Course code: 503101 | Subject title: MATHEMATICS I | ||||
Credits: 6 | Type of subject: Mandatory | Year: 1 | Period: 1º S | ||
Department: | |||||
Lecturers: | |||||
YANGUAS SAYAS, PATRICIA (Resp) [Mentoring ] |
Differential and integral calculus of a single variable, linear algebra.
Area: Applied mathematics.
LEARNING OUTCOMES ENAEE
ENAEE-1: Knowledge and understanding of the scientific and mathematical principles underlying the engineering branch.
Methodology - Activity | Attendance | Self-study |
A-1 Lectures | 45 | |
A-2 Practical lessons | 15 | |
A-3 Assignments | 5 | 5 |
A-4 Self-study | 70 | |
A-5 Exams, evaluation tests | 5 | |
A-6 Office hours | 5 | |
Total | 75 | 75 |
Proficiency | Formative activity |
CE1 | A-1, A-2, A-3, A-4, A-5, A-6 |
CB1- CB5 | A-1, A-2, A-3, A-4, A-5, A-6 |
CG2 | A-1, A-2, A-3, A-4, A-5, A-6 |
Learning outcome | Evaluation system | Weight (%) | Possibility of resit |
R1, R2, R3, R4, R5, R6, ENAEE-1. | Written exam | 85 | YES |
R1, R2, R3, R4, R5, R6, ENAEE-1. | Individual assignment | 15 | YES* |
Continuous evaluation:
To pass the subject in the continuous evaluation it is necessary to get at least 3 points in part A, 3 points in part B and 5 points in the average of the grades of the two parts (here part means written exam + individual assignment).
Resit evaluation:
*It is a written exam that corresponds to the whole subject. It represents the 100 % of the final grade. The students that have not passed the subject in the continuous evaluation are allowed to take this exam. The exam may include questions related to the individual assigments.
Number sets. Basic operations with real and complex numbers.
Functions, limits, continuity, differentiability, integrability. Basic concepts on real-valued functions of a single real variable. Elementary functions. Limits. Continuity of a function at a point. Properties of continuous functions. Differentiation, aplications of derivatives.
Definite and indefinite integrals, applications of integrals.
Vector spaces on R: subspaces. Basis and dimension.
Euclidean space: dot product and Euclidean norm, orthonormal bases, Gram-Schmidt orthogonalization.
Matrix diagonalization: eigenvalues and eigenvectors. Fundamental subspaces. Least-squares approximation.
Matrices: inverse matrix, linear systems, Rouché-Frobenius Theorem.
Determinants.
1. Real-valued functions of a real variable
Natural numbers, integers, rational numbers, real numbers and complex numbers. Real-valued functions of a real variable. Limits, continuity of a function at a point, properties of continuous functions. Derivative of a function at a point, chain rule, higher-order derivatives, properties of differentiable functions, the Newton-Raphson method, applications.
2. Integrals of real-valued functions of a real variable
The Riemann integral, fundamental theorems of integral calculus, elementary integration methods, applications.
3. Vectors and matrices. The dot product
Matrices and determinants. Fundamental concepts, operations, linear systems, direct resolution methods, applications. Real vector spaces. Dot product and Euclidean norm, orthogonal projection, orthonormal bases, least squares approximation. Linear maps.
4. Matrix diagonalization
Eigenvalues and eigenvectors. Characteristic polynomial. Eigenspaces. Algebraic and geometric multiplicity. Diagonalizable matrices.
Polynomial functions of matrices. Quadratic forms. Diagonalization and classification of quadratic forms.
Access the bibliography that your professor has requested from the Library.
BASIC BIBLIOGRAPHY:
Calculus: A Complete Course (8th edition), R. A. Adams and C. Essex, Pearson Education, Canada, 2013.
Calculus (6th Edition), K.J. Smith, M.J. Strauss, M.D. Toda, Kendall/Hunt Publishing Co, Iowa, United States, 2014.
Introduction to Linear Algebra (2nd edition), S. Lang, Undergraduate Texts in Mathematics, Springer, New York, 1986.
Linear Algebra and Its Applications (4th edition), G. Strang, Cengage Learning, United Kingdom, 2006.
SUPPLEMENTARY BIBLIOGRAPHY:
Calculus With Analytic Geometry (8th edition), R. Larson, R.P. Hostetler, Houghton Mifflin Company, 2005.
Calculus (3rd edition), J. Rogawski and C. Adams, W. H. Freeman Publishers, 2015.
Calculus: One and several variables (10th edition), S. Salas, E. Hille, G. Etgen, John Wiley & Sons Inc., United States of America, 2007.
Calculus With Analytic Geometry (2nd edition), G.F. Simmons, The McGraw-Hill Companies, Inc., New York, 1996.
Thomas' Calculus: Early Transcendentals (14th edition), G.B. Thomas, Jr., J. Hass, C. Heil, M. Weir, Pearson, Boston, 2018.
Linear Algebra and Its Applications: A first course, D.H. Griffel, Ellis Horwood Ltd., New York 1989.
Linear Algebra and Its Applications (5th edition), D.C. Lay, S.R. Lay and J.J. McDonald, Pearson Education Limited, Harlow (England) 2016.
Linear Algebra with Applications (7th edition), W.K. Nicholson, McGraw-Hill Ryerson Ltd., Toronto, 2013.
A course in Linear Algebra with Applications (2nd edition), D.J.S. Robinson, World Scientific Pub Co Inc., Singapore, 2006.
Mathematics for Life Sciences, C. Neuhauser, Prentice Hall PTR, 2001.