Course title 
Calculus 4 (Applications in Economics and Management) 
Semester 
1112 
Designated for 
DEPARTMENT OF ECONOMICS 
Instructor 
SERWEI FU 
Curriculum Number 
MATH4010 
Curriculum Identity Number 
201E49850 
Class 
01 
Credits 
2.0 
Full/Half Yr. 
Half 
Required/ Elective 
Required 
Time 
第9,10,11,12,13,14,15,16 週 Monday 3,4(10:20~12:10) Thursday 3,4,10(10:20~18:20) 
Remarks 
Restriction: within this department (including students taking minor and dual degree program) The upper limit of the number of students: 130. 


Course introduction video 

Table of Core Capabilities and Curriculum Planning 
Table of Core Capabilities and Curriculum Planning 
Course Syllabus

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Course Description 
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, 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 KuhnTucker 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 optimization problems in Economics 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. 
Course Objective 
Students would be familiar with Calculus as a tool and be able to apply it to derive important economic theories. 
Course Requirement 
Students participating in the course should have taken Calculus 1, 2, and 3.
They are expected to attend and participate actively in lectures as well as discussion sessions. 
Student Workload (expected study time outside of class per week) 
At least 4 hours. 
Office Hours 
Appointment required. Note: Office hours will be announced after the semester starts. Discussions before/after class or via email are welcomed. 
References 
1. James Stewart, Calculus Early Transcendentals, 9th edition.
2. Carl P. Simon and Lawrence Blume, Mathematics for Economics.
3. Michael W. Klein, Mathematical Methods for Economics.
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 
Designated reading 
Carl P. Simon and Lawrence Blume, Mathematics for Economics, Chap. 1819. 
Grading 
No. 
Item 
% 
Explanations for the conditions 
1. 
Exam 
50% 

2. 
Quiz 
20% 

3. 
Homework 
30% 


Adjustment methods for students 
Teaching methods 
Assisted by video 
Assignment submission methods 

Exam methods 

Others 
Negotiated by both teachers and students 

Week 
Date 
Topic 
Week 9 
4/17, 4/20 
Vectors and Spans (Linear Independence, Dimension)
Matrix (Row/Column Space, Rank, Determinant) 
Week 10 
4/24, 4/27 
Eigenvalues and Eigenvectors
Symmetric Matrices 
Week 11 
5/1, 5/4 
Definiteness of Quadratic Forms 
Week 12 
5/8, 5/11 
18.1 Constrained Optimization: Examples
18.2 Constrained Optimization: Equality Constraints
18.3 Constrained Optimization: Inequality Constraints 
Week 13 
5/15, 5/18 
18.4 Constrained Optimization: Mixed Constraints
18.5 Constrained Minimization Problems
18.6 KuhnTucker Formulation 
Week 14 
5/22, 5/25 
19.1 The Meaning of the Multiplier
19.2 Envelope Theorems 
Week 15 
5/29, 6/1 
19.3 Constrained Optimization: Second Order Conditions
19.5 Constraint Qualifications (*) 
Week 16 
6/5, 6/8 
19.6 Proofs of First order conditions (*) 
