| Section |
Content |
| 1. Introduction & Set Theory |
- Introduction to new course and teaching arrangement
- Chapter 1: Sets, Sequences and Vector Spaces - §1.1 Sets: Sets, Operations on Sets
|
| 2. Sets & Sequences |
- Chapter 1: Sets, Sequences and Vector Spaces - §1.1 Sets: Power sets, Relations, Functions
- Supremum and infimum of real number sets
- §1.2 Sequences and Convergence: Sequences
|
| 3. Sequences and Convergence |
- §1.2 Sequences and Convergence: Sequences, Convergence
|
| 4. Vector Spaces |
- §1.3 Vector Spaces: n-dimensional vectors, Vector operations, Euclidean space
|
| 5. Vector Spaces & Consumption-Production |
- §1.3 Vector Spaces: Convex sets and convex functions
- Chapter 2: Consumption and Production - §2.1 Consumer Behavior: Commodity space and consumption set
|
| 6. Consumer & Producer Behavior |
- Flipped Classroom (1): Lexicographic order
- Chapter 2: Consumption and Production - §2.1 Consumer Behavior: Preferences and utility functions, Budget sets, Demand sets
- §2.2 Generalized Preferences: Preference relations, Revealed preferences
- §2.3 Producer Behavior: Production sets, Firm profit, Supply sets and profit functions
|
| 7. Production Technology & Linear Programming |
- Convexity of production technology, Law of returns to scale
- Chapter 3: Linear Programming and Industrial Linkages - §3.1 Linear Programming Method: Linear programming problems
- §3.2 Input-Output Analysis: Industrial linkage theory, Non-negative matrices
|
| 8. Differentiation & Maximum Conditions |
- §4.2 Differentiation: Univariate differentiation, Partial and total differentiation, Differentiation of composite functions under general conditions
- §4.3 Second-order Differentiation: Slope and Hessian matrix, Definition of second-order differentiation, Properties of convex and concave functions
- Chapter 5: Maximum Conditions - §5.2 Applications of Maxima in Economics: Marginal productivity, Average cost and marginal cost, Golden rule of economic growth
|
| 9. Continuity & Differentiation |
- Chapter 6: Continuity and Differentiation - §4.1 Continuity and Some Topological Concepts: Concept of continuity
|
| 10. Differentiation & Maximum Applications |
- §4.2 Differentiation: Univariate differentiation, Partial and total differentiation, Differentiation of composite functions under general conditions
- §4.3 Second-order Differentiation: Slope and Hessian matrix, Definition of second-order differentiation, Properties of convex and concave functions
- Chapter 5: Maximum Conditions - §5.2 Applications of Maxima in Economics: Marginal productivity, Average cost and marginal cost, Golden rule of economic growth
|
| 11. Economic Growth & Flipped Classroom |
- Golden rule of economic growth (2)
- Flipped Classroom (2): Monopoly and oligopoly markets
|
| 12. Demand Function |
- Chapter 6: Demand and Supply - §6.1 Demand Function: Demand function, Minimum expenditure function, Compensated demand function
|
| 13. Slutsky Equation |
- §6.2 Slutsky Equation: Roy's identity, Slutsky equation
|
| 14. Utility Maximization |
- Roy's identity, Utility maximization conditions
|
| 15. Supply Function & Cost Function |
- §6.3 Supply Function: Production sets and prices, Properties of supply functions (Hotelling's lemma)
- §6.4 Cost Functions and Factor Demand: Cost minimization
|
| 16. Cost Minimization & Review |
- Cost minimization (2) (Shephard's lemma)
- Review guidance for final examination
|
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Professor Li Xiaochun is truly a kind and patient scholar. During lectures, he never forces us to absorb knowledge superficially due to slow progress, but instead explains each theorem in detail until we fully comprehend it. I sincerely feel fortunate to be one of Professor Li’s students in his classroom.
