Teaching GuideTerm
Faculty of Science
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Grao en Química
 Subjects
  Mathematics 1
   Contents
Topic Sub-topic
• Differentiation o Basic Rules of Differentiation.
o The Chain Rule.
o Techniques Differentiation.
o L'Hôpital's Rule. Taylor's Theorem.
o Applications of Differentiation.
o Maxima and Minima.
o Optimisation Problems.
o The Newton-Raphson Method.


• Integration o Integration as Summation.
o Fundamental Theorem of Calculus.
o Some Basic Integrals.
o Integration by Substitution.
o Integration by Parts.
o Integration of Rational Functions.
o Geometrical Applications of Integration.
o Numerical Integration. Simpson's Rule.
o Improper Integrals.

Integración numérica: método de Simpson.
Integrales impropias.
• Ordinary Differential Equations. o First Order Differential Equations.
o Separable First Order Differential Equations.
o Linear First Order Differential Equations.
o Applications of First Order Differential Equations.
o Second Order Linear Differential Equations with Constant Coefficients.
o Homogeneous Linear Systems with Constant Coefficients.
• Linear Algebra o Systems of Linear Equations
o Elementary operations.
o The Algebra of Matrices.
o Determinants. Basic properties.
o The determinant rank.
o Eigenvalues and Eigenvectors.
o Normal forms for matrices.
o Cayley-Halmiton theorem.
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