70463 - Principles of Mathematics 2

Course Unit Page

Academic Year 2018/2019

Learning outcomes

At the end of the course, the student is familiar with the basic tools of differential and integral calculus for functions of several variables and knows the most elementary methods for the solution of linear differential equations of second order. In particular, the student will be able to complete standard tasks related to differential and integral calculus for several variables (e.g., computation of free and constrained maxima and minima, the length of a curve, volumes, etc.), and solve certain second-order differential equations.

Course contents

Differential calculus for vector-valued functions of one real variable. Length of a curve. Differential and integral calculus for real-valued functions of more real variables. Free and constrained maxima and minima. Areas and volumes.


A good reference book, which however cannot replace a good set of notes from the class, is:

  • M. Bramanti, C. D. Pagani, S. Salsa, "Matematica: calcolo infinitesimale e algebra lineare", 2nd ed., Zanichelli, 2004

A useful companion book for the exercises is:

  • S. Salsa, A. Squellati, "Esercizi di matematica: calcolo infinitesimale. VOLUME 2", Zanichelli, 2002 (ISBN: 8808248941)


Teaching methods

Classroom lectures

Assessment methods

2-hour long written exam, comprising 4-6 questions, among which 1-2 theoretical questions. The remaining questions are problems of the types discussed in class and given as homework. Different scores may be assigned to different questions, depending on the importance of the topic and the difficulty of the problem. Partial scores are given for partial, or partially correct, answers.



Teaching tools

  • Class notes (to be studied together with the textbook).
  • Lecture-by-lecture syllabus of the course.
  • Homework problems, taken from the exercise book, from the list of sample problems written by the teacher and from the previous exams. Some of these problems are later solved and discussed in class.
  • Depending upon the economic resources of the School, elective problem-solving meetings coordinated by a Teaching Assistant.

Office hours

See the website of Marco Lenci