The course syllabus and the academic weekly planning may change due academic events or other reasons. Calculus I. Study: Bachelor in Industrial Technologies Engineering Department assigned to the subject: Department of Mathematics. Type: Basic Core.
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Toggle navigation USC. Contents - Numerical sequences and series: limit of a sequence and the sum of a series. Convergence criteria for numerical series. Introduction to power series. Scalar and vector functions. Domain, image, graph and level set of a multivariable function. Limits and continuity. Partial derivatives. Gradient and Jacobian matrix.
Tangent plane. Chain Rule. Directional derivatives. Taylor's Theorem. Critical points of multivariable functions: classification and characterization. Constraint extremes: Lagrange multipliers. Display of curves and surfaces. Symbolic calculation of derivatives and partial derivatives. Numerical approximation of first and second order derivatives.
Numerical solution of non-linear equations: Newton's method. Addison-Wesley Iberoamericana, Pearson Education. Volume I. Volume II. Prentice Hall, Addison-Wesley Iberoamericana, Fourth edition Universidade de Santiago de Compostela.
Competence - To be able to establish the convergence of numerical series with the convergence criteria explained in class. Teaching methodology There are 3 hours of theoretical-practical classes per week until finishing the subject credits. Practices are divided in 5 virtual and 10 contact ones.
As introduction to numerical method programming in the corresponding programme units it will be carried out a programming project. Assessment system - Attendance to problem seminars and to computer practices is compulsory.
Study time and individual work Contact hours: Theory: 30 h Practices: 10 h Virtual practices: 5 h Hours of personal work: Total volume of work: Recommendations for the study of the subject - To have studied Mathematics and Physics at the high school.
Grupo L Grupo T
Universidade de Santiago de Compostela
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