Calculus 3 – multivariable calculus, part 1

La duración total del curso es de 48 horas.

1. Introduction.
2. Analytical Geometry in the space.
   • Three-dimensional coordinate systems (Cartesian, cylindrical, spherical).
   • Equations of lines and planes in space.
3. Conec sections and Quadric surfaces.
   • Classification and properties of conic sections (ellipse, hyperbola, parabola).
   • General forms and classifications of quadric surfaces (ellipsoid, hyperboloid, paraboloid).
4. Topology in R^n.
   • Concepts of open, closed, and compact sets in higher dimensions.
   • Continuity and convergence in R^n.
5. Vector-valued functions.
   • Definition and properties of vector-valued functions.
6. Calculating arc length for parametric curves.
7. Real-valued functions of multiple variables.
   • Domain, range, and graphing of functions of two or three variables.
   • Level curves and level surfaces.
8. Definition of limit for functions of multiple variables.
9. Partial derivative and higher partial derivatives.
   • Statement and applications of the chain rule.
10. Linear approximation.
    • Linearization of functions and error estimation.
11. Gradient and directional derivatives.
12. Taylor’s formula.
    • Taylor series expansion for functions of multiple variables.
13. Lagrange multipliers.
    • Method of Lagrange multipliers for constrained optimization.

1. Conocimiento sólido de Cálculo 1 y Cálculo 2.
2. Familiaridad con Álgebra Lineal básica.

La realización del curso será completamente on-line y evaluado a través de un examen. Una vez superado el mismo, podrás recibir tu título, válido para toda España.

Una vez hayas completado el curso, puede realizar el test relacionado y obtener tu título.