Описание:Course Description: Development of the limit processes including continuity, functions, sequences, series, differentiation, and integration. Emphasis on proofs of the fundamental theorems of mathematical analysis, including Role's and Lagrange's theorems. Multivariable analysis, constrained optimization.
Student’s Learning Outcomes Upon successful completion of this course (if grade is >=80) students will understand:
1. Language of analysis. Sets, numbers and functions.
2. Limits of a sequence.
3. Sequences and Series
4. Series Convergence theorems
5. Limit of a function and continuity. Investigation of a single variable function.
6. Derivative. Applications of derivative.
7. Basic theorems of math analysis, such as Fermat, Lagrange, Role, Cauchy and Taylor.
8. Polynomials. Binomial Theorem. Vieta Theorem, Cubic and Quartic Equations
9. Nonstandard problems.
10. Multivariable calculus and optimization.
