Math for economyMM1005

How to find your way

  1. 1Search for the word that confuses you — the box at the top searches the whole course.
  2. 2Look it up in Concepts. Every concept links to the section that explains it. Concepts →
  3. 3Read the Watch out and Common error boxes: they show the mistakes that are actually made.
  4. 4Still stuck? Bring the question to the exercise session or send an email.

Lecturer: Eric Ahlqvist, eric.ahlqvist@math.su.se · Put “MM1005” in the subject line.
Prototype · for HT27

Mathematics for Economy and Statistical Analysis MM1005

The whole course in one place: the theory with figures and animations, the Facts with the reason behind each, problems that are checked instantly, and exam problems with full solutions. One lecture is one day's reading, and every lecture has two pages: Theory and Problems.

Start with lecture 1 →
  • 15lectures
  • 335problems
  • 169concepts
  • 81facts

Course path

One variable

  1. 1

    Linear, quadratic and polynomial functions

    • Linear functions
    • Quadratic functions
    • Polynomials
    Theory6 sections · 60 min Problems21
  2. 2

    Powers, exponentials, logarithms, and the derivative

    • Power functions
    • Exponential functions
    • Logarithms
    • The derivative
    • Increasing and decreasing functions
    Theory6 sections · 60 min Problems21
  3. 3

    The rules of differentiation

    • Limits
    • The rules that need no thought
    • Products and quotients
    • The chain rule
    • Higher-order derivatives
    Theory6 sections · 60 min Problems23
  4. 4

    Exponentials, logarithms, and approximation

    • The exponential function, and why $e$
    • The logarithm
    • Implicit differentiation
    • Linear approximation
    • Taylor polynomials
    Theory6 sections · 70 min Problems23
  5. 5

    The error term, limits, and $0/0$

    • The price of an approximation
    • Limits, properly
    • Continuity, and the licence to substitute
    • Reading the signal: l'Hôpital's rule
    Theory6 sections · 65 min Problems22
  6. 6

    Existence, and where to look

    • A sign change forces a root
    • Newton's method
    • Existence again: the extreme value theorem
    • Where to look
    • When a candidate is the answer
    Theory6 sections · 65 min Problems22
  7. 7

    Shape, and then turning round

    • Local extreme points
    • Inflection points
    • Turning round
    • The surprise: it measures area
    • Integration by parts
    Theory5 sections · 70 min Problems24

Series and two variables

  1. 8

    Infinite totals, and a second variable

    • Substitution: the last integration rule
    • Infinite totals
    • A second variable
    • Partial derivatives
    • Differentiating twice
    Theory6 sections · 75 min Problems32
  2. 9

    Contour maps, and walking on them

    • The map
    • What economists actually draw
    • More variables
    • Walking across the map
    • Walking along a contour
    Theory6 sections · 60 min Problems22

Optimisation

  1. 10

    Two directions are not enough

    • Where a maximum can be
    • What the firm's rule says
    • Concavity in two variables
    • What a constraint does
    Theory6 sections · 65 min Problems21
  2. 11

    Local extrema, existence, and constrained optimisation

    • Local extreme points
    • The second-derivative test
    • Existence: the extreme value theorem
    • The Lagrange multiplier method
    • Interpreting the multiplier
    Theory6 sections · 75 min Problems21

Matrices

  1. 12

    Matrices, vectors, and the algebra of linear systems

    • Matrices and vectors
    • Systems of linear equations
    • Addition and scalar multiples
    • Vectors and the inner product
    • Matrix multiplication
    Theory6 sections · 55 min Problems21
  2. 13

    Rules, the transpose, and solving the system

    • Rules for matrix multiplication
    • The identity matrix
    • Three rules that do not survive
    • The transpose
    • Gaussian elimination
    • The shape of the solution set
    Theory6 sections · 70 min Problems20
  3. 14

    Determinants and the inverse

    • Determinants of order 2
    • Determinants of order 3
    • The inverse of a matrix
    • Solving the system with the inverse
    Theory6 sections · 60 min Problems23
  4. 15

    One array, four questions

    • The method, and where the marks go
    • Finding the inverse by row operations
    • Many right-hand sides at once
    • Which tool for which question
    Theory6 sections · 55 min Problems19