# docenti.luiss.it

## Course Info

### Course Contents:

Matrices. Systems of Linear Equations, Linear Dependence and Linear Independence, The Inverse of a Matrix. Determinants
Subspaces. Vector Spaces and Subspaces. Null Spaces, Column Spaces, Linear Transformations. Change of Basis. Complex numbers. Eigenvalues and Eigenvectors. The Characteristic Equation. Diagonalization. Discrete Dynamical Systems. Applications to Difference Equations. Orthogonality.
The Dot Product. The Cross Product. Orthogonality and Least Squares. Orthogonal Sets. Orthogonal Projections. Gram-Schmidt orthogonalization. Least-Squares Problems. Applications to Linear Models. Inner Product Spaces. Curves, Geometry of Space and Vector Functions.
Curves defined by Parametric Equations. Calculus with parametric curves. Equations of Lines and Planes. Vector Functions and Space Curves. Derivatives of Vector Functions. Partial Derivatives. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Linear Approximations. The Chain Rule. Directional Derivatives and the Gradient Vector. Stationary Points.

### Textbook:

Title: Stewart J. – Calculus Early Trascendentals (7th-Edition), Brooks/Cole.

### Course Formative Objectives:

Provide the students with the basics of linear algebra and vector calculus and its applications. These contents represent the basic tools in a variety of fields, from operations research and optimization to statistics and econometrics.

### Prerequisites:

Standard tools in calculus: exponential and logarithmic function, derivatives.

### Teaching Method:

Traditional lectures and Teaching Assistant sessions.

### Assessment Method:

Written test and theory test exam, see also Exam Rules.

### Office Hours:

Friday, 11:30 – 12:30 and 16:00-17:00 (till December 2018)
Where: Professors room (408).

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