SM/0092 - MATHEMATICS 2
Academic Year 2021/2022
Free text for the University
FABIO ZUDDAS (Tit.)
- Teaching style
- Lingua Insegnamento
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1. Acquiring knowledge and understanding.
The course is devoted to students in the first year of the Bachelor's degree in Chemistry. It aims at providing a working knowledge of the main facts of real analysis (functions in one variable, derivatives and integrals) and of linear algebra (vectors and matrices). These topics are presented by providing a rigorous theoretical justification.
2. Applying knowledge and understanding.
Possible applications of the methods treated during the course will be discussed, both for the solution of mathematical problems and for the solution of problems arising in other disciplines like Chemistry and Physics.
3. Making informed judgements and choices.
This course allows assiduous students to achieve knowledge and understanding sufficient for applying the techniques studied to the solution of mathematical problems which typically appeared in chemical sciences.
4. Communicating knowledge and understanding.
The evaluation of the written test takes into account the ability of the student to give a methodical and consistent exposition of the topics of the program necessary to find the solutions of the assigned exercises.
5. Abilities to continue learning.
This course allows assiduous students to acquire a basic expertise which provides the basis to attend the consecutive exams of Mathematics as well as the disciplines, like chemistry, whose language is expressed in a mathematical way.
It is necessary that the student has already passed "Matematica 1". In particular, the students must be able to: articulate logical reasoning in a mathemaical context, with mathematical language; be familiar with elementary set theory; know the real numbers; be familiar with the concept of function and the properties of functions and their graphs (in particular, of the absolute value, polinomials, exponentials, logarithms and trigonometric functions); basics of analytic geometry in the plane. The student must also be able to solve equations and inequalities that involve the functions mentioned above.
0. Recalls on elementary functions
1. Limits: Definition. Arithmetic operations. Useful theorem about limits. Indeterminate forms. Calculus of limits.
2. Continuity: definitions and properties. Main theorems on continuous functions defined on a finite closed interval.
3. Differentiable functions of one variable: Definition of derivative. Geometrical and physical interpretations of the derivative. Equation of the tangent line in a given point of the graph of a given function. Connection between continuity and differentiability. Calculus of the derivative: arithmetic operations, chain rule and derivative of the inverse function. Differential. Mean value theorem (aka Lagrange theorem) and its consequences. Extreme values and criteria to identify them. Concavity and convexity. L'Hospital's rule. Taylor's theorem. Application: how to plot the graph for a given function.
4. Antiderivatives: Definition and properties. Calculus of easy antiderivatives. Change of variables and integration by parts. Riemann integrals: Definition. Geometrical interpretation of the Riemann integral. Properties of the Riemann integrals and mean value theorem. Fundamental theorem of calculus and its consequences. Improper Integral: definition and properties.
5. Linear Algebra: vectors, coordinates, scalar product, cross product and norm of vectors; matrices: determinant, rank.
The course consists of 48 lecture hours. Lectures will be given by using either chalk and blackboard or slides. In order to make the teaching as efficient as possible, the theoretical topics are immediately accompanied by exercises and solutions of grading written tests. Furthermore, the teacher and the tutor will lead 20-25 (total amount) hours of tutorial activity to assist the students. During this tutorial activity, the homework will be discussed and solved in a detailed way. The teacher offers constant assistance to the students during the whole year both by personal interviews and by means of e-mail messages.
Verification of learning
The verification of learning of the students is assessed by means of a written exam and an oral exam. The written exam includes exercises which require operative skills and knowledge of the theory on the entire contents of the course. To pass the exam, the student should obtain at least 18/30.
To pass the exam, the student should show to have acquired a sufficient knowledge of all of the topics of the course. To obtain the maximal grade (30-30 with “cum laude”), the student should show to have acquired an excellent knowledge of all of the topics of the course.
The final score of the exam is calculated by summing the scores obtained from each exercise (which depend then on the specific exercises of the exam).
Indicatively, we have
18-20: sufficient (text comprehension and knowledge of basic formulas)
21-24: more than sufficient (ability to use the formulas in order to answer to specific points)
25-27: good (good knowledge of the course's program)
28-30: very good (very good knowledge of the course's program)
30 cum laude (ability to answer to more theoretical questions)
1) C. D. Pagani, S. Salsa, Analisi Matematica Vol. 1, Zanichelli
2) Teacher's notes
In the teaching material's website are available also the old exam tests (including correction) and several exercises (some including correction).
Regarding the book recommended in the Section "Testi di riferimento": in his lessons, the teacher does not follow faithfully the book, either for the topics or for the order they are presented. This book (but this would hold true for any other text the teacher could choose) necessarily contains
much more topics than the ones selected by the teacher for the course and its presentation reflects its author's tastes, which do not fully coincide with the teacher's ones.
Despite being, to the teacher's knowledge, the text closest to the course's style, the book is intended only as a reference to explore and deepen the topics of the lessons, and to stimulate comparisons and then new considerations with its different presentation.
For a text faithfully reproducing the lessons' contents, the teacher's notes are already available in the teaching material's website: however, we warn that these notes are usually subject to small changes and additions when these turn out to be necessary during the course, so we suggest
to the student not to print them all at the beginning of the course. These possible changes will be made available weekly during the course.
Our University provides support for students with specific learning disability (SLD). Those interested can find more informations at this link: