Course code: 252101 | Subject title: MATHEMATICS I | ||||
Credits: 6 | Type of subject: Basic | Year: 1 | Period: 1º S | ||
Department: Estadística, Informática y Matemáticas | |||||
Lecturers: | |||||
LIZASOAIN IRISO, INMACULADA (Resp) [Mentoring ] | ALBIAC ALESANCO, FERNANDO JOSÉ [Mentoring ] | ||||
QUEMADA MAYORAL, CARLOS [Mentoring ] |
At the end of this course, students will be able to
Methodology - Activity | Attendance | Self-study |
A-1 Lectures | 45 | |
A-2 Practical clases | 15 | |
A-3 Self-study | 75 | |
A-4 Exams, tests, and office hours | 15 | |
Total | 75 | 75 |
Proficiency | Activities |
CG3: Knowledge of basic and tecnological subjects to have the ability to learn new methods and theories, and versatility to adapt to new situations | A-1 Lectures A-2 Practical clases A-3 Self-study A-4 Exams, tests, and office hours |
CG4: Problem solving proficiency with personal initiative, decision making, creativity and critical reasoning. Ability to elaborate and communicate knowledge, abilities and skills in industrial engineering | A-1 Lectures A-2 Practical clases A-3 Self-study A-4 Exams, tests, and office hours |
CFB1: Ability to solve mathematical problems in engineering. Ability to apply theoretical knowledge on linear algebra, geometry, differential geometry, calculus, differential equations, numerical methods, algorithms, statistics and optimization | A-1 Lectures A-2 Practical clases A-3 Self-study A-4 Exams, tests, and office hours |
Learning outcome |
Assessment activity |
Weight (%) | It allows test resit |
Minimum required grade |
---|---|---|---|---|
O1, O2, 03, O4, O5 | Recurrent written quizzes that assess the daily work of the students | 30% | YES | NO |
O1, O2, 03, O4, O5 | Final exam (long answer questions and practical cases) | 70% | YES | To pass the course, the minimum required grade in this part is 4 out of 5. |
This subject has two parts: Calculus (1/3 of the subject matter) and Linear Algebra (the remaining 2/3 of the subject matter). The weight of each part in the final grade is in accord with that distribution of credit hours.
A Calculus midterm exam will take place right after finishing Unit 2. This test may leave out the Calculus part from the First Final Exam.
If a student does not fulfill the minimum requirements to pass the subject in some of the evaluation activities, the maximum grade that he or she will obtain is 4.9 out of then (failing grade).
Vector Spaces. Matrices and determinants. Linear systems. Diagonalization of matrices.
Analytic and differential geometry. Euclidean geometry equations.
Functions of a real variable. Limits. Introduction to Differential Calculus. Differentiation. Applications.
Integration techniques. Introduction to Integral Calculus of functions of one real variable. Applications.
Lesson 1. Calculus in one single variable
Differentiation of functions: review.
Taylor polynomials.
Approximation of functions by polynomials.
Taylor theorem with Lagrange's remainder.
Lesson 2. Integration of functions of one variable.
The Riemann integral: definition and properties.
Mean value theorem for integrals.
Fundamental Theorems of Calculus.
Integration techniques. Integration by parts.
Change of variable.
Improper integrals.
Lesson 3. Matrices and linear systems
Systems of linear equations. Matrix notation.
Matrix multiplication: block matrices and block multiplication.
The inverse of a matrix.
Row reduction and echelon forms: The Gaussian row reduction algorithm.
Gaussian elimination.
Elementary matrices.
Solution sets of linear systems.
Determinants.
Lesson 4. Vector Spaces
Definitions and examples.
Linear combinations and linear independence.
Subspaces.
Bases and dimension.
The change of basis matrix in a vector space.
Row space and column space of a matrix.
Solutions of linear systems.
Lesson 5. Linear Transformations.
Definitions and examples. Matrix associated to a linear transformation.
Operations with linear transformations.
Change of bases and linear transformations.
The null space of a linear transformation.
Kernel, image and isomorphisms. Rank+Nullity theorem.
Lesson 6. Diagonalization of linear transformations and matrices.
Linear transformations from a vector space into itself.
Eigenvalues and eigenvectors.
Diagonalization of matrices.
Lesson 7. Orthogonality.
Euclidean spaces. Scalar product.
Orthogonal projections. Gram-Schmidt method.
Orthogonal diagonalization of symmetric matrices.
Lesson 8. Least-squares approximations.
Approximate solutions of inconsistent systems.
Optimal least-squares solutions.
Normal equations.
Access the bibliography that your professor has requested from the Library.