Calculus I Linear Algebra

1. Ability to state, solve and understand mathematically problems related to Industrial Technologies. 2. Comprehensive approach to the euclidean n-dimensional space, specially in dimension three and the most relevant subsets. 3. Knowledge of the main properties of the functions in several variables, scalar and vectorial cases, their continuity, differentiability and integrability. 4. Resolution of problems of optimization with and without constraints. 5. Applications of integrals, among them the calculus of areas, volumes, moment of inertia and center of gravity of rigid solids. 6. Integration on lines and surfaces and the theorems by Green, Stokes and Gauss.

Chapter 1. n-dimensional Euclidean Space. Topologic structure. Functions of several variables. Limits and continuity. Partial derivatives and differentiability. Gradient vector. Jacobian matrix. Chain rule and directional derivatives. Differential operators. Chapter 2. Hessian matrix. Local extrema. Extremum problems with constraints. Lagrange multipliers. Chapter 3. Integration in R^n. Iterated integrals. Fubini's Theorem. Change of variables. Applications. Chapter 4. Line integrals. Conservative fields. Surface integrals. Green, Stokes and Gauss' Theorems.

The learning activities will include: 1.- Master sessions. 2.- Problems sessions. 3.- Selfevaluations. 4.- Partial tests. 5.- Final exam. 6.- Tutorial activities.