The purpose of the course is to let students from different backgrounds learn the main and fundamental mathematical tools and laguage. In particular, the subject concerns notions that are necessary for more advanced mathematics and statistics subjects, as well as for courses in physics, appraisal, structural mechanics. The fundamental notions as well as the methods for analysis and solution of problems are given from a conceptual perspective, leaving to use of appropriate software the solution of computationally intensive problems. After the course, the students should indeed be able to read, interpret and present problems and results of mathematical nature. In the last lectures of the course, some mathematical models of interest in Architecture are treated in detail.

This course provides the students with essential mathematical tools, suitable to understand and tackle problems requiring differential calculus (mostly on the real line), inegral calculus, linear algebra and statistics. These tools are essential also in view of applications in other subjects of the Architecture programme. The students will learn how to use the mathematical tools in the various sub-fields of the Architecture profession. They will learn to recognize them, to solve simple problems and to develop models of their own interest.

Students should be familiar with high school mathematics concepts and notions, such as solutions of first and second degree algebraic equations, elementary equations and inequalities involving trigonometric functions, definitions and properties of logartihmic and exponential functions.

Linear algebra lineare and geometry: matrices, vectors and vector calculus; applications of vector calculus to determine equations of straight lines and planes; systems of linear algebraic equations; eigenvalues and eigenvectors; conic curves.
Differential calculus: functions and their graphs; elementary functions (rational and irrational functions, exponential functions and logarithms, trigonometric functions, hyperbolic functions); limits of functions, calculation of limits in simple cases; continuous functions and related theorems; derivatives and their applications; De L'Hôpital rules; fundamental theorems concerning monotonicity intervals, concavity and convexity; behaviour of functions at their domain boundaries;qualitative graph of functions.
Integral calculus in one real variable: definite integrals and calculation of area; indefinite integral and simple antiderivatives. Two variables functions, surfaces, quadric surfaces, identification of critical points and their properties, tangent plane. Differential equations and systems of differential equations. Descriptive statistics: numerical and grafical representations of data sets, position and variability indeces, correlations between data sets. Mathematical models: cross section of pillars; development of green areas; elsatic curve of cantilever. Further examples from mathematical physics.

The assessment is done by grading solutions of exercises and discussing orally theoretical aspects of the course.

Material available on the theacher's web page

R. A. Adams and Essex, Calculus, a complete course, Pearson (2010)