Calculus DSBA2020

Syllabus

The discipline gives the fundamentals of mathematics, provides the foundation for mathematical modeling, and introduces the first concepts of data analysis. The prerequisites are high school algebra and trigonometry. Prior experience with calculus is helpful but not essential.

Lecturers and teaching assistants

Group	191	192	193
Lecturer	Vasily Goncharenko vgoncharenko@hse.ru
Teachers	Olga E. Orel	V. Goncharenko vgoncharenko@hse.ru	Olga E. Orel
Assistant	Anna Matveeva	Filipp Prokofyev	Igor Karpov

Grading system

The academic year is divided into 4 modules. At the end of the second and fourth modules the students pass a written exam (E). During the year students must also complete weekly home assignments. Professors can ask students to present their written solutions orally. Quizzes are held regularly in classes. Solving specific problems marked by the lecturer or class teachers, students may receive bonus points that influence the final term grade. This influence is expected not to exceed 10% of the grade. Here is the rule that defines the grade of each term. We compute the quantity Q1 = roundoff (min (0.4*RA + 0.6*E+B, 10))

at the end of the first term and

Q2 = roundoff (min (0.4*RA + 0.6*E+B, 10))

at the end of the second term,

where RA is the grade for the regular activity, E is the exam grade, and B is the total bonus. Regular activity grade (RA) consists of grades for tests passed at class and weekly home assignments. Problems solved in class are 3-10 times more valuable than problems solved at home. The grade of each problem is announced by the teacher before this problem is given to students. The standard mathematical rule is applied for the round off: if the fractional part of the grade lies within the interval [0, 0.5), then the grade is rounded off downward (to the greatest integer less than or equal to the grade), if the fractional part of the grade lies within the interval [0.5, 1), then the grade is rounded off upward. We insist that the round off is applied only once when Q is computed. Any intermediate grades are not rounded. The grade Q1 is the result of the first term (fixed in December). The final course grade (FCG) is defined as FCG = 0.4*Q1 + 0.6*Q2.

Reading list

- Calculus early transcendentals, Stewart J., 2012
- Friedman, A. (2007). Advanced Calculus (Vol. Dover edition). Mineola, N.Y.: Dover Publications.
- William H. Press, Saul A. Teukolsky, William T. Vetterling, & Brian P. Flannery. (1992). Numerical Recipes in C: The Art of Scientific Computing. Second Edition.

Additional reading:

- Курс дифференциального и интегрального исчисления. Т.1: ., Фихтенгольц Г. М., 2001
- Никитин А. А., Фомичев В. В.-МАТЕМАТИЧЕСКИЙ АНАЛИЗ. УГЛУБЛЕННЫЙ КУРС 2-е изд., испр. и доп. Учебник и практикум для академического бакалавриата-М.:Издательство Юрайт,2019-460-Бакалавр. Академический курс-978-5-534-00464-9
- Сборник задач и упражнений по математическому анализу : учеб. пособие для вузов, Демидович Б. П., 2004