LEARNING OUTCOMES OF THE COURSE UNIT
Knowledge and understanding of the basic symbols and vocabulary concerning functions of several variables, and of the relevant theorems in the field.
Ability to apply the knowledge acquired to solve simple practical problems, and to understand the mathematical machinery employed in non-mathematical courses.
Mathematical analysis 1, Geometry and linear algebra
COURSE CONTENTS SUMMARY
Elements of differential calculus in several variables and ordinary differential equations
E. Acerbi e G. Buttazzo, Secondo corso di analisi matematica, ed. Pitagora, Bologna 2016
ASSESSMENT METHODS AND CRITERIA
Final exam, with three easy theoretical/practical questions and three exercises
Frontal lectures with exemples (2/3), exercises (1/3)
All information on the course may be found at http://calcvar.unipr.it/Didattica/analisi2.html
Fundamental graphs: line, plane, sphere, ellipsoid, paraboloid, saddle, cylinder, cone.
Curves: velocity, length, integral, work.
Continuity and differentiability.
Free and constrained extrema, Lagrange multipliers.
Ordinary differential equations; linear equations of first and second order; equations with separable variables.
Multiple integrals and surface integrals.