**Course Contents:**

**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. **Multiple Integrals**. Double Integrals over rectangles. Iterated Integrals. Double Integrals over General Regions. Triple Integrals. Change of Variables in Multiple Integrals. **Infinite Sequences and Series**. Sequences. Series. Improper Integrals. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Representations of Functions as Power Series. Taylor and Mac-Laurin Series. Applications of Taylor Polynomials.

**Textbook:**

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

Chapters: 11, 12, 13, 14, 15, 16.

**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, 10:30 – 12:00

Where: Professors room (408).