MA0035 Physical motivation for teaching mathematics 2

Faculty of Education
Spring 2022
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Taught in person.
Teacher(s)
RNDr. Břetislav Fajmon, Ph.D. (seminar tutor)
Mgr. Jitka Panáčová, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Břetislav Fajmon, Ph.D.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable of Seminar Groups
MA0035/01: Mon 14:00–15:50 učebna 70, B. Fajmon
Prerequisites
MA0034 Math. motivation in physics 1
Successful completion of MA0034 is a good prerequisite for this subject, as far as physical concepts are concerned. As for the mathematical part, no special prerequisites are needed but a course on mathmatical analysis at a university level -- this should stand for the concepts taught in MA0034 in case has not finished MA0034.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 9 fields of study the course is directly associated with, display
Course objectives
i) To impart some topis from the theory of machanical solids and sets of particles and corresponding matematical tools; ii) to inspire future secondary school teachers to motivate students with technical examples while teaching some mathematical concepts; iii) to present some areas of mathematical analysis set within the framework of specific areas of physics
Learning outcomes
After a successful completion of the course the students will be able to a) use exponential and logarithmic functions in physical models involving differential equations; b) work with a curve integral in calculations of work along the curve; c) use definite integrals to determine the centre of gravity; d) work with the concept of a force impulse, work out the description of direct and skewed collisions; e) use doble and triple integral to calculate a moment of inertia for solids of different shapes; f) describe situations in mechanics involving rolling, torque (= moment of force) and rotational momentum.
Syllabus
  • The syllabus is built on physical concepts:
  • 1-2) Physical concepts: work and kinetic energy, work of a varying force, work of an elastic force, power. Mathematical concepts: exponential and logarithmic functions and their properties, integration methods (indefinite integral), solution of some differential equations (separable equations, linear equations of the first order);
  • 3-4) Physical concepts: potential energy, independence of conservative forces on the trajectory, preservation of energy, work of outer and nonconservative forces. Mathematical concepts: parametrization of a curve, curve integral of the 1st and 2nd kind;
  • 5-6) Physical concepts: centre of gravity, momentum, preservation of momentum, outer forces and changes ofinner energy. Mathematical concepts: definite integral and its computation, area, volume of a rotational solid.
  • 7-8) Physical notions: force impulse, direct and skewed collisions. Mathematical notions: curve integral of the 2nd kind revisited;
  • 9-10) Physical concepts: rotational movement, angle speed, angle acceleration, relationship between angular and circumferential description of movement; kinetic energy of rotational movement, moment of inertia, moment of force, momentum. Mathematical concepts: double and triple integral to calculate moment of inertia
  • 11-12) Physical concepts: triple integral (moment of inertia for solids in pictures d,h,j, page 274 of the Physics textbook).
