PAU Applied Mathematics for Social Sciences II - Canary Islands / ULPGC & ULL study plan

Compute sums, products, transposes and powers of 2×2 and 3×3 matrices by hand and state when a product is defined

Calculate determinants of order 2 and 3 using cofactor expansion and apply the properties of determinants to simplify before computing

Determine the rank of a matrix by row reduction and identify inconsistent or dependent rows at a glance

Solve square systems with Cramer's rule and check the answer by substitution

Apply Gaussian elimination to classify a system as compatible determined, compatible indeterminate or incompatible

State and use the Rouché–Capelli theorem comparing rank of the coefficient matrix with rank of the augmented matrix

Solve matrix equations of the form AX = B and XA = B by inverting A and justify when the inverse exists

Discuss one-parameter systems and express the solution set in terms of the free parameter

Translate a word problem in two variables into a system of linear inequalities and identify the objective function

Draw the feasible region accurately, label every vertex and detect unbounded or empty regions

Evaluate the objective function at the vertices and apply the fundamental theorem of linear programming to locate the optimum

Recognise integer or excluded-boundary constraints and adjust the vertex search accordingly

Solve two-variable linear programming problems algebraically by intersecting constraint lines instead of relying on the drawing

Interpret the dual problem and the shadow price of a binding constraint in a small two-variable model

Analyse how the optimal vertex changes when one coefficient of the objective function varies, and state the range of optimality

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

Resolve the indeterminacies 0/0, ∞/∞, ∞−∞ and 0·∞ using factorisation, conjugates, common denominators and L'Hôpital's rule

Determine asymptotic behaviour, horizontal and vertical asymptotes and one-sided limits at the boundary of the domain

Decide continuity of a function at a point and find the value of a parameter that makes a piecewise function continuous

Differentiate using the product, quotient, chain and implicit rules, and write the tangent line at a given point

Find intervals of increase and decrease from the sign of the first derivative and classify extrema

Determine concavity, convexity and inflection points from the sign of the second derivative

Sketch a complete curve from its domain, asymptotes, monotonicity and concavity without plotting software

Optimise one-variable economic functions such as cost, revenue and profit, and interpret the marginal values at the optimum

Compute immediate integrals of elementary functions and apply integration by substitution and by parts where required

Apply Barrow's rule to evaluate definite integrals and compute the area between two curves, including finding the intersection points

Solve counting problems using permutations, combinations and the multiplication principle

Apply conditional probability, independence, the total probability theorem and Bayes' theorem to a stated problem

Distinguish discrete from continuous random variables and compute expectation and variance from a table or a density function

Compute binomial probabilities and identify when the binomial model applies

Standardise a normal variable, use the standard normal table and compute probabilities for intervals and inverse problems

Decide when the normal approximation to the binomial is valid and apply the continuity correction