COURSE GOALS: Understanding and being able to use elementary techniques of Mathematical analysis.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.2. recognize and follow the logic of arguments, evaluate the adequacy of arguments and construct well supported arguments;
2.3. use mathematical methods to solve standard physics problems;
3. MAKING JUDGMENTS
3.1. develop a critical scientific attitude towards research in general, and in particular by learning to critically evaluate arguments, assumptions, abstract concepts and data;
4. COMMUNICATION SKILLS
4.2. present complex ideas clearly and concisely;
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
After a successful completion of the course Mathematical analysis 2 students will be able to:
* define and use effectively in problems and exercises the notions listed in the course description;
* recognize, discuss and explain these notions within problems;
* employ, analyse and connect these notions and techniques with problems in other courses in continuation of their stud of Physics (e.g. notions of definite and indefinite integrals, elementary functions, sequences and series);
* decide and effectively use the proper technique from the course to compute integrals and determine convergence of sequences;
1. Integration: introduction, definite integral, fundamental theorems of calculus, inverse integration and definite integral, proofs of fundamental theorems;
2. Elementary functions: logarithmic and exponential function, inverse trigonometric functions, separable differential equation, hyperbolic functions, L'Hospital rule;
3. Techniques of integration: substitution, partial integration, integrating rational functions, integrating trigonometric functions, applications of integrals;
4. Sequences and series: integral test, comparing sequences, absolute convergence, Taylor's formula;
REQUIREMENTS FOR STUDENTS:
Students must attend lectures; solve two homework (written in TeX), pass two written exams that consists of theory (40%), and problems (60%).
GRADING AND ASSESSING THE WORK OF STUDENTS:
* Attendance to lectures and exercises can bring 50 points, each homework can add 25 points, and the big exams are 150 points each. There is a possibility of correction exam that covers first or the second half or the whole semester (it brings 150, 150 or 300 points respectively). Some students can have presentations on a material that expands the course and earn 50 points. The grading scale is 200-249 (grade 2), 250-299 (grade 3), 300-349 (grade 4), and 350 or more (grade 5).