Math205BKK
Calculus 2
Faculty
Andrey Kechin
Master of Science fellow
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
Calculus II builds on the fundamental concepts of differential and integral calculus, extending students’ understanding of mathematical analysis. The course covers advanced integration techniques, applications of definite integrals, improper integrals, sequences and series, convergence tests, and power series. Emphasis is placed on analytical problem-solving, mathematical reasoning, and the application of calculus to problems in machine learning and data science.
Learning highlights
- Differentials: Understand the concept of differentials and their use in approximating changes in functions.
- Functions of Multiple Variables: Explore functions of several variables, their domains, and their graphical representations.
- Derivatives: Calculate and interpret derivatives, including partial derivatives, and apply differentiation rules to solve mathematical problems.
- Extrema of Functions: Identify and classify local and global maxima and minima using derivative-based methods.
- Methods of Integration: Apply various integration techniques, including substitution, integration by parts, and partial fractions, to evaluate indefinite and definite integrals.
Course outline
15 classes
Session 1
Review of calculus 1
Derivatives
Integrals
Session 2
Geometric series
Taylor series
Convergence tests
Session 3
Extrema of a function.
Maxima, Minima, and saddle points
Session 4
Partial derivatives.
Mean value theorem.
l`Hopital`s rule.
Session 5
Practice
Session 6
Limits. Continuity and discontinuity.
Session 7
Chain rule.
Inverse functions and their Derivatives.
Session 8
Midterm exam
Session 9
Fundamental theorem and its consequences.
Integration by parts.
Double and triple integrals.
Session 10
Practice
Session 11
Polar coordinates and complex numbers
Session 12
Differential equations.
Simple differential equations and approximate solution.
Session 13
Practice
Session 14
Review
Session 15
Final exam
Prerequisites
Python (needed to read and understand the code in some practical tasks)
Math notation techniques and proving techniques
Methodology
The methodology is based on mixing PBL (problem-based learning) and IVL (interactive and visual learning) technologies. PBL is based on presenting real-world problems and guiding students to apply discrete math concepts like graph theory or combinatorics to solve them. IVL technology considers using visualisation tools in lecture studies.
Each class can be divided into three parts:
* Lection part
* Active learning (discussion, Q&A)
* Problem-solving part.
Students are encouraged to solve a task during the class that follows the homework. The homework is discussed at the beginning of the following class.
The Exams is splitted into two parts: theory and practice. 1/3rd of the score is theory 2/3 is practice.
Grading
Andrew graduated from Siberian Federal University and obtained the Master of Science degree in Physics in 2021.
The scientific interests are in biophysics, medicine, and modelling of real biology features in-silico. The master article is devoted to the quantum modelling of an Endothelial Growth Factor Receptor`s ligand as a target for positron emission tomography. Andrew is an awardee of a students olympiad and an active member of a math book translation team.
See full profileApply for this course
Calculus 2
by Andrey Kechin
Total hours
45 Hours
Dates
Nov 09 - Nov 27, 2026
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.