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7.18. Linear Algebra I (Mandatory)

7.18.1. Justification ↑ Back to top

This course introduces the fundamental concepts of linear algebra, providing the mathematical foundations for the study of vector spaces, linear transformations, and systems of linear equations. It develops abstract thinking and problem-solving skills through matrices, determinants, and vectors. The course is fundamental for applications in science, engineering, and computing.

7.18.2. Generales Goals ↑ Back to top

1. Understand the concepts of vector spaces and subspaces.
2. Master matrix operations and determinants.
3. Solve systems of linear equations using different methods.
4. Apply linear transformations and compute eigenvalues and eigenvectors.

7.18.3. Contribution to Outcomes ↑ Back to top

ABET-1) An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics. (Familiarity)

7.18.4. Content ↑ Back to top

7.18.4.1. Matrices and Systems of Linear Equations (28 hours) [Skills ABET-1] ↑ Back to top

Bibliography: (Lay et al., 2016; Strang, 2016; Anton and Rorres, 2014)

Topics

1. LU, QR, and Cholesky factorizations for solving engineering linear systems
2. Singular Value Decomposition (SVD) and least squares solutions

Learning Outcomes

1. Solve systems of linear equations arising in structural, circuit, and fluid engineering problems [Usage]
2. Apply the SVD to solve over-determined systems in data fitting and signal processing [Usage]

7.18.4.2. Vector Spaces and Linear Transformations (22 hours) [Skills ABET-1] ↑ Back to top

Bibliography: (Lay et al., 2016; Strang, 2016; Anton and Rorres, 2014)

Topics

1. Vector spaces, subspaces, bases, and dimension
2. Linear transformations and their matrix representations in coordinate changes

Learning Outcomes

1. Formulate and interpret coordinate system transformations for engineering geometry problems [Assessment]

7.18.4.3. Eigenvalues and Inner Product Spaces (20 hours) [Skills ABET-1] ↑ Back to top

Bibliography: (Lay et al., 2016; Strang, 2016; Anton and Rorres, 2014)

Topics

1. Eigenvalues, eigenvectors, and diagonalization with applications to vibration and stability
2. Inner product spaces, orthogonality, and the Gram-Schmidt process

Learning Outcomes

1. Perform eigenvalue decomposition on symmetric matrices for modal analysis of mechanical structures [Assessment]

7.18.5. Bibliography ↑ Back to top

Lay, D. C., Lay, S. R., and McDonald, J. J. (2016). Álgebra Lineal y sus Aplicaciones. Pearson, 5th edition.

Strang, G. (2016). Introduction to Linear Algebra. Wellesley-Cambridge Press, 5th edition.

Anton, H. and Rorres, C. (2014). Álgebra Lineal con Aplicaciones. Limusa Wiley, 11th edition.