15968 - Physics and Mathematics

Learning outcomes

MATHEMATICS (Teaching Unit 1)

At the end of the course, the student knows the technical mathematical tools and their use for the quantitative study of phenomena. The student is then able to set up and solve problems and to assimilate new concepts from the experience and previous knowledge.

 

PHYSICS (Teaching Unit 2)

The course introduces some base elements of classical mechanics, fluid mechanics, and thermodynamics, with the relative methodologies and applications in the fields of physiology, biology, and chemistry.

 

Course contents

MATHEMATICS (Module 1)

1. Elements of set theory. Definition of set. Subset and proper subset. Union and intersection among sets. Empty set. Numerical sets: natural, integer, rational, irrational, and real numbers. Numerical intervals.

2. Functions. Concept of relation. Properties of relations. Definition and properties of functions. Domain and codomain of a function. Inverse function. Composite function. Elementary functions domain.

3. Theory of limits. Neighborhood of a point, accumulation points. Limits for functions. Continuity of a function. Infinite limit. Right and left limit. Properties of limits. Limits of elementary functions. Special limits.

4. Derivatives. Definition of incremental ratio. Derivative of a function. Properties of derivatives. Derivative of elementary functions. Derivative of inverse and composite funcitons. Second derivative. Increasing, decreasing, monotone functions. Convexity and concavity. Maximum, minimum and inflection points. De l’Hopital theorem.

5. Functions study. Domain. Intersections with the axes. Vertical, horizontal and oblique asymptotes. Maximum, minimum and inflection points. Concavity.

6. Elements of statistics and data analysis. Aritmethic and geometric mean, median, fashion. Root mean square, variance, standard deviation. Covariance, correlation, linear regression, least square method.

PHYSICS (Module 2)

1. Measurement. Measurement of a physical quantity, dimensions and units, conversions, significant figures, rounding and truncation, scientific and normalized notation, precision and accuracy, experimental errors, law of averages, mean value.

2. Vectors. Vectors and scalars, notation and representation of vectors, vectorial algebra, vector components, dot and cross product.

3. Kinematics. Motion and reference system, rectilinear motion, uniform motion, average and instantaneous velocity, average and instantaneous acceleration, uniformly accelerated motion, circular motion, harmonic motion.

4. Dynamics. Forces, First Newton’s law, inertial systems, Second Newton’s law, universal gravity law, gravity acceleration, mass and weight, elastic force, normal force, simple pendulum, friction force, centripetal force, fundamental forces.

5. Energy and Work. Work of a constant force, work of gravity and elastic force, Kinetic energy, efficiency, power, conservative forces, potential energy, conservation law of mechanic energy, gravitational and elastic potential energy, harmonic motion energy, dissipative forces, moment of a force, static equilibrium.

6. Fluid Mechanics. Density, pressure, Stevin’s law, Pascal’s Law, atmospheric pressure, buoyancy, fluid dynamics, ideal fluids, continuity equation, Bernoulli’s theorem, real fluids, Poiseuille’s law, turbulent flow, Reynolds number, Stokes’ law, sedimentation, superficial tension, capillarity.

7. Thermodynamics. Temperature and its scales, kinetic theory of gas, laws of gases, Avogadro’s number and mole, law of perfect gases, heat and work, thermal capacity and specific heat, change of phase, latent heat.

Readings/Bibliography

The slides shown during class, both for Mathematics and Physics, will be available on the online institutional platform for teaching support (https://virtuale.unibo.it/) in few days after having been shown, or, under specific request, before.

These will contain, in a schematic way, all the teaching material necessary to perform the exam. The students willing to integrate their knowledge, or deepen some specific topics, can refer to the following volumes.

When available, the students can refer to the volumes of Mathematics and Physics used at the high school. In this case, they should be checked by the teacher in order to verify the coverage of the course topics.

MATHEMATICS (Module 1)

Claudio Caprara, “Mathematics for Agricultural and Life Sciences: Principles of Calculus with Solved Problems”, Nova Science Publishers, Inc., New York, USA. ISBN: 978-1-53618-027-5.

Some exercises will be available on the online platform Virtuale.

The online resource, available for all students of University of Bologna: https://almaorienta.unibo.it/it/almamathematica

PHYSICS (Module 2)

Ezio Ragozzino, Principi di fisica, Ed. EdiSES (Napoli)

Alessandro Lascialfari, Ferdinando Borsa, Anna Maria Gueli, Principi di Fisica per indirizzo biomedico e farmaceutico, Ed. EdiSES (Napoli).

Electronic exercises book available from the web page: http://ishtar.df.unibo.it/Uni/bo/farmacia/all/navarria/stuff/eser/eser.html

Teaching methods

The course will cover the topics of the program through classroom teaching, both for lectures and for exercises.

For the latter, it is possible to contact the course tutor to organize additional classes for exercises, revision and exam simulations.

Assessment methods

To pass the exam and achieve the final evaluation (that is one for the two teaching units), the two tests (Mathematics and Physics) should be passed, separately.

The single tests will be passed with a minimum evaluation of 18/30.

The aggregated evaluation of the course will be given by the average of the two tests, rounded up. The achievement of 30/30 in both tests provides a final evaluation of 30 and laudation.

The grade registration will be accomplished only under the explicit acceptance of the final grade by the student to the teacher responsible for the course. This can be fulfilled by e-mail as well (sent to filippo.zaniboni@unibo.it), by reporting in the text the date and grades of the two exams, the final evaluation, and an explicit acceptance of the latter.

In lack of this consent, the final evaluation won’t be recorded.

In the following, the details on the single tests are reported.

MATHEMATICS (Module 1)

The exam is done through a written test, with grades expressed in thirtieths.

The test consists of a set of 10 brief exercises, concerning the topics listed in the Course Contents section, that should be completed in 90 minutes unless specific derogation which has to be agreed upon before the exam.

The exercises are subdivided as follows: one about sets (3 points); two about function domain (one providing 3 points and one, more difficult, 4 points); three about limits (two providing 3 points and one, more difficult, 4 points); three about derivatives (two providing 3 points and one, more difficult, 4 points); one simple study of function (3 points). The total is 33 points.

The written test is passed with a grade higher or equal to 18. For grades exceeding 30, the evaluation will be “30 e lode”. Correct portions of exercices will be evaluated as well.

For the written test no notebooks, tablets, smartphones, or pocket calculators are allowed: the computation are really simple.

The degree has not expiration date.

The student who passes the written test can choose to refuse the grade and take the examination at the next session. Should a new test be delivered, the previous evaluation will be invalidated.

PHYSICS (Teaching Unit 2, Dott. Zaniboni)

2 hours written test made of 6 exercises concerning the course contents.

For the test, the use of books, personal notes, class slides, and a calculator is admitted. It is strictly forbidden the use of communication devices (smartphone, tablet, notebook).

The test will be passed should the evaluation reach at least 18. Three correct exercises (numerical result included) will be evaluated 6 points each, and are then sufficient to pass the written test; further correct exercises will be scored 4 points each.

Correct exercise pieces are accounted for as well.

The grade has not expiration date. The test can be repeated, but the delivery of a new trial will invalidate the previous grade.

Teaching tools

PC and video projector.

Spreadsheet software (Microsoft Excel or open-source equivalent) for examples of data analysis and visualization.

Office hours

See the website of Filippo Zaniboni