課程資訊

Engineering Mathematics (2)

102-2

ME2002

502 20002

02

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1022ME2002_02

1. Vector Calculus:
vector functions, differentiation of vector functions, curves and surfaces, tangents and normals, integration of vector functions, line integrals, surface integrals, gradient, divergence and curl, Green`s theorem, Gauss` theorem, Stokes` theorem, potential theory

2. Fourier Analysis:
Fourier series, convergence of Fourier series, Fourier integrals, Fourier transforms, properties of Fourier transform, complex Fourier transforms, Fourier spectra, power spectra, discrete Fourier transform

3. Orthogonal Expansions: (if time permits)
special functions (Legendre, Bessel), orthogonal polynomials, Sturm-Liouville theory, eigenfunction expansions

4. Linear Partial Differential Equations:
method of separation of variables, eigenvalue problems, eigen-solutions, heat equations, wave equations, Laplace equations, non-homogeneous equations and boundary conditions, Laplace and Fourier transforms for solving boundary-value problems

5. Complex Analysis:
complex variables and complex functions, analytic functions, differentiation and integration of complex functions, multi-valued functions, branch point and branch cut, Cauchy integral theorem, power series, Taylor and Laurent series representation of functions, singularities, residue theorem, application on real integrals

Office Hours

'Advanced Engineering Mathematics', 7th ed. (custom publishing),
P. V. O’Neil, Cengage, 2012.

(僅供參考)

 No. 項目 百分比 說明 1. 6次小考 70% 2. 期末考 40% 3. 作業 0% 指定各章節習題，但無須繳交，亦不予評分。 4. (1)+(2)=學期成績 110% 原始分數將轉換成等第制

 課程進度
 週次 日期 單元主題 第1週 2/17,2/19 Vector differential calculus -- vector functions, curves (length, tangent, normal, curvature and torsion), Frenet formulas, velocity & acceleration of particle 第2週 2/24,2/26 Vector differential calculus -- vector field, streamlines, gradient of scalar field, directional derivative, physical interpretation of gradient, divergence & curl of vector field, physical interpretation of divergence & curl 第3週 3/03,3/05 Vector differential calculus -- important vector identities; Vector integral calculus -- line integrals of scalar & vector fields, conservative vector field & potential theory, representations of surfaces, surface area 第4週 3/10,3/12 Vector integral calculus -- surface integral of scalar field, surface integral of vector field, flux across a surface; ** 1st quiz (tentative schedule) 第5週 3/17,3/19 Vector integral calculus -- Green’s theorem, extension of Green’s theorem, divergence (Gauss) theorem, Green’s identities, Stokes theorem, Stokes theorem & potential theory 第6週 3/24,3/26 Fourier series & Fourier Integrals -- Fourier series (concept & idea), Fourier coefficients, Fourier-series representation of functions, piecewise continuous & piecewise smooth functions 第7週 3/31,4/02 Fourier series & Fourier Integrals -- convergence properties of Fourier series; ** 2nd quiz (tentative schedule); * no class on 4/2 (spring break) 第8週 4/07,4/09 Fourier series & Fourier Integrals -- Fourier cosine & sine series, differentiation & integration of Fourier series, Parseval theorem, Fourier-series representation of periodic functions, Fourier spectrum, complex Fourier series; Fourier series & Fourier Integrals -- Fourier integrals, convergence of Fourier integral 第9週 4/14,4/16 Fourier series & Fourier Integrals -- Fourier cosine & sine integrals, complex Fourier integrals; Fourier transforms -- idea of Fourier transform, Fourier transform & inverse Fourier transform, Fourier spectrum; ** 3rd quiz (tentative schedule) 第10週 4/21,4/23 Fourier transforms -- properties of Fourier transform, convolution, applications of Fourier transform, windowed Fourier transform, filtering & Dirac delta function, lowpass & bandpass filters, Fourier cosine & sine transforms, discrete Fourier transform, power spectrum; Partial differential equations (PDE) -- types of PDE (heat equation, wave equation, Laplace equation) 第11週 4/28,4/30 Partial differential equations (PDE) -- methods of separation of variables, solutions to unsteady heat equation with different boundary conditions; ** 4th quiz (tentative schedule) 第12週 5/05,5/07 Partial differential equations (PDE) -- unsteady heat conduction in infinite media, steady heat equation (Laplace equation), Laplace equation in polar coordinates, Laplace equation for unbounded domain 第13週 5/12,5/14 Partial differential equations (PDE) -- wave equation, wave equation for infinite string, d’Alembert solution of wave equation; Partial differential equations (PDE) -- heat equation in cylindrical and spherical coordinates 第14週 5/19,5/21 Partial differential equations (PDE) -- equations in multiple spatial coordinates, non-homogeneous equation & non-homogeneous boundary conditions; ** 5th quiz (tentative schedule) 第15週 5/26,5/28 Partial differential equations (PDE) -- method of Laplace transform, method of Fourier transforms; Complex analysis -- complex variables & complex functions, Cauchy-Riemann conditions, analytic functions, power series, complex exponential & trigonometric functions, multi-valued functions (complex logarithm & fractional powers), branch point & branch cut 第16週 6/02,6/04 * no class on 6/2 (national holiday); ** 6th quiz (tentative schedule) 第17週 6/09,6/11 Complex integrations -- Cauchy integral theorem, Cauchy integral formula, power series representation of function (Taylor & Laurent series), singularities (poles), residue theorem, application of residue theorem, evaluation of real integrals using complex integration techniques 第18週 6/16 ** 6/16 final exam (according to school’s schedule)