Insegnamento a.a. 2026-2027

• Set Theory elements; union, intersection, Morgan laws. Power set and partitions.
• Numbers. Sum of real numbers; main cases. Product of real numbers. Factorial, binomial coefficients.
• Mention to sequences of real numbers and their sum: geometric sequence.
• Real functions of one real variable; the graph of a function. Properties; maxima and minima. Elementary functions. Piecewise functions.
• Composition of functions. Inverse function. Solving equations.
• Derivatives. Elementary derivatives. The tangent line. Algebra of derivatives. The chain rule.
• Stationary points. Monotonicity and derivatives. First order test for maxima and minima.
• Second order derivative; concavity/convexity test. Second order test for maxima and minima.
• Plotting the graph of a function. Inequalities.
• Real functions of two real variables; 3D plot and level curves. Upper and lower sets.
• Partial derivatives and gradient. Stationary points.

• Understand and explain the main set operations.
• Recognize relevant sums and the appropriate methods to calculate them.
• Select the correct methodology for arguing main properties of a real valued function

• Calculate sums of real numbers in the relevant cases.
• Properly calculate derivatives of a real function.
• Apply calculus to analyze the main properties of a function and to plot a qualitative graph.
• Use basic functions to solve equations and to analyze inequalities.

• Lectures
• Practical Exercises

     Traditional whiteboard lessons with slide support projected into the classroom.

Assessment is included in the assessment procedures for code 50277.

There will be no additional assessment procedures.

All teaching material will be available on Bboard classes at the beginning of the preparatory course.