Literature
    required literature
  • HALLIDAY, David, Robert RESNICK and Jearl WALKER. Fyzika : vysokoškolská učebnice obecné fyziky. Translated by Jan Obdržálek - Jiří Komrska - Petr Dub. Vyd. 1. V Brně: Vutium, 2000, 1 sv. ISBN 8021418680. info
    recommended literature
  • BUŠEK, Ivan and Emil CALDA. Matematika pro gymnázia : základní poznatky z matematiky. 1. vyd. v bodovém písmu. Brno: Středisko pro pomoc studentům se specifickými nároky Masarykovy univerzity v Brně, 2005, 214 s. ISBN 8021038233. info
  • MACHÁČEK, Martin. Fyzika pro gymnázia : astrofyzika. 2., upr. vyd. Praha: Prometheus, 2004, 143 s. ISBN 8071962775. info
  • ŠTOLL, Ivan. Fyzika pro gymnázia : fyzika mikrosvěta. 3., přeprac. vyd. Praha: Prometheus, 2002, 190 s. ISBN 8071962414. info
  • LEPIL, Oldřich. Fyzika pro gymnázia : mechanické kmitání a vlnění. 3. přeprac. vyd. Praha: Prometheus, 2001, 129 s. ISBN 8071962163. info
  • LEPIL, Oldřich and Zdeněk KUPKA. Fyzika pro gymnázia :optika. 2. vyd. Praha: Prometheus, 2001, 167 s. ISBN 80-85849-71-2. info
  • BARTUŠKA, Karel. Fyzika pro gymnázia :speciální teorie relativity. 3. přeprac. vyd. Praha: Prometheus, 2001, 63 s. ISBN 80-7196-209-0. info
  • HRUBÝ, Dag and Josef KUBÁT. Matematika pro gymnázia : diferenciální a integrální počet. 2., upr. vyd. Praha: Prometheus, 2001, 210 s. ISBN 8071962104. info
  • ODVÁRKO, Oldřich. Matematika pro gymnázia : goniometrie. 3. vydání. Praha: Prometheus, 2001, 139 stran. ISBN 8071962031. info
  • ODVÁRKO, Oldřich. Matematika pro gymnázia : posloupnosti a řady. 2. vyd. Praha: Prometheus, 2001, 126 s. ISBN 8071961957. info
  • BOČEK, Leo, Jaroslav ZHOUF and Jura CHARVÁT. Matematika pro gymnázia : rovnice a nerovnice [Prometheus, 2001]. 3. vyd. Praha: Prometheus, 2001, 221 s. ISBN 80-7196-154-X. info
  • CALDA, Emil. Matematika pro gymnázia :komplexní čísla. 3. vyd. Praha: Prometheus, 2001, 134 s. ISBN 80-7196-187-6. info
  • LEPIL, Oldřich and Přemysl ŠEDIVÝ. Fyzika pro gymnázia : elektřina a magnetismus. 5. přeprac. vyd. Praha: Prometheus, 2000, 342 s. ISBN 8071962023. info
  • BEDNAŘÍK, Milan and Miroslava ŠIROKÁ. Fyzika pro gymnázia : mechanika. 3. přeprac. vyd. Praha: Prometheus, 2000, 288 s. ISBN 9788071961765. info
  • POMYKALOVÁ, Eva. Matematika pro gymnázia. 4. upr. vyd. Praha: Prometheus, 2000, 206 s. ISBN 8071961744. info
  • KOČANDRLE, Milan and Leo BOČEK. Matematika pro gymnázia :analytická geometrie. 2. upr. vyd. Praha: Prometheus, 2000, 220 s. ISBN 80-7196-163-9. info
  • CALDA, Emil and Václav DUPAČ. Matematika pro gymnázia : kombinatorika, pravděpodobnost, statistika. 4., upr. vyd. Praha: Prometheus, 1999, 170 s. ISBN 9788071961475. info
  • POMYKALOVÁ, Eva. Matematika pro gymnázia :stereometrie. 3. vyd. Praha: Prometheus, 1995, 223 s. ISBN 80-7196-178-7. info
  • BARTUŠKA, Karel and Emanuel SVOBODA. Fyzika pro gymnázia : molekulová fyzika a termika. 2. vyd. Praha: Prometheus, 1994, 254 s. ISBN 8085849461. info
  • POMYKALOVÁ, Eva. Matematika pro gymnázia :planimetrie. 4., upr. vyd. Praha: Prometheus, 1993, 206 s. ISBN 80-7196-174-4. info
Teaching methods
Presentation, task for groups or individuals.
Assessment methods
The credits will be approved on the basis of an active cooperation in class and with 60 per cent of success in the final test.
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://matematicky.rozhovor.cz/predmety/mafy/0002matematika-a-fyzika.php
The course is also listed under the following terms Spring 2019, Spring 2020, Spring 2021, Spring 2023, Spring 2024.
  • Enrolment Statistics (Spring 2022, recent)
  • Permalink: https://is.muni.cz/course/ped/spring2022/MA0035