AMP_2 Applied mathematics

Institute of Technology and Business in České Budějovice
summer 2025
Extent and Intensity
2/4. 7 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Zdeněk Dušek, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
AMP_2/P01: Tue 9:40–11:10 E7, D. Smetanová
AMP_2/S01: Wed 9:40–11:10 I316, Thu 13:05–14:35 I316, D. Smetanová
Prerequisites (in Czech)
AMP_1 Applied mathematics 1
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of the course is to build on Mathematics I. (applications of complex numbers, linear algebra, functions of real variables and infinitesimal calculus) with simple solutions of differential equations applied in engineering practice. In addition, extend the basic knowledge with advanced applications of complex numbers and the fundamentals of vector analysis applied to physical fields, both scalar and vector.
Learning outcomes
Student knows advanced techniques of differential and integral calculus and their applications, in particular partial derivatives and their importance, multiple integral and its practical application, special differential equations in real and complex domain, differential operators used in physics.
Syllabus
  • 1. Differential and integral calculus of functions of two or more variables, partial derivative, total differential.
  • 2. Derivation of a composite function of several variables, derivation of functions in implicit and parametric form.
  • 3. Double and triple integral of more complex problems of engineering practice.
  • 4. First order differential equations, their meaning and applications in engineering practice.
  • 5. 2nd order differential equations, their meaning and applications in engineering practice.
  • 6. Partial differential equations, their meaning and applications in engineering practice.
  • 7. Demonstration of differential equations in the complex domain.
  • 8. Application of complex numbers in electrical engineering, especially for solving alternating processes.
  • 9. Fundamentals of vector analysis, vector function of scalar and vector argument.
  • 10. Examples of scalar and vector physical fields.
  • 11. Scalar stationary fields, gradient operator of a scalar function.
  • 12. Vector stationary field, vector divergence operator.
  • 13. Rotation and divergence operators and their applications.
Literature
    required literature
  • MOUČKA, J. a P. RÁDL, 2015. Matematika pro studenty ekonomie. 2., upravené a doplněné vydání. Praha: Grada. Expert. ISBN 978-80-247-5406-2.
  • SIMMONS, G. F., 2017. Differential Equations with Applications and Historical Notes. Taylor & Francis. ISBN 978- 1498702591.
  • CONWAY, J. B., 2018. A First Course in Analysis. Cambridge University Press. ISBN 978-1107173149.
    recommended literature
  • DOŠLÁ, Z. a P. LIŠKA, 2014. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. Praha: Grada. ISBN 978-80-247-5322-5.
  • KŘÍŽ, O., J. NEUBAUER a M. SEDLAČÍK, 2021. Základy statistiky: Aplikace v technických a ekonomických oborech. 3. rozš. vyd. Praha: Grada. ISBN 978-80-271-3421-2.
  • CHLÁDEK, P., 2012. Matematika I. České Budějovice: Vysoká škola technická a ekonomická v Českých Budějovicích. ISBN 978-80-7468-004-5.
Forms of Teaching
Lecture
Seminar
Consultation
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Brainstorming
Critical Thinking
Individual Work– Individual or Individualized Activity
Teaching Supported by Multimedia Technologies
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Lectures40 
Preparation for Seminars, Exercises, Tutorial40 
Preparation for the Final Test24 
Attendance on Lectures26 
Attendance on Seminars/Exercises/Tutorial/Excursion52 
Total:1820
Assessment Methods and Assesment Rate
Test – mid-term 30 %
Test – final 70 %
Exam conditions
To successfully complete the course, it is necessary to achieve the sum of the continuous and final assessment of at least 70% under the conditions set out below. V~30 points can be obtained in the continuous assessment, i.e. 30%. In the final assessment, it is possible to a total of 70 points, i.e. 70 %. Intermediate evaluation Intermediate test(s) - 30 points (i.e. 30 %) Final assessment Final test - 70 points (i.e. 70%) A 100 – 90, B 89,99 – 84, C 83,99 – 77, D 76,99 – 73, E 72,99 – 70, FX 69,99 – 30, F 29,99 – 0 A full-time student is required to take contact classes, i.e. everything except lectures, to meet the mandatory 70% attendance.
Language of instruction
Czech
Teacher's information
A full-time student is required to take contact classes, i.e. everything except lectures, to meet the mandatory 70% attendance.
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