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Contents Course description: This is a second course in the Mathematics sequence. Topics include a continuing study on differential and integral calculus and a first course on differential equations. Detailed Syllabus: 1. Partial derivatives. Differential calculus. Chain rule. Directional derivatives. Finding maxima and minima of functions. Lagrange multipliers.
Change to polar coordinates. Change to cylindrical and spherical coordinates. Some applications of the multiple integrals. Rotational and divergence. Parametrized curves. Arc length. Integrals on a curve. Path integrals.
Integration of vector functions on a curve. Line integrals. Conserving fields. Green's theorem. Parametrized surfaces. Integrals of functions on a surface. Theorems of Gauss and Stokes. Generalities on solutions. Problems of initial value. Equations of separable, homogenous, exact and linear variables. Applications of the ODE of the first order. Introduction to ODE's numerical resolution. Euler's method. Algebraic properties of the solution. The homogeneous equation with constant coefficients.
Inhomogeneous equation. Applications of the linear ODE of the second-order. Conditions for the existence of the Laplace transform. Laplace transform for piecewise continuous functions. Properties of linearity and traslation. Laplace transform of the derivative and of the integral. Inverse Laplace transform. Application of the Laplace transform to ODE's resolution.
DELS with constant coefficients. Applications of the DELS. Basic and complementary bibliography - Ayres, F. Ecuaciones diferenciales. McGraw-Hill Serie Schaum. Ecuaciones diferenciales y problemas con valores frontera. Editorial Limusa. Prentice Hall Internacional. Ecuaciones diferenciales elementales con aplicaciones. Prentice Hall. Addison Wesley. Problemas resueltos. Fundamentos de ecuaciones diferenciales. Mc-Graw Hill. Grupo Editorial Iberoamericana. Ecuaciones diferenciales con aplicaciones de modelado.
International Thomson Editores. Competence - To know the principal concepts, skills and applications of the differential and integral calculus of multivariable functions. Teaching methodology 3 hours of classroom a week where the different contents of the matter will be developing in the waxing. From time to time some collections of proposed problems will be submitted to the student, some of them will be corrected in the waxing at the end of every topic.
In addition, the overhead projection of transparencies will be used for the development of certain contents of the matter in these cases there will be facilitated to the student a copy of the projected transparencies.
Assessment system There will be realized, in the official dates, the examination of the summons of February and of the summons of September. Recommendations for the study of the subject - Participative assistance to class and daily study of the subject.
Edwards Penney Textbooks
Universidade de Santiago de Compostela