PAU Applied Math ACS II (Galicia) study plan

Compute 2x2 and 3x3 determinants by cofactor expansion and by the rule of Sarrus, and state when a matrix is invertible from its determinant.

Calculate the inverse of a 3x3 matrix using the adjugate method and verify the result by multiplying to get the identity.

Determine the rank of a matrix by Gaussian elimination, identifying the number of linearly independent rows.

Classify a square system of linear equations as compatible determined, compatible indeterminate, or incompatible using Rouché–Fröbenius (rank of coefficient matrix versus augmented matrix).

Solve a system with one parameter using Gaussian elimination and express the solution set in terms of the parameter.

Apply Cramer's rule to a 3x3 compatible determined system and justify when Cramer's rule is valid.

Model a small word problem (e.g. a mixture or cost-allocation problem) as a linear system and solve it.

Detect and correct common sign and arithmetic errors by checking solutions in the original equations.

Compute limits of rational and piecewise functions at a point and at infinity, resolving 0/0 and infinity/infinity indeterminacies.

Determine the domain and the points of discontinuity of a piecewise-defined function and classify each discontinuity.

Apply the definition of continuity at a point and find the value of a parameter that makes a piecewise function continuous.

Differentiate using the product, quotient, and chain rules, and compute derivatives of exponential and logarithmic functions.

Find the equation of the tangent line to a curve at a given point using the derivative as slope.

Locate critical points, determine intervals of increase and decrease, and classify local extrema with the first or second derivative test.

Solve a constrained optimisation word problem (cost, revenue, or profit maximisation) by building the objective function and optimising it.

Interpret the derivative as a marginal rate in an economic context and state the result in context.