課程大綱

課程資訊

課程名稱

應用數學上
Applied Mathematics (1)

開課學期

112-2

授課對象

理學院物理學系

授課教師

吳俊輝

課號

Phys2024

課程識別碼

202 20411

班次

學分

3.0

全/半年

全年

必/選修

必帶

上課時間

星期二8,9,10(15:30~18:20)

上課地點

新物111

備註

限本系所學生(含輔系、雙修生)
總人數上限：80人
外系人數限制：2人

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課程概述

This course is the first part of two which provide the foundation of mathematical methods commonly needed in the study of physics.

課程目標

This is to prepare for the students majoring in physics.
Dates for lecture series I (21 lectures): 2/20, 2/27, 3/5, 3/12, 3/19, 3/26, 4/2
Date of mid-term exam: 4/9
Dates for lecture series II (21 lectures): 4/16, 4/23, 4/30, 5/7, 5/14, 5/21, 5/28
Date of final exam: 6/4

課程要求

There will be a mid-term exam and a final exam following the university calendar.
Homework will not be graded but with the support from the TA.
The attendance is not required.

預期每週課後學習時數

Office Hours

每週五 13:20~14:10 備註：新物 111 助教：黃福祥(Fu-Hsiang Huang) r10222098@g.ntu.edu.tw (Office: 615, Office time: Anytime, if I'm free), 吳安基 r12222068@ntu.edu.tw

指定閱讀

The lecture materials are compiled from various books in the reference list. The students should refer to whatever suitable for their needs.

參考書目

G. Arfken and H. J. Weber (2005). Mathematical Methods for Physi- cists, 6th edition. Academic Press.
Strang/ Introduction to Linear Algebra International Edition.
E Kreyszig (2011). Advanced Engineering Mathematics, 8th edition. Wiley (10th edition available).
K F Riley, M P Hobson & S J Bence (2002). Mathematical Methods for Physics and Engineering. 3rd ed., Cambridge University Press. (Available online via http://idiscover.lib.cam.ac.uk).
J W Dettman (1988). Mathematical Methods in Physics and Engineering. Dover (Dover Books on Physics).

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	Mid-term exam	50%	The exam date follows the university calendar, unless otherwise announced.
2.	Final exam	50%	The exam date follows the university calendar, unless otherwise announced.

課程進度

週次	日期	單元主題
第1-16週		Linear Algebra (6 weeks) Linear vector spaces. Matrices, determinants and traces. Minors, cofactors, and inverse of a matrix. Orthogonal transformation, rotations, reflections, similarity transformation, and Wronskian. Hermitian, anti-Hermitian, unitary, adjoint operator, and unitary transformation. Inner product (scalar product) and other products of vectors and matrices. Linear equations. Diagonalisation, eigenvalues and eigenvectors. Quadratic and Hermitian forms. Stationary property of the eigenvalues. Orthogonality relations for sine and cosine. Fourier series. (1 week) ODE (2 weeks) First order equations: separable equations; linear equations, integrating factors. Examples involving substitution. Second-order linear equations with constant coefficients; exp (ax) as trial solution, including degenerate case. Superposition. Particular integrals and complementary functions. Constants of integration and number of necessary boundary/initial conditions. Particular integrals by trial solutions. Examples including radioactive sequences. Resonance, transients and damping. PDE (1 week) Linear second-order partial differential equations; physical examples of occurrence, verification of solution by substitution. Linear superposition. Method of separation of variables (Cartesian coordinates only). Vector calculus (1 week) Suffix notation. Einstein summation convention. Contractions using δij and εijk. Reminder of vector products, grad, div, curl, del2, and their representations using suffix notation. Vector differential operators in orthogonal curvilinear coordinates, e.g. cylindrical and spherical polar coordinates. Jacobians. Green’s functions (1 week) Response to impulses, delta function (treated heuristically), Green's functions for initial and boundary value problems. Fourier transform (1 week) Fourier transforms; relation to Fourier series, simple properties and examples, convolution theorem, correlation functions, Parseval's theorem and power spectra. Elementary probability theory (1 week) Discrete probability distribution: binomial, Poisson. Continuous probability distribution: uniform, lifetime, Gaussian (normal), chi-square. Central limit theorem. Error types. Likelihood analysis. Moments and cumulants.