Number of Credits: 3 (Theory: 2, Exercises: 1) – Time Distribution: 15 Weeks

Goal description (This course equips students with)

Head standard

out CDIO

Output standard

Training

G1

Basic knowledge of: Matrix, determinant, system of linear equations, derivative, differential, differential equation

fractions and their applications in economics.

1.1, 1.2

ELO2

G2

Modeling, analysis and reasoning skills to solve practical problems in economics applying advanced mathematics;

Creative thinking skills, critical thinking;

Skills in using advanced math problem solving software applied in economics;

Self-study skills, reading documents according to teacher's instructions.

2.1, 2.2,

2.4

ELO2

G3

Teamwork, communication and presentation skills to explain problems in groups as well as in front of the class.

2.5,

3.1,3.2

ELO2

Describe

(After completing this course, students will be able to)

CDIO output standard

G1

1

State the concept of matrix and determinant

1.2

2

Recognize linear equations.

1.2

3

Understand market equilibrium models, Leontief input/output models,

IS-LM model

1.2

4

Understand the concept of function, derivative, differential

1.2

5

Understand the concepts of average, margin, and elasticity

1.2

6

The statement defines partial derivatives and differentials of functions of two variables.

1.2

7

Write algorithms to find maximum, minimum, largest and smallest values

of two variable functions

1.2

8

State the concepts of indefinite integral and definite integral.

1.2

9

State the concept of first-order and second-order differential equations.

1.2

10

Present the steps to find the solutions of some differential equations.

1st and 2nd order differential equations and applied differential equations in economics.

1.2

G2

1

Perform matrix operations, calculate determinants, and perform elementary transformations.

rank, find matrix rank, find inverse matrix

2.1; 2.2

2

Application of matrix operations in economics

2.1

3

Solve and discuss linear equations

2.1;2.2

4

Application of linear equations to equilibrium models

market, Leontief input/output model, IS-LM model

2.1

5

Survey and draw graphs of explicit functions. Calculate limits and examine connectivity.

continuity, derivative of functions, approximation

2.1;2.2

6

Application of differential calculus of functions of one variable in economics

2.1

7

Calculate limits, partial derivatives and find extreme values, maximum and minimum values

first,... of a function of two variables

2.1;2.2

8

Model and solve extreme value problems in economics such as: extreme

maximize profits, minimize costs.

2.1

9

Calculate integrals applied in economics

2.1

10

Applying theoretical methods to find general solutions,

Particular solutions of some types of first-order and second-order differential equations and types of differential equations in economics.

2.1

11

Modeling skills using the language of Mathematics from there

Solve practical problems in economics

2.1.6

12

Creative thinking skills, critical thinking

2.4.7;

2.4.8

13

Skills to apply advanced mathematical knowledge in practical business practice

economy

2.2.5

14

Have the ability to read and study the self-study sections in the documents

teacher requested

2.4.15

G3

1

Have a positive attitude of cooperation with teachers and other students during learning and doing homework.

2.5, 3.1,

3.2

2

Assign work within a team effectively.

3.2.6

3

Ability to present and report group work results in front of the class

class.

3.2.5

Content

Time

KT Tools

KT output standard

Ratio (%)

Self-study

40

KT1

Matrix – Determinant – System of Linear Equations

Week 5

Small homework in class

G1.1, G1.2,

G1.3, G2.1,

G2.2, G2.3, G2.11, G2.13

10

KT2

Calculus

Week 10

Small homework in class

G1.4, G1.5,

G1.6, G2.5,

G2.6, G2.7, G2.11,

G2.13

10

Do group exercises at home

G3.1, G3.2,

G3.3

20

Final exam

60

- The content covers important output standards of the subject.

- Test time 90 minutes.

End of term

Content

Teaching methods

HP output standard

1

Chapter I. Matrix and Determinant

1.1. Basic concepts of matrices

1.1.1. Matrix concept

1.1.2. Matrix Classification

1.1.3. Relationship between matrices

1.2. Operations with matrices

1.2.1. Matrix addition

1.2.2. Multiplication of a number with a matrix

1.2.3. Multiplication of two matrices

- Lecture

- Presentation

- Brainstorming

G1.1,

G2.1,

G2.2, G2.12

2

Chapter I (cont.)

1.3. Matrix transformations, step matrices

1.3.1. Elementary transformations on rows of a matrix

1.3.2. Step matrix

1.4. Inverse matrix

1.4.1. Concept of inverse matrix

1.4.2. Properties of the inverse matrix

1.4.3. Algorithm for finding the inverse matrix

1.4.4. Matrix equations

1.4.5. Some applications of matrices in economics

- Lecture

- Presentation

- Brainstorming

G1.1,

G2.1,

G2.2,

G2.11, G2.12

Chapter I (cont.)

