Algebra and Analytical Geometry-LEQF

 

T - Theoretical; TP - Theory and practice; PL - Laboratory; S - Seminar; OT - Tutorial.

 

• Algebra and Analytical Geometry

  1. Perform calculations with matrices and determinants. Discuss and solve systems of linear equations.
  2. Recognize the concepts of vector space and linear application and use them in these areas. Determine
  eigenvalues and eigenvectors and diagonalize a matrix.
  3. Calculate and interpret the inner, cross and scalar triple product. Apply the concepts covered in this
  course in problem solving analytic geometry.
  4. Identify and use the themes in solving engineering problems.

• Syllabus:

  1. Matrices. Definition and notations. Algebra of matrices. Elementary operations. Rank of a matrix.
  Systems of linear equations. Inverse matrix.
  2. Determinants. Definition. Properties. Laplace's theorem.
  3. Vector spaces. Definition and examples. Subspaces. Linear dependence. Generators.
  Base and dimension. Change of base
  4. Linear applications. Definition and examples. Matrix representation of a linear transformation. Kernel and
  Image. Operations with linear applications.
  5. Euclidean spaces. Definition and examples. Norma, distance, angles. Cross product.
  Scalar triple product. Applications.
  6. Analytical geometry. Affine space. Straight line and plane analytical representation. Quadrics.

• Evidence of the syllabus coherence with the curricular unit’s intended learning outcomes:

  The objectives 1. to 4. are met in the syllabus, in which the abilities of calculation, interpretation and
  deductive reasoning are developed. In particular it also allows to show that linear algebra and analytic
  geometry are indispensable tools for the study of engineering.

• Teaching methodologies (including assessment):

  Teaching methodologies: Theoretical and theoretical-practical lectures in which the exposure of matter of
  this course is always accompanied by examples. It is provided a list of exercises, which are discussed or
  solved in theoretical-practical classes. The evaluation has two forms: continuous evaluation or final exam
  evaluation.
  Continuous evaluation: Two partial tests (T1 and T2): T1>=7.5, T2>=7.5
  Formula for the calculation of Final Grade (NF):
  NF=(T1+T2)/2: NF>=9.5
  Final exam evaluation: Final Exam(FE)>=9.5
  Formula for the calculation of Final Grade (NF):
  NF = FE
  Rounded to units. By defect, beneath five tenths, per excess, from five tenths.

• Evidence of the teaching methodologies coherence with the curricular unit’s intended learning outcomes:

  The topics covered in this course are accompanied by examples and application exercises enabling
  effective learning and follow the several given topics.

• Bibliografia principal:

  1. Anton, H., Rorres., C., “Elementary Linear Algebra”, Wiley
  2. Anton, H., Rorres, C., “Álgebra Linear com Aplicações”, Bookman
  3. Lay, D., Linear ”Algebra and its Applications”, Pearson, Addison Wesley
  4. Cabral, I., Perdigão, C., Saiago, C., “Álgebra Linear”, Escolar Editora
  5. Santana, A. P., Queiró, J. F., “Introdução à Álgebra Linear”, Gradiva
  6. Strang, G., “Linear Algebra and its Applications”, HBJ Publishers
  7. Steinbruch, A., Winterle, P., “Álgebra Linear”, McGraw Hill