At the end of Mathematics I, students should be able to:
R1. Be able to write in mathematical language physical problems comprising the contents of this subject.
R2. Calculate, handle and apply symbolic matrix expressions. Apply these contents to solve systems of linear equations. Evaluate, discuss and apply the results obtained.
R3. Define and identify the concepts of linear dependence, linear independence, generating system and basis. Describe the subspaces of a vector space through their different expressions. Calculate the coordinates of a vector in different reference systems.
R.4 Describe the concept of linear application. Calculate a linear application. List its properties. Classify a linear application. Determine a linear application with its bases fixed. Interpret the information obtained from a linear application.
R5. Determine whether a matrix is diagonalisable or not. Interpret the concept of diagonalisation in the framework of endomorphisms. Apply the diagonalisation of matrices to the calculation of the nth power of a matrix.
R6. Know the concept of scalar product and its properties. Relate the concept of distance associated with a scalar product. Apply the Gram-Schmidt orthonormalisation process. Interpret endomorphisms with geometric meaning. Calculate the projection of a vector on a subspace.
R7. Know the calculus of functions (both real functions of real variable and functions of several variables) and apply the knowledge acquired to problem solving.
R8. Use the scientific software Maxima to solve problems associated with the contents of the subject.
