states and their stability
Phase portraits of systems
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Mathematics for еconomists. (Week 1-12) презентация
Содержание
- 2. Mathematics for Economists II Week #12 Review
- 3. Week 1: Sets: Unions, intersections, Venn Diagrams
- 4. Weeks 3 and 4: Solve simultaneous equations
- 5. Weeks 3 and 4:
- 6. and Eigenvectors!
- 7. and Eigenvectors!
- 8.
- 9. Week 5: Taylor/Maclaurin series Week 6:
- 10. Week 9: The Lagrange multiplier Using multiple
- 11. Mathematics for Economists II Week #12 Review
- 12.
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- 15. Mathematics for Economists II Week #12 Review
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- 25. Mathematics for Economists II Week #12 Review
- 26.
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- 35. Mathematics for Economists II Week #12 Review
- 36.
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- 40. Mathematics for Economists II Week #12 Homework10.docx
Mathematics for Economists II
Week #12 Review Predator-prey relationships Solving simultaneous first order differential equations Steady states and their stability Phase portraits of systems
Слайд 2Mathematics for Economists II
Week #12
Review
Predator-prey relationships
Solving simultaneous first order differential equations
Steady
Слайд 3Week 1: Sets: Unions, intersections, Venn Diagrams Functions: Definition, notation, types Slopes Linear programming Week 2: Derivative
as a limit
Power rule, chain rule, product rule
f'(x), slope, f''(x), concavity
exponential functions, natural logs, TVM
Слайд 4Weeks 3 and 4: Solve simultaneous equations Writing equations in matrix form: Ax
= B
Rules for adding, subtracting, multiplying matrices
Identity matrix: Iij=1 if i=j, and 0 if i≠j
Rank (How many "leading ones"?)
Row operations
Transposed matrices
Calculating determinants
Testing for invertibility and calculating A-1
Cramer's Rule
Eigenvalues
Слайд 9Week 5: Taylor/Maclaurin series Week 6: Quadratics in matrix form Positive/negative definite, positive/negative semidefinite, indefinite
matrices
Week 8:
Unconstrained optimization
The Hessian matrix
Determining max/min from the Hessian definiteness
Слайд 10Week 9: The Lagrange multiplier Using multiple multipliers for multiple constraints Week 10: Kuhn-Tucker inequality
constrained optimization
Jacobian matrix and bordered Hessian
Week 11:
Ordinary differential equations
Integrating factors
Separable differential equations
Слайд 11Mathematics for Economists II
Week #12
Review
Predator-prey relationships
Solving simultaneous first order differential equations
Steady
states and their stability
Phase portraits of systems
Phase portraits of systems
Слайд 15Mathematics for Economists II
Week #12
Review
Predator-prey relationships
Solving simultaneous first order differential equations
Steady
states and their stability
Phase portraits of systems
Phase portraits of systems
Слайд 25Mathematics for Economists II
Week #12
Review
Predator-prey relationships
Solving simultaneous first order differential equations
Steady
states and their stability
Phase portraits of systems
Phase portraits of systems
Слайд 35Mathematics for Economists II
Week #12
Review
Predator-prey relationships
Solving simultaneous first order differential equations
Steady
states and their stability
Phase portraits of systems
Phase portraits of systems
Слайд 40Mathematics for Economists II
Week #12
Homework10.docx due by next Monday
Next week: FINAL
EXAM!
Dobře se bav! :-)
Dobře se bav! :-)
COMPLETE!
