Teaching GuideTerm
Faculty of Science
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Grao en Química
 Subjects
  Mathematics 2
   Contents
Topic Sub-topic
Differentiation of functions of several variables Functions of several variables.
Topological notions. Flat curves and parametric equations. Surfaces in space. Polar, cylindrical and spherical coordinates. Real functions of several variables. Scalar and vector functions. Graphs and level sets. Concept of continuity.
Differentiation of functions of several variables.
Partial derivatives. Directional derivative. Differential of a function. Higher order partial derivatives. Jacobean Matrix. Chain rule. Taylor's theorem. Plane tangent to a surface. Function ends of two variables. Lagrange multipliers.


Integration of functions of several variables Multiple integration. Integral line.
Iterated integrals. Double integrals. Change of variables: polar coordinates. Triple integrals Change of variables: cylindrical and spherical coordinates. Applications. Line integrals of scalar and vector functions. Applications. Green and Stokes theorem.
Differential Equations First order differential equations.
Separable variables. Homogeneous equations.
Exact equations
Linear equations.
Differential equations as mathematical models.
Linear differential equations of order n.
Homogeneous linear differential equations.
Variation of parameters. Indeterminate coefficients.
Linear systems of differential equations.
Modeling with systems of differential equations.
Descriptive statistics Statistical description of a variable
Joint statistical description of several variables
Regression curves: least squares.
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