Knowledge from bachelor-level mathematics, physics, and thermodynamics is expected. Students will make use of their understanding of solving systems of linear equations and numerical methods for finding the solutions of nonlinear functions. The topic of unsteady-state balancing is also related to formulating differential equations and solving them.

SEMINARS:
To receive course credit, students must participate regularly and actively in the exercises (which means no more than two excused absences), submit all assigned tasks, successfully pass the written tests, and complete a semester project carried out in small student groups. The project focuses on solving a selected example, allowing students to verify their understanding of balancing theory and demonstrate that the acquired knowledge can be applied to more complex problems. The criterion for earning the course credit is obtaining more than half of the total points available from the ongoing written tests.

Attendance at lectures is not formally monitored; however, completing the tasks in the exercises requires knowledge gained from the lectures.
EXAM:

The examination consists of three parts: a written test, computational problems, and an oral component.

• Written test – This part assesses knowledge of the material covered in both lectures and exercises. The test contains 15 to 20 questions (the exact number may vary depending on the assignment). Questions may involve multiple-choice answers (A, B, C), simple calculations, or explanations of specific issues (sketches, descriptions, equations).
• Computational problems – Students solve 2 to 3 calculation-based tasks, which may include solvability analysis, checking problem understanding, formulating balance equations, and, where required, solving them.
• Oral part – Students explain selected slides from the presentations used during the semester.

Each part is assessed separately on a scale from A to F, and each part carries the same weight. A student must achieve at least an E in each part. An F is awarded if the student demonstrates less than half of the required knowledge (e.g., less than half of the points on the written test, solving none or only one of the computational problems, etc.). If a student receives an F in any part, they must repeat the entire examination. In all other cases, the final grade reflects the performance in each part.

After completing the course, students will:

• Gain an overview of different types of balance problems, their complexity, and methods for constructing mass balances.
• Learn that balancing is a general methodology based on the laws of conservation of mass, energy, and substances.
• Be able to analyse balance problems in terms of the number of known and unknown variables, and formulate balance equations for cases involving mixing, splitting, and separating multiple material streams, both without chemical reactions and with simple reactions defined by a given conversion level.
• Understand various ways of expressing energy balances for different types of systems.
• Be able to solve simpler problems without computational tools or a computer, and solve selected cases with support from MS Excel.
• Gain an understanding of how balancing relates to other methods used to evaluate projects from a sustainability perspective.
• Understand how the EU Taxonomy influences the design of production technologies and processes.
• Be able to apply balance-related knowledge to prepare data for non-financial reporting.
• Be capable of creating basic Sankey diagrams as a visualization of material and energy flows.
• Become familiar with the principles of greenhouse gas emissions reporting and understand key terminology in both English and Czech.
• Gain orientation in mass-flow mapping and be able to visualize and inventory flows within basic systems.
• Strengthen their ability to construct mass and energy balances for fundamental processes, including those that produce or utilize secondary raw materials as substitutes for primary resources.
• Be able to distinguish different categories of environmental impacts across environmental compartments and identify the flows that may contribute to them.

Selected knowledge from the course can be tested in an e-learning module available in Czech.

• Programme N-PRI-P Master's 1 year of study, winter semester, compulsory, profile core courses