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Courses offered in English
Calculus

Contents

Chapter 1: Introduction to Differential and Integral Calculus

  • Real valued functions of one variable.

Chapter 2: Real Valued Functions of Several Variables

  • Limits and continuity.
  • Partial derivatives. Directional derivatives.Tangent line. Differentiability. Tangent plane. Taylor polynomial. Hessian matrix.
  • Optimization: Local maxima and minima. Constrained optimization. Global maxima and minima.

Chapter 3: Multiple Integrals

  • Double integrals.
  • Triple integrals.
  • Geometric and physics applications.

Chapter 4: Ordinary Differential Equations

  • First order ordinary differential equations.
  • Higher order ordinary differential equations.
  • Systems of differential equation.

Bibliography

  • Spivak, M. Calculus. Addison Wesley, 1967.
  • Marsden, J.E., Tromba, A.J., Vector Calculus. WH Freeman and Co., 2003.
  • Larson, R., Hostetler, R.P., Edwards, B.H., Calculus II. Houghton Miffin Co., 2005.
  • García López, A., García Castro, F. Cálculo II. Teoría y problemas de funciones de varias variables. Clagsa, 2002.
  • Boyce, W.E., DiPrima, R.C., Elementary differential equations and boundary value problems. John Wiley & Sons., 2001.
  • Zill, D.G., A first course in differential equations with modeling applications. Brooks/Cole Cengange Learning, 2005.
  • García López, A., García Castro, F. et al. Ecuaciones diferenciales ordinarias. Teoría y problemas. Clagsa, 2006.
  • Patiño, E., Galán, P., Ecuaciones diferenciales de primer orden I y II. Cuadernillos nº 3-88-01 y 3-88-02. Instituto Juan de Herrera, E.T.S. de Madrid, 2012.
  • Patiño, E., Galán, P., Ecuaciones diferenciales de orden superior I y II. Cuadernillos nº 402.01 y 403.01. Instituto Juan de Herrera, E.T.S. de Madrid, 2013.