Eleven notes covering an introductory mathematics sequence for the social sciences, from functions, limits, and systems of equations through derivatives, optimization, matrix algebra, and the mathematics of saving and borrowing.
The number systems a social science student actually uses, how to solve and read an inequality, and the basic vocabulary of a function: domain, range, and the vertical line test.
Special functions such as the piecewise and absolute value function, combining and composing two functions, inverse functions, and how a translation or reflection reshapes a graph without changing its underlying rule.
Reading the slope of a line as a marginal cost, then building up to the limit of a function and the continuity that makes the rest of calculus possible.
The parabola as a model of revenue and cost, solving linear and nonlinear systems of equations, and two worked applications: market equilibrium with a tax and the break even point of a firm.
From the formal definition of the derivative to the product, quotient, and chain rules, with marginal cost, marginal revenue, and marginal profit as the running example.
Using the first and second derivative tests to find where a function is increasing, decreasing, or at its best possible value, worked through real revenue, cost, and profit problems.
Compound interest, continuous compounding, and present value, all built on the exponential and logarithmic functions that make them work.
What changes when a function depends on two variables instead of one, and how the second partials test finds a maximum, a minimum, or a saddle point.
Sequences, infinite series, and the geometric series in particular, the mathematics behind a monthly savings plan, a loan, and a depreciating asset.
The future and present value of an ordinary annuity and an annuity due, how a loan payment is built from the same formulas, and the sinking fund that saves toward a future replacement cost.
Organizing data into matrices, representing a system of equations as a single matrix equation, solving by row reduction, and using the inverse of a matrix to solve for the unknowns directly.