Guia docente 2023_24 Centro Universitario de la Defensa de la Escuela Naval Militar de Marín

Contents

Topic	Sub-topic
Lesson 1. Limits and continuity in R.	Bolzano's theorem. Bisection's method.
Lesson 2. Differential calculus in R.	Optimization. Rolle's theorem. Mean value theorem. Taylor's polynomial. Newton-Raphson's method.
Lesson 3. Integral calculus of one variable.	Properties of the indefinite integral. Fundamental integration techniques. The definite integral. Applications of the definite integral.
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 5. Limits and continuity of real functions of several variables.	The euclidean space Rn. Concept of a function of several variables. Limit of a function of several variables. Continuity of functions of several variables. Properties of the continuous functions.
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.