微積分4-在經濟商管的應用

這是一門半學期的課，主題是限制條件下的最佳化問題，目的是裝備學生用微積分工具探討重要的經濟學議題。
課程前三周簡介處理最佳化問題所需的線性代數工具；內容包含矩陣的秩、行列式、特徵值與特徵向量，和對稱矩陣的正負定性。
最佳化問題討論在等式限制條件，不等式限制條件，與混和限制條件下求目標函數極值的解法。同時我們還介紹Kuhn-Tucker陳述式，說明 Lagrange 乘子的意義(影子價格)，推導包絡定理，並講解限制條件下的二階微分測試，以判斷臨界點是局部極大或極小值。
課堂上將講解定義並推導重要定理，以培養學生邏輯推理與分析能力；同時會示範最佳化問題在經濟學的應用，幫助學生將微積分與專業科目結合。本課程還設有習題課，學生將在助教的帶領下熟練微積分的計算。

The goal of this course is to employ tools from Calculus and develop mathematical theory to tackle important problems, specifically constrained optimization problems, in Economics.

We shall begin with a crash course in linear algebra. We will define the rank, determinant, eigenvalues and eigenvectors, and definiteness of matrices. These concepts will be used to solve optimization problems with equality or inequality constraints (or a mix of both). Then we proceed to discuss the Kuhn-Tucker formulation, the economic interpretation of Lagrange multipliers as shadow prices, the envelope theorem and the second order test under constraints which determine the nature of a critical point.
 
Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides discussion sessions in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants.

其他相關資訊 
微積分統一教學網站: http://www.math.ntu.edu.tw/~calc/Default.html

台大微積分考古題:  http://www.math.ntu.edu.tw/~calc/cl_n_34455.html

數學知識網站: http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal 

免費線上數學繪圖軟體Desmos Calculator: https://www.desmos.com/calculator 

免費知識型計算引擎: https://www.wolframalpha.com  」