31C01100 - Taloustieteen matemaattiset menetelmät, Luento-opetus, 13.9.2021-17.12.2021

Osion kuvaus

• Lecture Slides
  • Valitse aktiviteetti Lecture 1

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 1 Tiedosto PDF

    Course introduction; Systems of linear equations; Gauss-Jordan elimination method

  • Valitse aktiviteetti Lecture 2

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 2 Tiedosto PDF

    Systems of linear equations in matrix form; Rank of a matrix; Existence and multiplicity of solutions for systems of linear equations

  • Valitse aktiviteetti Lecture 3

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 3 Tiedosto PDF

    Matrix algebra; Nonsingular and invertible matrices; Determinant of a matrix; Cramer's rule

  • Valitse aktiviteetti Exercise from Lecture 3 (updated 28.9.2021)

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Exercise from Lecture 3 (updated 28.9.2021) Tiedosto PDF

    This document contains the detailed steps on how to obtain the inverse matrix in the Exercise at the end of Lecture 3

  • Valitse aktiviteetti Lecture 4 (updated 27.9.2021)

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 4 (updated 27.9.2021) Tiedosto PDF

    Vectors in \( \mathbb{R}^n \); Linear combinations; Linear independence; Basis and dimension of subsets of \( \mathbb{R}^n \)

  • Valitse aktiviteetti Lecture 5

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 5 Tiedosto PDF

    Functions of several variables; Limits; Continuity; Partial derivatives

  • Valitse aktiviteetti Lecture 6

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    Lecture 6 Tiedosto PDF

    Total differential and linear approximations; Open and closed sets; Continuously differentiable functions; Chain rule; Higher-order derivatives and Hessian matrix

  • Valitse aktiviteetti Lecture 7

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 7 Tiedosto PDF

    Implicit function theorem; Homogeneous functions

  • Valitse aktiviteetti Lecture 8

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    Lecture 8 Tiedosto PDF

    Concave and convex functions; Definite and semidefinite matrices

  • Valitse aktiviteetti Lecture 9 (updated 11.10.2021)

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 9 (updated 11.10.2021) Tiedosto PDF

    Unconstrained optimization; Weierstrass theorem; Local and global extrema

  • Valitse aktiviteetti Lecture 10

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    Lecture 10 Tiedosto PDF

    Quadratic forms; Positive monotone transformations

  • Valitse aktiviteetti Lecture 11 (updated 19.10.2021)

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 11 (updated 19.10.2021) Tiedosto PDF

    L'Hôpital's rule; Infinite series; Review

  • Valitse aktiviteetti Lecture 12

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    Lecture 12 Tiedosto PDF

    Two-variable optimization problems with one equality constraint

  • Valitse aktiviteetti Lecture 13

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 13 Tiedosto PDF

    Optimization problems with n variables and m equality constraints

  • Valitse aktiviteetti Lecture 14 (updated 16.11.2021)

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 14 (updated 16.11.2021) Tiedosto PDF

    Optimization problems with inequality constraints; Kuhn-Tucker formulation

  • Valitse aktiviteetti Lecture 15 (updated 17.11.2021)

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 15 (updated 17.11.2021) Tiedosto PDF

    Optimization problems with mixed constraints; Envelope theorems

  • Valitse aktiviteetti Lecture 16

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 16 Tiedosto PDF

    Envelope theorems; First-order linear difference equations

  • Valitse aktiviteetti Lecture 17

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    Lecture 17 Tiedosto PDF

    Systems of first-order linear difference equations; Eigenvalues and eigenvectors

  • Valitse aktiviteetti Lecture 18

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    Lecture 18 Tiedosto PDF

    Nonhomogeneous systems of first-order linear difference equations; Repeated and complex eigenvalues

  • Valitse aktiviteetti Exercises from Lecture 18

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    Exercises from Lecture 18 Tiedosto PDF
  • Valitse aktiviteetti Lecture 19

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    Lecture 19 Tiedosto PDF

    First-order ordinary differential equations; Separable first-order differential equations; Linear first-order differential equations

  • Valitse aktiviteetti Lecture 20

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    Lecture 20 Tiedosto PDF

    Linear second-order differential equations; Stability

  • Valitse aktiviteetti Lecture 21

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 21 Tiedosto PDF

    Systems of ordinary differential equations; Stability

  • Valitse aktiviteetti Lecture 22

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Lecture 22 Tiedosto PDF

    Review