COURSE GOALS: Student should be introduced to a computer algebra system (like Sage, Ipython+modules, Mathematica, Maple or similar). He should be able to represent numerically and graphically mathematical objects from courses in mathematics and general physics. He should be able to solve corresponding mathematical problems with one-line computer code and, if necessary, with more complex programming. Using these skills he should be able to simulate physical systems on a computer. Main goal of the course is to equip student with skills necessary for computer problem solving.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
1. KNOWLEDGE AND UNDERSTANDING
1.6. list and describe the methods for manipulating data, basic principles of databases and fundamental algorithms in programming;
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.3. use mathematical methods to solve standard physics problems;
2.4. prepare and perform classroom physics experiments and interpret the results of observation;
2.5. describe the basic concepts of digital technology;
2.6. apply fundamental algorithms in programming;
2.7. use computing technology to solve scientific and technological problems
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
After successfully finishing this course student will be able to
1. Perform calculations of standard problems from mathematical analysis and linear algebra (symbolic and numeric solving of normal and differential equations, symbolic and numeric integration and differentiation, manipulations with matrices and vectors) withing computer algebra environment.
2. Perform statistical analysis of data and fit parameters of models to data
3. Graphically represent functions or numerical arrays
4. Develop simple computer programs
5. Numerically simulate and graphically visualize simple physical systems.
1. Introduction to course and to computer algebra systems (3 hrs)
2. Interface 2.1 Worksheet and cells 2.2 Elementary calculations 2.3 Help system 2.4 Error messages (3 hrs)
3. Programming 3.1 Lists and other containers (6 hrs) 3.2 Flow control 3.3 Functions (3 hrs) 3.4 Plotting (4 hrs)
4. Mathematics 4.1 Symbolic expressions (2 hrs) 4.2 Equations (3 hrs) 4.3 Mathematical analysis (3 hrs) 4.4 Linear algebra (3 hrs) 4.5 Differential equations (5 hrs) 4.6 Statistics (2 hrs) 4.7 Fitting of model parameters to data (2 hrs)
5. Examples from physics: Mechanics (6 hrs)
REQUIREMENTS FOR STUDENTS:
Doing homework's, online exams and final computer project.
GRADING AND ASSESSING THE WORK OF STUDENTS:
Students do homework's and online exams (60 percent of grade), and a final project (40 percent of grade).