1.5. Determinant

1.5.1. Concept of determinant

1.5.2. Properties of determinants

1.6. Some applications of determinants

1.6.1. Invertibility conditions and how to find the invertible matrix

1.6.2. Rank of the matrix

- Lecture

- Presentation

- Brainstorming

- Think in pairs

G1.1,

G2.1,

G2.2, G2.12

4

Chapter II. Systems of Linear Equations

2.1. Basic concepts

2.1.1. General linear equation system

2.1.2. Coefficient matrix and additional matrix

2.1.3. Solutions of linear equations

2.1.4. Equivalent systems and equivalent transformations

2.1.5. Conditions for existence of solution

2.1.6. Matrix form of linear equation system

2.2. Solve linear equations

2.2.1. Gramer system – Gramer method

2.2.2. Triangular system of equations

2.2.3. Stepwise system of equations

2.2.4. General form of equation system – Gauss method

- Lecture

- Presentation

- Brainstorming

- Think, pair, share

G1.2,

G2.3,

G2.4, G2.12

5

Chapter II (cont.)

2.3. Homogeneous linear equation system

2.3.1. Concept

2.3.2. Solution

2.3.3. Solve the system of equations

2.3.4. Homogeneous linear equation system

2.4. Some linear models in economics

2.4.1. Simple market equilibrium model

2.4.2. General market equilibrium model

2.4.3. Leontief Input – Output Model

2.4.4. Leontief exchange model

- Lecture

- Presentation

- Brainstorming

- Think, pair, share

G1.2,

G1.3,

G2.3,

G2.4,

G2.11, G2.13

6

Chapter 1, 2 exercises

- Teamwork

G1.2,

G1.3,

G2.3,

G2.4,

G2.11,

G2.13,

G2.14,

G3.1, G3.2, G3.3

Chapter III. Differential Calculus of Functions

3.1. Derivative of a function at a point

3.1.1. Concept

3.1.2. One-sided derivative

3.1.3. Infinite derivatives

3.1.4. Geometric meaning of derivative

3.2. Derivative of a function in an interval

3.2.1. Concept

3.2.2. Derivatives of basic elementary functions

3.2.3. Rules for calculating derivatives

3.2.4. Higher derivatives

- Lecture

- Presentation

- Problem solving

G1.4, G2.5, G2.6

8

Chapter III (cont.)

3.3. Differential of functions

3.3.1. Concept

3.3.2. Differential expressions

3.3.3. Higher-order differential

3.4. Applications of derivatives and differentials

3.4.1. Investigation of monotonicity of functions

3.4.2. Survey of extreme values ​​of functions

3.4.3. Find the largest and smallest values

3.4.4. Using differentiation for approximation

3.5. Applications of derivatives and differentials in economics

3.5.1. Economic significance of derivatives

3.5.2. The problem of finding the output level to maximize profit

3.5.3. The problem of finding the optimal level of labor utilization

- Lecture

- Do group exercises in class

- Guide to teamwork skills

G1.4,

G1.5,

G2.5,

G2.6,

G2.11, G2.13

9

Chapter III (cont.)

3.6. Differentiation of functions of two variables

3.6.1. Concept of partial derivatives

3.6.2. Differential concept

3.7. Bivariate function

3.7.1. Concept

3.7.2. Extreme value survey

3.7.3. Find the smallest and largest values

3.8. Application of differential functions of two variables in economics

3.8.1. Meaning of partial derivatives in economics

3.8.2. The problem of finding the output level to maximize profit

3.8.3. Input selection problem to maximize profit

3.8.4. Product distribution problem to maximize profit

- Lecture

- Do group exercises in class

- Guide to teamwork skills

G1.6,

G1.7,

G2.7,

G2.8,

G2.11, G2.13

Chapter 3 exercises

Ask the group to present the results to the class.

G1.4,

G1.5,

G1.6,

G1.7,

G2.7,

G2.8,

G2.11,

G2.14,

G3.1, G3.2, G3.3

11

Chapter IV. Integral Calculus

4.1. Indefinite integral

4.1.1. Concept

4.1.2. Some basic integrals

4.1.3. Integration of rational functions

4.1.4. Variable transformation method

4.1.5. Method of integration by parts

- Lecture

- Presentation

G1.8, G2.5 G2.6

12

Chapter IV(cont.)

4.2. Definite integral

4.2.1. Basic concepts

4.2.2. Newton-Leibnitz formula

4.2.4. Variable transformation method

4.2.5. Method of integration by parts

4.2.6. Application of integration in economics

- Lecture

- Do group exercises in class

- Guide to teamwork skills

G1.8,

G2.9,

G2.13,

G3.1,

G3.2, G3.3

13

Chapter V. Differential Equations

5.1. First order differential equations

5.1.1. Basic concepts

5.1.2. Separating variable equation

5.1.3. Class Equation

5.1.4. Linear equations

- Lecture

- Presentation

G1.9,

G1.10, G2.10

14

5.2. Second-order differential equations

5.2.1. Basic concepts

5.2.2. Reduced second-order equations

5.2.3. Second-order linear equation with constant coefficients

5.2.4. Some applications of differential equations in economics

- Lecture

- Do group exercises in class

G1.9,

G1.10,

G2.10, G2.13

15

Exercises chapter 4, 5.

n sets

- Lecture

- Do group exercises in class

G1.9,

G1.10,

G2.10,

G2.14,

G3.1,

G3.2, G3.3