Ternopil Ivan Puluj National Technical University
Каф. конструювання верстатів, інструментів та машин
Mathematical modeling by PC of Engineering problems
syllabus
1. Educational programs for which discipline is mandatory:
#  Educational stage  Broad field  Major  Educational program  Course(s)  Semester(s) 

1  bachelor's  13. Механічна інженерія  131. Прикладна механіка (бакалавр)  2  3 
2. The course is offered as elective for all levels of higher education and all educational programs.
4. Information about the course 


Study hours structure 
Lectures: 32 Practical classes: 32 Laboratory classes: 0 Amount of hours for individual work: 58 ECTS credits: 3 
Teaching language  english 
Form of final examination  credit 
Link to an electronic course on the elearning platform of the university  https://dl.tntu.edu.ua/bounce.php?course=5402 
5. Program of discipline
Description of academic discipline, its goals, subject of study and learning outcomes
This course allows you to reveal the content and peculiarities of using computer technology in the implementation of typical algorithms and in the formation of mathematical models of tasks for the analysis and solving of engineering problems. Each student can acquire skills in specialized packages for performing design, graphic and research work, adapted to the conditions of work in the field of training.
Practical works forms students' practical skills for the using Windows operating environment and the MathCAD V7.0 PRO multifunctional package (MathCAD 2000 PRO, MathCAD 15).
Practical works forms students' practical skills for the using Windows operating environment and the MathCAD V7.0 PRO multifunctional package (MathCAD 2000 PRO, MathCAD 15).
The place of academic discipline in the structural and logical scheme of study according to the educational program
Prerequisites. List of disciplines, or knowledge and skills, possession of which students needed (training requirements) for successful discipline assimilation
mathematics
Contents of the academic discipline
Lectures (titles/topics)
3.1. Lectures
№ з/п Topic and contents in brief Number of hours
Fulltime Parttime
1 Topic № 1. Introduction. Characteristics of the MathCAD package. Subject and objectives of the course. Overview of CAD systems and MathCAD packages. The structure of the MathCAD package. Interface and MathCAD package panels.
Topic № 2. Working with variables in the MathCAD package. The concept of a mathematical expression. General characteristics of the variables in the MathCAD package. The notion of distinguish lowercase and uppercase in the MathCAD package. Characteristics of four types of range variable. Rules for the formation of mathematical expressions in the MathCAD package.
2 Topic № 3. The concept of function in the package MathCAD. Characteristics of functions in the MathCAD package. Rules for forming a function in the MathCAD package. Analysis of user function structure. Methods for describing arguments using builtin functions and user functions.
Topic № 4. Organization of work with data arrays in the MathCAD package.
Organization of ordered arrays. The procedure for creating matrices. Characteristics of elements of ordered arrays and matrices. Service variable ORIGIN.
3 Topic № 5. Construction of charts in the package MathCAD. Algorithm for plotting. Features of constructing graphs of functions with several arguments. Construct function graphs for various arguments.
Topic № 6. Editing the area of the graphs.
Construct graphs of functions in different colors and different types of lines (marks). Editing the graph area. Zoom and Trace commands. Modification of the coordinate plane for plotting.
4 Topic № 7. The solution of linear and nonlinear equations in the MathCAD package.
The solution of polynomials. Algorithm for using builtin functions of the package (function ROOT) for finding solutions of equations. Use the Polyroots function to find the polynomial roots.
Topic № 8. Solving systems of linear and nonlinear equations in the MathCAD package.
Using the GivenFind solvers block to find solutions to systems of linear and nonlinear equations. Using the GivenMinerr deployment block to investigate common functions.
5 Topic № 9. Conditioned range operator (CRO).
The essence of the use of conditional ranked operator. Analysis of individual examples of CRO use for the study of functional dependencies.
Topic № 10. Range Conditional Branching operator.
The algorithm of formation and the principle of the ranks of conditional transition operators. The use it for constructing composite functions. 2
2 
6 Topic № 11. The essence of the least squares method (LSM). Analytical transformations in the MathCAD package. Understand the essence of the least squares method. The analys the research algorithm for the discrete set of LSMs. A describe the mechanism for implementing the simplest analytical transformations in the MathCAD package
Topic № 12. The linear form of MNC and its implementation with builtin functions of the package.
A describe the sequence of actions using the internal Intercept and Slope functions.
7 Topic № 13. Linear regression of the general type in the package MathCAD.
To reveal the essence of the method of least squares through the realization of linear regression of the general form. To analyze the algorithm of research of a discrete set of points of LSM using the Linfit function.
Topic № 14. Nonlinear regression of the general type in the package MathCAD.
To reveal the essence of the method of least squares through the realization of nonlinear regression of the general form. To analyze the algorithm of research of a discrete set of points of LSM using the Genfit function.
№ з/п Topic and contents in brief Number of hours
Fulltime Parttime
1 Topic № 1. Introduction. Characteristics of the MathCAD package. Subject and objectives of the course. Overview of CAD systems and MathCAD packages. The structure of the MathCAD package. Interface and MathCAD package panels.
Topic № 2. Working with variables in the MathCAD package. The concept of a mathematical expression. General characteristics of the variables in the MathCAD package. The notion of distinguish lowercase and uppercase in the MathCAD package. Characteristics of four types of range variable. Rules for the formation of mathematical expressions in the MathCAD package.
