Lesson 2. Differential calculus in R. |
Optimization.
Rolle's theorem.
Mean value theorem.
Taylor's polynomial.
Newton-Raphson's method. |
Lesson 4. Sequences and Series. |
The real numbers.
Definition and basic concepts of sequences.
Convergence of sequences.
Convergence criteria and limits calculation techniques.
Definition and basic concepts of series.
Convergence of series.
Convergence criteria for series. |
Lesson 6. Differential calculus of real functions of several variables. |
Directional derivatives. Partial derivatives.
Gradient vector and Jacobian matrix.
Differentiability of a real function of several variables.
Conditions for the differentiability.
Higher order differentiability. Hessian matrix.
Local behaviour of differentiable functions. |