Last Modified Jan 29, 2022

Math for Economics Review Notes

Anthony Tay
email: anthonytay at smu.edu.sg

These notes are intended as math review/support notes for students in my BSc and MSc courses at the Singapore Management University. They are incomplete, are updated from time-to-time according to no particular schedule, with new topics added as and when the need arises. They grew out of notes I put together for my students when I taught Intermediate Math for Economics. At the moment the notes cover mainly intermediate calculus and matrix algebra (these two sets can be read independently). These notes are not intended to substitute for any textbook, and draw from several math and math for econ textbooks, including the ones listed below. For more complete coverage, you should go to the textbooks. For math for econ, I highly recommend:

▸Sydsaeter, K., and P. Hammond, Essential Mathematics for Economic Analysis, 5-th ed., FT-Prentice Hall

▸Sydsaeter, K., and P. Hammond, A. Seierstad, and A. Strom, Further Mathematics for Economic Analysis, FT-Prentice Hall

I also recommend calculus and matrix algebra textbooks used in UG math programmes. For matrices, I recommend:

▸Strang, G. Introduction to Linear Algebra, 4th ed., Wellesley-Cambridge Press.

Of course, there are a lot of math for econ resources on the Web which you should explore.

Calculus
▸Introduction ▸Elementary Set Theory, Logic Notation, Proof, etc ▸Summation Notation ▸Solving Simultaneous Equations ▸Functions of One Variable ▸Sequences and Series ▸Limits of a Function ▸Derivatives ▸Elasticities ▸2nd Order Derivatives, Concavity ▸Optimization (one-variable) ▸Linear Approximation ▸L'Hopital's Rule ▸Implicit Differentiation ▸Integration ▸Intro to Differential Equations ▸Functions of Many Variables ▸Partial Derivatives ▸Chain Rule for Functions of Many Variables ▸Multivariable Linear Approximations and Differentials ▸Unconstrained Multivariate Optimization ▸Constrained Optimization

Linear Algebra
▸Matrices: Definitions, Basic Ops ▸Matrix Multiplication ▸Intro to the Inverse Matrix ▸Solving Systems of Linear Equations ▸Finding the Inverse Using Elementary Row Operations ▸Intro to Determinants, Cramer's Rule ▸Laplace Expansion ▸Properties of Determinants ▸Rank and Linear Dependence ▸A Formula for the Inverse ▸Partitioned Matrices ▸Kronecker Product and the Vec Operator ▸Eigenvalues, Eigenvectors ▸Vectors of Random Variables ▸Differentiation of Matrix Forms
See also: ▸Summation Notation ▸Intro to Complex Numbers

Additional Topics
▸Intro to Complex Numbers ▸The Dot Product