10802 自然科學學群 物理學系

應用數學入門〡遠距版

林秀豪 教授

物理學系
國立清華大學物理系      特聘教授 
美國加州大學聖塔芭芭拉分校物理       博士

【榮譽】 國立清華大學95、99、102校傑出教學獎
【網站】 https://reurl.cc/01abY9
【研究 統計場論  結合理論建模、數值模擬、機器學習等研究工具,
   興趣】 應用於凝態物理、材料科學、網絡動力學、計算神經科學、醫學影像分析
  等研究課題。

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Syllabus

課程大綱

Applied Mathematics is a two-semester course, emphasizing the basic mathematical training encountered in science and engineering. 
 
 
 
課程簡述
Brief course description 
Applied Mathematics is a two-semester course, emphasizing the basic mathematical training encountered in science and engineering. Facing the modern frontiers with brand-new challenges, the course contains the following key modules:
 It is important to maintain the balance between mathematical rigor and hands-on applications. Meanwhile, the last module (numerical methods) will be integrated into other modules to facilitate complementary usage of analytic and numeric techniques.

(1)

Complex Analysis
(2)

 Partial Derivative

(3) Linear Algebra
(4) Quantum Operators
(5) Fourier Transform
(6) Vector calculus
 
  
 
 
課程大綱
Syllabus 
Syllabus for Applied Mathematics (2020)
Applied Mathematics is a two-semester course, emphasizing the basic mathematical training encountered in science and engineering. Facing the modern frontiers with brand-new challenges, the course contains the following key modules: 
(1)  Preliminary
(2)  Partial differentiation
(3) Matrices and vector spaces
(4) Vector calculus
(5) Ordinary differential equations
(6) Integral transforms
(7)  Operators and special functions
(8) Partial differential equations
(9)  Probability and statistics
(10)  Numerical methods
It is important to maintain the balance between mathematical rigor and hands-on applications. Meanwhile, the last module (numerical methods) will be integrated nto other modules to facilitate complementary usage of analytic and numeric techniques.

 
 
Textbook
Mathematical Methods for physics and engineering (3rd edition)
  by Riley, Hobson and Bence
 
 
 In the first semester, we will cover the following key modules subjected
      to dynamical readjustments:
(1) Preliminary (4 lectures) – chap 1,2,3,4
(2)  Partial differentiation (2 lectures) – chap 5
(3) Matrices and vector spaces (8 lectures) – chap 7,8,9
(4) Vector calculus (6 lectures) – chap 10,11
 (5) ntegral transforms (4 lectures) – chap 12,13
 (6)  Ordinary differential equations (6 lectures) 
  – chap 14,15,16
   

 

 
 
 

 

Keyword

關鍵字

  • applied mathematics
  • partial differentiation
  • matrices
  • vector calculus
  • ordinary differential equations
  • numerical methods

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林秀豪 教授

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