Fundamental concepts. Real numbers. Inequalities. Trigonometry. Exponential functions and logarithm. Factorials and binomial coefficients. Newton's formula for binomials. Real functions of a real variable. Sequences and limits. Continuous functions. Derivatives and tangent line to the graph of a function. Fundamental theorem of Calculus. Absolute and relative maxima and minima. Trigonometric and exponential functions. Logarithms. Definite and indefinite integral
Walter Dambrosio
Analisi Matematica fare e comprendere il
Zanichelli editore
Marco Abate
Matematica e statistica
Mc Graw Hill
Learning Objectives
Basic knowledge of calculus as required by a scientific degree course. Namely the basic concepts of differential calculus will be explained devoting a special care to their possible practical applications.
We will teach which are the most important elementary functions and their use in applications. The concepts of derivative and integral will be explained, showing how to use them in applied sciences.
We do expect that, at the end of this course, students will be able to understand which problems are likely to be studied using derivatives and integrals and hence could handle and compute elementary functions, derivatives and integrals
Prerequisites
The knowledge of fundamental concepts and ideas of mathematics is required. Specifically basic knowledge of algebra and analytic geometry is required as well as trigonometry, logarithms and exponentials
Teaching Methods
Classroom lessons and training. Lots of time will be devoted to the solution of exercises and to the basic concepts of algebra, analytic geometry, trigonometry and logarithms
Further information
During the course students will be shown which arguments to study to pass the OFA test
Type of Assessment
Written exam. Candidates have two hours and thirty minutes to solve a number of exercises (ranging from 3 to 5) dealing with derivatives, integrals, limits and the study of a function
Course program
Fundamental concepts. Real numbers. Inequalities. Trigonometry. Exponential functions and logarithm. Factorials and binomial coefficients. Newton's formula for binomials. Real functions of a real variable. Sequences and limits. Continuous functions. Derivatives and tangent line to the graph of a function. Fundamental theorem of Calculus. Absolute and relative maxima and minima. Trigonometric and exponential functions. Logarithms. Definite and indefinite integral. Introduction to multivariable calculus: gradient and critical point