Departamento de Matemática Aplicada Sección E.T.S. de Arquitectura

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.

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Bibliography

• Spivak, M. Calculus. Addison Wesley, 1967.
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• 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.