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

Osion kuvaus

• Lecture Slides
  • 

    Lecture 1 Tiedosto

    Pdf-tiedosto

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

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

  • 

    Lecture 2 Tiedosto

    Pdf-tiedosto

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

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

  • 

    Lecture 3 Tiedosto

    Pdf-tiedosto

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

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

  • 

    Exercise from Lecture 3 (updated 28.9.2021) Tiedosto

    Pdf-tiedosto

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

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

  • 

    Lecture 4 (updated 27.9.2021) Tiedosto

    Pdf-tiedosto

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

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

  • 

    Lecture 5 Tiedosto

    Pdf-tiedosto

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

    Functions of several variables; Limits; Continuity; Partial derivatives

  • 

    Lecture 6 Tiedosto

    Pdf-tiedosto

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

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

  • 

    Lecture 7 Tiedosto

    Pdf-tiedosto

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

    Implicit function theorem; Homogeneous functions

  • 

    Lecture 8 Tiedosto

    Pdf-tiedosto

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

    Concave and convex functions; Definite and semidefinite matrices

  • 

    Lecture 9 (updated 11.10.2021) Tiedosto

    Pdf-tiedosto

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

    Unconstrained optimization; Weierstrass theorem; Local and global extrema

  • 

    Lecture 10 Tiedosto

    Pdf-tiedosto

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

    Quadratic forms; Positive monotone transformations

  • 

    Lecture 11 (updated 19.10.2021) Tiedosto

    Pdf-tiedosto

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

    L'Hôpital's rule; Infinite series; Review

  • 

    Lecture 12 Tiedosto

    Pdf-tiedosto

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

    Two-variable optimization problems with one equality constraint

  • 

    Lecture 13 Tiedosto

    Pdf-tiedosto

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

    Optimization problems with n variables and m equality constraints

  • 

    Lecture 14 (updated 16.11.2021) Tiedosto

    Pdf-tiedosto

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

    Optimization problems with inequality constraints; Kuhn-Tucker formulation

  • 

    Lecture 15 (updated 17.11.2021) Tiedosto

    Pdf-tiedosto

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

    Optimization problems with mixed constraints; Envelope theorems

  • 

    Lecture 16 Tiedosto

    Pdf-tiedosto

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

    Envelope theorems; First-order linear difference equations

  • 

    Lecture 17 Tiedosto

    Pdf-tiedosto

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

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

  • 

    Lecture 18 Tiedosto

    Pdf-tiedosto

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

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

  • 

    Exercises from Lecture 18 Tiedosto

    Pdf-tiedosto

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

    Lecture 19 Tiedosto

    Pdf-tiedosto

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

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

  • 

    Lecture 20 Tiedosto

    Pdf-tiedosto

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

    Linear second-order differential equations; Stability

  • 

    Lecture 21 Tiedosto

    Pdf-tiedosto

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

    Systems of ordinary differential equations; Stability

  • 

    Lecture 22 Tiedosto

    Pdf-tiedosto

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

    Review