Mathematics for Information Science-1

Limits revisited with the formal definition and one-sided tests, continuity and its failure modes, the derivative built as a limit of difference quotients, and linear approximation extended to Taylor series. Everything later in the course rests on this module, which is why it starts from the definitions rather than the rules.

Functions of two variables, seen through graphs, level curves and contours; limits and continuity extended to the plane, where the path you approach along starts to matter; and partial derivatives as the rate of change in one variable with the others held still.

The chain rule extended to compositions and to several variables, the gradient as the vector form of the derivative, directional derivatives, and the second-derivative test that classifies critical points as maxima, minima or saddles.

Optimisation once the variables are no longer free: elimination of a variable, Lagrange multipliers, iterative descent by following the negative gradient, and linear programming solved graphically and by the simplex procedure.