Math205BKK
Calculus – 2
Faculty
Mikhail Romanov
Senior Machine Learning Engineer, Yandex, Expert
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
This course is built on top of the Calculus - 1: Technique. It provides insightful derivations of the lessons learned in the first part of the programme and it expands on them. Moreover, it gives a solid background for understanding the more advanced calculus areas such as: probability theory, functional analysis, field theory, and optimization theory.
Learning highlights
- We will build on what we learned about basic calculus and prove most of the facts we memorized in the first part.
- After that, we will continue with the advanced calculus notions, such as: series, definition of integral and derivative.
Course outline
15 classes
Session 1
Numbers: natural, integer, rational, irrational. Sequence. Limit of a sequence definition. Examples of limits. Proving the limit.
Session 2
Computing the limits. Limit’s properties. Proofs. Limit of a function: two definitions and their equivalence.
First and second special limits.
Side limits. Continuous and discontinuous functions. Discontinuities of 1st and 2nd type.
Session 3
Derivative as the limit of a function. Proofs of the derivatives formulas. Existence of a derivative. Side derivatives. Smoothness.
Session 4
Exercises
Session 5
Differential definition. Physical meaning of the differential.
O-large and o-small definitions
Session 6
Exercises
Session 7
Maclaurin’s Formula with Peano remainder. Taylor’s Formula. Physical meaning
Session 8
Exercises
Session 9
Integral as limit. Reihmann’s integral definition. Existence of an integral.
Session 10
Exercises
Session 11
Differential equations. Assembling a differential equation. Solving simple differential equations.
Session 12
Exercises
Session 13
Infinite summation problem. Series. Definition of series. Convergence of series.
Main hint: geometric progression.
Convergence tests: Positive Series, Sign-alternating series, any series. Absolute convergence.
Session 14
Exercises
Session 15
Final Exam
Prerequisites
Calculus - 1
Methodology
We will work in the lecture-seminar system. First, a set of theories will be presented (in an interactive manner); next, the practical part will start, and we will solve the problems.
Grading
Mikhail Romanov, PhD, is a deep learning researcher and engineer. His experience includes deep learning for production, scientific computing and research, accompanied by teaching mathematics and machine learning in general.
His academic experience includes teaching courses at MIPT, HSE, Harbour Space Universities and online platforms. As a researcher, he has conducted research at the Technical University of Denmark, Mail.ru, Samsung Research, Quantori, and Yandex. In his research, his main areas of interest are depth estimation, optical flow, optimisation of neural networks, multi-task learning, self-supervised learning, LLMs and diffusion models. He has published papers on tomography, deep learning, scientific computing, computer vision, generative AI, and diffusion models.
See full profileApply for this course
Calculus – 2
by Mikhail Romanov
Total hours
45 Hours
Dates
Nov 10 - Nov 28, 2025
Fee for single course
€1500
Fee for degree students
€750
How to secure your spot
Complete the form below to kickstart your application
Schedule your Harbour.Space interview
If successful, get ready to join us on campus
FAQ
Will I receive a certificate after completion?
Yes. Upon completion of the course, you will receive a certificate signed by the director of the program your course belonged to.
Do I need a visa?
This depends on your case. Please check with the Spanish or Thai consulate in your country of residence about visa requirements. We will do our part to provide you with the necessary documents, such as the Certificate of Enrollment.
Can I get a discount?
Yes. The easiest way to enroll in a course at a discounted price is to register for multiple courses. Registering for multiple courses will reduce the cost per individual course. Please ask the Admissions Office for more information about the other kinds of discounts we offer and what you can do to receive one.