Cálculo III

Unit 1 §

Vector Spaces §

Vector Space

• Inner Product
• Norm
• Law of Cosines
• Vectorial Function
  • Continuous Vectorial Function

Topology §

Metric Space

Sets:

• Open Ball
• Open Set
• Closed Set
• Closure
• Infinite Collection of Sets
• Compact Set

Points:

• Interior Point
• Accumulation Point
• Boundary Point
• Limit Point

Contouring:

• Level Set and Contour Line
• Open Cover

Unit 2 §

There is a theorem that tells us whether a vectorial function is continuous in all of ${\mathbb{R}}^n$ or not.

Vectorial functions can be differentiated. Since vectorial functions have multiple partial derivatives, it’s convenient to place them all in a special matrix called a Jacobian matrix.