Chapter 1

Differential Equations

First-order differential equations

medium • 1 min read

Qualitative theory and stability analysis

medium • 2 min read

Phase diagrams

medium • 3 min read

Applications to continuous time economic models

medium • 4 min read

Solow growth model and its dynamics

medium • 5 min read

Chapter 2

Linear Algebra

Vector spaces: algebraic and geometric properties

medium • 1 min read

Matrix operations and properties

medium • 2 min read

Determinants and their properties

medium • 3 min read

Systems of linear equations

medium • 4 min read

Eigenvalues and eigenvectors

medium • 5 min read

Chapter 3

Functions of Several Real Variables

Geometric representations: graphs and level curves

medium • 1 min read

Partial derivatives and directional derivatives

medium • 2 min read

Differentiability and the total derivative

medium • 3 min read

Implicit function theorem and comparative statics

medium • 4 min read

Homogeneous and homothetic functions

medium • 5 min read

Chapter 4

Multi-Variable Optimization

Unconstrained optimization: local and global extrema

medium • 1 min read

First and second-order conditions in multivariable analysis

medium • 2 min read

Constrained optimization with equality constraints

medium • 3 min read

Lagrange multipliers and envelope theorem

medium • 4 min read

Optimization with inequality constraints (Kuhn-Tucker conditions)

medium • 5 min read

Chapter 5

Dynamics and Economic Applications

Systems of differential equations

medium • 1 min read

General phase plane analysis

medium • 2 min read

Stability of equilibrium states

medium • 3 min read

Economic application to multi-market models

medium • 4 min read

Intertemporal optimization in economics

medium • 5 min read