Energy Engineering

Sequences and series of functions Pointwise and uniform convergence. Power series. Taylor series. Differential calculus for functions of several variables Limits and continuity. Partial and directional derivatives. Differentiability. Total differential theorem. Higher-order derivatives. Schwarz’s theorem. Free extrema. Integration on two- and three-dimensional domains Double and triple integrals. Change of variables (polar, cylindrical, spherical coordinates). Computation of volumes and areas. Surface integrals. Vector fields Curves and oriented lines. Line integrals of scalar and vector functions. Green’s, Gauss’s, and Stokes’ theorems (statements and applications). Curl, divergence, gradient. Conservative and potential fields.

Solid knowledge of Calculus 1: differential and integral calculus for functions of one real variable, sequences and numerical series, basic notions of linear algebra. Familiarity with formal mathematical language, ability to understand rigorous proofs .

Course notes and supplementary materials will be available on the course’s Google Classroom.

Attendance is not mandatory but strongly recommended.

The assessment consists of a written exam and an optional oral exam. The written exam includes computational exercises, theoretical questions, and proofs. It aims to assess the student's mastery of analytical tools, problem-solving skills, and understanding of theoretical concepts. The oral exam is optional and allowed only if the student obtains a mark of at least 26 out of 30 on the written test. It is intended to explore theoretical aspects in greater depth and clarify any uncertainties that emerged in the written exam.

The course is delivered through traditional in-person lectures. Almost every lecture includes exercises and interactive activities. Students are strongly encouraged to attend regularly and actively participate in all proposed activities.