2 Topic № 3. The concept of function in the package MathCAD. Characteristics of functions in the MathCAD package. Rules for forming a function in the MathCAD package. Analysis of user function structure. Methods for describing arguments using builtin functions and user functions.
Topic № 4. Organization of work with data arrays in the MathCAD package.
Organization of ordered arrays. The procedure for creating matrices. Characteristics of elements of ordered arrays and matrices. Service variable ORIGIN.
3 Topic № 5. Construction of charts in the package MathCAD. Algorithm for plotting. Features of constructing graphs of functions with several arguments. Construct function graphs for various arguments.
Topic № 6. Editing the area of the graphs.
Construct graphs of functions in different colors and different types of lines (marks). Editing the graph area. Zoom and Trace commands. Modification of the coordinate plane for plotting.
4 Topic № 7. The solution of linear and nonlinear equations in the MathCAD package.
The solution of polynomials. Algorithm for using builtin functions of the package (function ROOT) for finding solutions of equations. Use the Polyroots function to find the polynomial roots.
Topic № 8. Solving systems of linear and nonlinear equations in the MathCAD package.
Using the GivenFind solvers block to find solutions to systems of linear and nonlinear equations. Using the GivenMinerr deployment block to investigate common functions.
5 Topic № 9. Conditioned range operator (CRO).
The essence of the use of conditional ranked operator. Analysis of individual examples of CRO use for the study of functional dependencies.
Topic № 10. Range Conditional Branching operator.
The algorithm of formation and the principle of the ranks of conditional transition operators. The use it for constructing composite functions. 2
2 
6 Topic № 11. The essence of the least squares method (LSM). Analytical transformations in the MathCAD package. Understand the essence of the least squares method. The analys the research algorithm for the discrete set of LSMs. A describe the mechanism for implementing the simplest analytical transformations in the MathCAD package
Topic № 12. The linear form of MNC and its implementation with builtin functions of the package.
A describe the sequence of actions using the internal Intercept and Slope functions.
7 Topic № 13. Linear regression of the general type in the package MathCAD.
To reveal the essence of the method of least squares through the realization of linear regression of the general form. To analyze the algorithm of research of a discrete set of points of LSM using the Linfit function.
Topic № 14. Nonlinear regression of the general type in the package MathCAD.
To reveal the essence of the method of least squares through the realization of nonlinear regression of the general form. To analyze the algorithm of research of a discrete set of points of LSM using the Genfit function.
Practical classes (topics)
Introduction. Characteristics of the MathCAD package
Working with variables in the MathCAD package.
The concept of a mathematical expression.
The concept of function in the MathCAD package
Arranging work with data arrays in the MathCAD package
Build charts in the MathCAD package
Editing the graph area
The solution of linear and nonlinear equations in the MathCAD package.
The solution of polynomials
The solution of systems of linear and nonlinear equations in the MathCAD package
Conditioned range operator
Range Conditional Branching operator
Linear form of the LSM and its implementation with internal functions of the package
Linear regression of the general form in the MathCAD package
Nonlinear regression of the general form in the MathCAD package
Working with variables in the MathCAD package.
The concept of a mathematical expression.
The concept of function in the MathCAD package
Arranging work with data arrays in the MathCAD package
Build charts in the MathCAD package
Editing the graph area
The solution of linear and nonlinear equations in the MathCAD package.
The solution of polynomials
The solution of systems of linear and nonlinear equations in the MathCAD package
Conditioned range operator
Range Conditional Branching operator
Linear form of the LSM and its implementation with internal functions of the package
Linear regression of the general form in the MathCAD package
Nonlinear regression of the general form in the MathCAD package
Learning materials and resources
1. Makarov E.G. Tutorial MathCAD 14. Electronic Learning Officer
2. Gursky D.A., Turbina E.S. Calculations in MathCAD 12.  SPb .: Piter, 2006. ―544 p.
3. Kiryanov D. SelfTeacher MathCAD 11.  SPb .: BHV, 2003. ―560 p.
4. Shanaida V.V. MathCAD package in engineering calculations.  Ternopil: Publishing house of the TSTU, 2001.  163 p.
5. Herger M., Partol H. MathCAD 2000: a complete guide: Trans. from Germanic . K .: Publishing Group BHV, 2000.  416 p.
2. Gursky D.A., Turbina E.S. Calculations in MathCAD 12.  SPb .: Piter, 2006. ―544 p.
3. Kiryanov D. SelfTeacher MathCAD 11.  SPb .: BHV, 2003. ―560 p.
4. Shanaida V.V. MathCAD package in engineering calculations.  Ternopil: Publishing house of the TSTU, 2001.  163 p.
5. Herger M., Partol H. MathCAD 2000: a complete guide: Trans. from Germanic . K .: Publishing Group BHV, 2000.  416 p.
6. Policies and assessment process of the academic discipline
Assessment methods and rating system of learning results assessment
You will receive an option with problems to solve at the end of the semester. Each option has three tasks. You will have 1 hour to solve these problems. This is a necessary condition for obtaining credit.
Table of assessment scores:
Assessment scale  
VNZ (100 points) 
National (4 points) 
ECTS 
90100  Excellent  А 
8289  Good  B 
7581  C  
6774  Fair  D 
6066  E  
3559  Poor  FX 
134  F 
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