Course 2017-2018 a.y.

Classes: 25 (I sem.)

Instructors:
Class 25: EMANUELE BORGONOVO

The purpose of this course is to teach the student the basic notions of calculus, linear algebra and discrete mathematics together with the basic techniques and applications that accompany them.

• Mathematical logic.
• Elements of topology of the real line.
  
• Functions. Real functions of a real variable. Injective, surjective functions. Inverse functions. Maxima, minima. Concave and convex functions.
• Limits of real functions. Theorems about limits. Fundamental limits. Continuity.
• Derivative, differential. Theorems of differential calculus. Taylor's theorem. Extrema of functions.
• Riemann definite integral. Properties. Integrable functions.
• Antiderivatives & indefinite integrals. Integration techniques. The FToC.
• Generalized integrals.
• Relations. Cardinality of sets. Counting and discrete probability.
• Sequences, recursive Sequences and difference equations.
• Numerical Series. Series of functions.
• Matrices. Operations with matrices.
• Inverse matrix. Rank of a matrix. Determinant. Simultaneous equations.
• Numerical linear algebra with Matlab.
  

For attending students
Grading percentages is:

• 20% on completion of problem sets.
• 10% on completion of Matlab problem sets.
• 70% on two written exams.

Each written exam (midterm and final) contains a mix of open ended and multiple choice questions. The exam is closed book. Students are required to solve numerical and theoretical exercises, give definitions and prove theorems.

For non attending students
Grading is based on a written examination with a mix of open ended and multiple choice questions. The exam is closed book. Students are required to solve numerical and theoretical exercises, give definitions and prove theorems.

• S. Cerreia Vioglio, M. Marinacci, E. Vigna, Principles of Mathematics for Economics.
• Other materials provided online.