EMII - CIVL 2003 ENGINEERING MATHEMATICS II Version 1.1 1 2...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
1 CIVL 2003 ENGINEERING MATHEMATICS II Version 1.1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 先生講課要允許學生打瞌睡,你講得不好還一定讓人家听 ,與其睜着眼听着没味道,不如睡覺還可以養養神。可以 不听,稀稀拉拉。 考試可以交頭接耳,冒名頂替,你答對了,我抄你的,下 來也算是好的。
Background image of page 2
3 Reference book list : Advanced Engineering Mathematics – E Kreyszig Advanced Engineering Mathematics – C R Wylie Schaum’s Outline Series : Advanced Calculus : – M R Spiegel Complex Variables and Application – J W Brown and R V Churchill Schaum’s Outline Series : Linear Alegbra : – S Lipschultz
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 CONTENTS Chapter 1 - Fourier Series and Fourier Transform 1.1 Linear Regression 1-1 1.2 Approximation of periodic functions by Fourier Series 1-2 1.3 Bessel Inequality and Perservial Identity 1-11 1.4 Approximation of functions defined in [- , ] 1-13 1.5 Fourier integral 1-16 1.6 Fourier consine and sine transform 1-17 1.7 Linearity and differentiation of Fourier cosine and sine transform 1-17 1.8 Fourier transform 1-20 Appendix 1 1-22 Chapter 2 - Partial Differential Equation 2.1 First order and second order differential equations 2-1 2.2 Partial differential equations 2-2 2.3 Separation of variables 2-2 2.4 Solution for heat equation/consolidation equation 2-3 2.5 Solution for wave equation 2-8 2.6 Solution for Laplace equation 2-11 2.7 Solution for Poisson equation 2-14 2.8 Applications of Fourier Transform 2-16 Appendix 2 2-19 Chapter 3 – Complex variable 3.1 Complex number 3-1 3.2 Functions of complex number 3-3 3.3 Limit and differentiation of complex functions 3-10 3.4 Cauchy- Reimann conditions 3-11 3.5 Solution for Laplace equation 3-13 3.6 Integration of complex functions 3-17 3.7 Cauchy intergral theorems 3-21 3.8 Cauchy integral formula 3-26 3.9 Power series 3-29 3.10 Taylor series 3-29 3.11 Laurant series – Residue integration 3-33 3.12 Methods for determination of resdiue 3-35 3.13 Application of residue integration 3-39 Appendix 3 3-43
Background image of page 4
5 Chapter 4 – Linear Algebra 4.1 Solution of simultaneous equation 4-1 4.2 Determinant 4-11 4.3 Eigenvalue and eigenvector 4-17 4.4 Applications of eigenvalue problems 4-21 4.5 Orthogonality of eigenvector 4-26 4.6 Diagonalization 4-28 4.7 Quadratic form 4-33 Appendix 4 4-37 Tutorials
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
1-1 Chapter 1 - Fourier Series and Fourier Transform 1.1 Linear Regression Given a set of experimental results (Figure 1.1), one can easily obtain the linear trend line. Figure 1.1 Mathematically, a linear trend line can be expressed as : y = a x + b ( 1 . 1 ) where a and b are constants. The constants can be determined by the least square method . Exercise 1.1 (least square) Find the coefficients ( a and b ) by the method of least square. Solution - Error = ε ε 2 = Σε 2 = S = Minimize with respect to a and b 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 012345 x y
Background image of page 6
1-2 a S = 0 and b S = 0 If the results exhibit a non-linear relationship, one can use a higher order polynomial for the approximation, that is y = a 0 + a 1 x + a 2 x 2 + …… (1.2) where a i are constant coefficients. The coefficients can also be determined by the method of least square.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 162

EMII - CIVL 2003 ENGINEERING MATHEMATICS II Version 1.1 1 2...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online