PAU Applied Math ACS II (La Rioja) study plan

Compute determinants of 2x2, 3x3 and 4x4 matrices using cofactor expansion and row reduction, and state when a matrix is invertible

Invert 2x2 and 3x3 matrices by the adjoint method and by Gauss-Jordan elimination, checking the result by multiplication

Classify and solve square systems with Cramer's rule and with the inverse matrix, and interpret the determinant of the coefficient matrix as a compatibility test

Set up the matrix form Ax=b of a word problem (mixing, equilibrium, networks) and solve it without arithmetic errors

Apply Rouché-Frobenius to decide whether a system is incompatible, determined or indeterminate, including cases with a parameter

Solve parameter-dependent systems by discussing the values of the parameter that change the rank of the coefficient and augmented matrices

Express the solution set of an indeterminate system in parametric form and give two particular solutions

Solve a matrix equation of the form AX+B=C or AX=XA for the unknown matrix X

Formulate a linear programming problem from a written statement: define decision variables, write the objective function and all constraints including non-negativity

Solve two-variable problems graphically, shading the feasible region and identifying vertices, bounded and unbounded cases

Apply the fundamental theorem of linear programming to justify that an optimum lies at a vertex, and detect infeasible or unbounded problems

Convert a two-variable problem to standard form and solve it by the simplex method, reading the optimal value from the final tableau

Solve integer and mixed LP problems in two variables by enumerating integer points in the feasible region

Interpret the dual problem and use duality to check the optimal value of a primal problem

Compute one-sided and two-sided limits of rational, radical and piecewise functions, and resolve 0/0 and infinity/infinity indeterminacies

Determine the value of a parameter that makes a piecewise function continuous at a point

Differentiate composite, implicit, exponential, logarithmic and trigonometric functions fluently, including logarithmic differentiation

Apply the mean value theorem and Rolle's theorem to justify statements about a function on an interval

Find intervals of monotonicity, extrema and inflection points from the sign of f' and f''

Optimize a real-world quantity (cost, area, volume) by building a one-variable model and verifying the extremum with the second derivative

Compute definite integrals using Barrow's rule, substitution and integration by parts

Apply the area formula between two curves, identifying intersection points and which function is upper on each subinterval

Optimize an area or volume defined by a parameter using the derivative, combining domains 3 and 4

State and apply the hypotheses of the fundamental theorem of calculus to a function defined by an integral with variable limits

Apply the addition and multiplication rules, conditional probability and independence to multi-stage experiments, using tree diagrams and contingency tables

Use Bayes' theorem to revise a probability after new information in a two-event and three-event setting

Identify a binomial or normal model for a stated random variable and compute probabilities, mean and variance, using standardization for the normal case

Construct a confidence interval for a population mean with known and unknown variance, and interpret the confidence level correctly

Review all six domains by re-solving the errors logged in weeks 1-7 rather than re-reading notes

Complete two full timed mock exams under PAU conditions (90 minutes each) and self-mark against a rubric

Diagnose remaining weak points by domain and do targeted practice on the two weakest domains

Finalize a one-page formula sheet covering determinants, Cramer, simplex, derivatives, integrals and probability that can be mentally reconstructed on exam day