1. Scalar functions of several variables: basic concepts, limits and continuity, partial derivatives, total differential, composite functions, Taylor expansion, unconstrained and constrained extrema, double and triple integrals.
2. Vector-valued functions: basic concepts, parametric representation of curves, gradient, directional derivative, divergence and curl, line and surface integrals, Green’s theorem, Gauss’s theorem, and Stokes’s theorem.

Learning Outcomes

This course is a core Applied Mathematics course. Its content aims to introduce students to fundamental concepts of calculus for scalar functions of several variables, as well as vector-valued functions. The knowledge acquired is essential for the course on Differential Equations taught in the following semester, as well as for many core and specialized courses in Civil Engineering.

Upon successful completion of the course, the student will be able to:

• Effectively use calculus of scalar functions of several variables and vector-valued functions.
• Perform mathematical modeling of Civil Engineering problems in which concepts from the above mathematical topics are applied.