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
Översikt
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Lecture 1 FilPDF-dokument
Course introduction; Systems of linear equations; Gauss-Jordan elimination method
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Lecture 2 FilPDF-dokument
Systems of linear equations in matrix form; Rank of a matrix; Existence and multiplicity of solutions for systems of linear equations
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Lecture 3 FilPDF-dokument
Matrix algebra; Nonsingular and invertible matrices; Determinant of a matrix; Cramer's rule
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Exercise from Lecture 3 (updated 28.9.2021) FilPDF-dokument
This document contains the detailed steps on how to obtain the inverse matrix in the Exercise at the end of Lecture 3
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Lecture 4 (updated 27.9.2021) FilPDF-dokument
Vectors in \( \mathbb{R}^n \); Linear combinations; Linear independence; Basis and dimension of subsets of \( \mathbb{R}^n \)
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Lecture 5 FilPDF-dokument
Functions of several variables; Limits; Continuity; Partial derivatives
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Lecture 6 FilPDF-dokument
Total differential and linear approximations; Open and closed sets; Continuously differentiable functions; Chain rule; Higher-order derivatives and Hessian matrix
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Lecture 7 FilPDF-dokument
Implicit function theorem; Homogeneous functions
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Lecture 8 FilPDF-dokument
Concave and convex functions; Definite and semidefinite matrices
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Lecture 9 (updated 11.10.2021) FilPDF-dokument
Unconstrained optimization; Weierstrass theorem; Local and global extrema
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Lecture 10 FilPDF-dokument
Quadratic forms; Positive monotone transformations
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Lecture 11 (updated 19.10.2021) FilPDF-dokument
L'Hôpital's rule; Infinite series; Review
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Lecture 12 FilPDF-dokument
Two-variable optimization problems with one equality constraint
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Lecture 13 FilPDF-dokument
Optimization problems with n variables and m equality constraints
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Lecture 14 (updated 16.11.2021) FilPDF-dokument
Optimization problems with inequality constraints; Kuhn-Tucker formulation
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Lecture 15 (updated 17.11.2021) FilPDF-dokument
Optimization problems with mixed constraints; Envelope theorems
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Lecture 16 FilPDF-dokument
Envelope theorems; First-order linear difference equations
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Lecture 17 FilPDF-dokument
Systems of first-order linear difference equations; Eigenvalues and eigenvectors
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Lecture 18 FilPDF-dokument
Nonhomogeneous systems of first-order linear difference equations; Repeated and complex eigenvalues
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Exercises from Lecture 18 FilPDF-dokument
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Lecture 19 FilPDF-dokument
First-order ordinary differential equations; Separable first-order differential equations; Linear first-order differential equations
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Lecture 20 FilPDF-dokument
Linear second-order differential equations; Stability
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Lecture 21 FilPDF-dokument
Systems of ordinary differential equations; Stability
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Lecture 22 FilPDF-dokument
Review
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