SM/0091 - MATHEMATICS 1
Academic Year 2021/2022
Free text for the University
MARINA MUREDDU (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 good knowledge of the basic facts of mathematics which are systematically used in the other two courses of Mathematics. In particular, the students should be able to plot graphs of exponential, logarithmic and trigonometric functions as well as to solve algebraic, exponential, logarithmic and trigonometric equations or inequalities.
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 and physical 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. The communicating knowledge is further analyzed during the oral interview.
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.
Since the main objective of the course is to introduce the basic topics of Mathematics, few prerequisities are required. In particular, the students must be able to: manage simple algebraic calculations, know the rules to factorize numbers and polynomials.
1. Mathematical language: sets and related terminology. Sets of numbers: natural numbers, integer numbers, rational numbers and real numbers. Absolute value of a real number. The concept of function: definition and examples. Domain and range of a function. Injective and surjective function.
2. Analytical geometry in the plane. The cartesian plane. Equations of straight lines and circles. Diagram of functions (at this point mainly diagram of straight lines and functions where the absolute value of some terms appear). Algebraic first order equations and inequalities. Equations and inequalities where the absolute value of some terms appear. Canonical form of conic section.
3. Polinomyal, power, esponential and logaritm functions. Polinomyal: definition and examples. The concept of the inverse function: definition and examples. Diagrams of the powers, exponential and logarithmic functions. Equations and inequalities of algebraic equations of degree two. Equations and inequalities of algebraic equation with degree larger than two. Exponential, logarithmic, irrational and trigonometric equations and inequalities.
4. Trigonometric functions: definitions and their diagrams. The inverse of the trigonometric functions and their diagrams. Goniometric equations and inequalities.
5. Complex numbers. Algebraic and trigonomeric representations of complex numbers. Moivre's formula and n-th roots of a complex number. Euler's formula.
6. Cartesian Reference in R^3. Vectors in R^3: Inner product and cross product: defintions and properties. A very brief introduction on the equations of planes and quadric surfaces.
7. Complements on the real line: Infimum and supremum of a subset of real numbers. Accumulation point of a subset od a real numbers. Open and closed sets.
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.
The main tools to support teaching are the teacher's personal web site: http://people.unica.it/francescodemontis/
It provides information updated in real time, including: a diary reporting the topics treated in each lecture, information on teaching activities, additional documents to support learning, texts and solutions of tests similar to the final grading tests.
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. Only students who have scored at least 18/30 in the written exam will be admitted to the oral exam. The oral exam- which usually lasts 20 minutes- consists of a discussion on the exercises of the written exam where some difficulties have been detected.
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 instead show to have acquired an excellent knowledge of all of the topics of the course.
An alternative grading mode is available for those students who regularly attend the lectures. It consists of two written tests and a final oral exam. The first written test concerns the topics studied in the first 20 lecturing hours and it takes place immediately after the first half of the lectures has been delivered. The second written test concerns the remaining topics (but it also requires a global understanding of the program of the course) and it takes place, approximately, one week before the first official grading date. The oral exam follows for those students who have obtained at least 18/30 in both the written tests. The oral exam follows the same rules described above.
S. Montaldo, A. Ratto, Matematica: 2^3 capitoli per tutti, Liguori Editore [http://www.liguori.it/schedanew.asp?isbn=5511], (2011).
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