31C01100 - Taloustieteen matemaattiset menetelmät, Luento-opetus, 13.9.2021-17.12.2021
This course space end date is set to 17.12.2021 Search Courses: 31C01100
Topic outline
-
-
Lecture 1 File PDF
Course introduction; Systems of linear equations; Gauss-Jordan elimination method
-
Lecture 2 File PDF
Systems of linear equations in matrix form; Rank of a matrix; Existence and multiplicity of solutions for systems of linear equations
-
Lecture 3 File PDF
Matrix algebra; Nonsingular and invertible matrices; Determinant of a matrix; Cramer's rule
-
Exercise from Lecture 3 (updated 28.9.2021) File PDF
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) File PDF
Vectors in \( \mathbb{R}^n \); Linear combinations; Linear independence; Basis and dimension of subsets of \( \mathbb{R}^n \)
-
Lecture 5 File PDF
Functions of several variables; Limits; Continuity; Partial derivatives
-
Lecture 6 File PDF
Total differential and linear approximations; Open and closed sets; Continuously differentiable functions; Chain rule; Higher-order derivatives and Hessian matrix
-
Lecture 7 File PDF
Implicit function theorem; Homogeneous functions
-
Lecture 8 File PDF
Concave and convex functions; Definite and semidefinite matrices
-
Lecture 9 (updated 11.10.2021) File PDF
Unconstrained optimization; Weierstrass theorem; Local and global extrema
-
Lecture 10 File PDF
Quadratic forms; Positive monotone transformations
-
Lecture 11 (updated 19.10.2021) File PDF
L'Hôpital's rule; Infinite series; Review
-
Lecture 12 File PDF
Two-variable optimization problems with one equality constraint
-
Lecture 13 File PDF
Optimization problems with n variables and m equality constraints
-
Lecture 14 (updated 16.11.2021) File PDF
Optimization problems with inequality constraints; Kuhn-Tucker formulation
-
Lecture 15 (updated 17.11.2021) File PDF
Optimization problems with mixed constraints; Envelope theorems
-
Lecture 16 File PDF
Envelope theorems; First-order linear difference equations
-
Lecture 17 File PDF
Systems of first-order linear difference equations; Eigenvalues and eigenvectors
-
Lecture 18 File PDF
Nonhomogeneous systems of first-order linear difference equations; Repeated and complex eigenvalues
-
Exercises from Lecture 18 File PDF
-
Lecture 19 File PDF
First-order ordinary differential equations; Separable first-order differential equations; Linear first-order differential equations
-
Lecture 20 File PDF
Linear second-order differential equations; Stability
-
Lecture 21 File PDF
Systems of ordinary differential equations; Stability
-
Lecture 22 File PDF
Review
-