 1995.
參考書目
| Kreszig, E., Advanced Engineering Mathematics, 9th ed., Prentice-Hall, 2006. |
| Greenberg, M. D., Advanced Engineering Mathematics, 2nd ed., John-Wiley, 1998. |
| Noble, B. and Daniel, J. W., Applied Linear Algebra, 3rd., Prentice-Hall, 1988. |
| Haberman, R., Elementary Applied Partial Differential Equations, Prentice-Hall, 1987. |
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