Course title |
Calculus 4 (Applications in Economics and Management) |
Semester |
111-2 |
Designated for |
DEPARTMENT OF ECONOMICS |
Instructor |
SER-WEI 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. |
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Course introduction video |
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Table of Core Capabilities and Curriculum Planning |
Table of Core Capabilities and Curriculum Planning |
Course Syllabus
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Please respect the intellectual property rights of others and do not copy any of the course information without permission
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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 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 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. |
Designated reading |
Carl P. Simon and Lawrence Blume, Mathematics for Economics, Chap. 18-19. |
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 |
Grading |
No. |
Item |
% |
Explanations for the conditions |
1. |
Exam |
50% |
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2. |
Quiz |
20% |
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3. |
Homework |
30% |
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Adjustment methods for students |
Teaching methods |
Assisted by video |
Assignment submission methods |
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Exam methods |
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Others |
Negotiated by both teachers and students |
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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 Kuhn-Tucker 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 (*) |
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