Math205BKK
Calculus 2
Faculty
Veronika Shukhman
Data Platform Engineer at Clarify
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
This course builds upon Calculus 1 and develops students’ understanding of limits, sequences, infinite series, convergence, and approximation. The course begins with an intuitive and computational study of limits, followed by sequences, partial sums, geometric series, and convergence tests. In the final part of the course, students explore power series, Taylor polynomials, and Taylor series as tools for representing and approximating functions.
Learning highlights
- Understand and compute limits.
- Analyse the convergence of sequences and infinite series.
- Select and apply appropriate convergence tests.
- Determine intervals and radii of convergence of power series.
- Use Taylor polynomials and Taylor series to represent and approximate functions.
- Develop mathematical communication skills by presenting clear solutions and reasoning.
Course outline
15 classes
Session 1
Short Calculus-1 diagnostic. Intuitive limits. Graphical and numerical interpretation.
Session 2
Computing limits. Continuity and discontinuities. Limits at infinity.
Session 3
Sequences and convergence.
Session 4
Exercises and group work.
Session 5
Infinite series and partial sums. Geometric series.
Session 6
Exercises and quiz.
Session 7
Positive-term series and comparison tests.
Session 8
Alternating series and absolute convergence.
Session 9
Exercises: choosing convergence tests.
Session 10
Midterm.
Session 11
Power series. Radius and interval of convergence.
Session 12
Exercises.
Session 13
Taylor polynomials and introduction to Taylor series.
Session 14
Taylor series: exercises and applications.
Session 15
Final assessment.
Prerequisites
Successful completion of Calculus 1.
Familiarity with basic algebra, functions, derivatives, and mathematical notation.
Ability to explain the main steps of a mathematical solution.
Methodology
The course is hands-on and concept-focused. New ideas are introduced through intuitive explanations, worked examples, graphical representations, and structured problem-solving. Regular exercise sessions allow students to consolidate techniques and receive feedback before moving to the next topic.
The course uses the following learning formats:
* Lectures: introduction of key concepts and methods through examples and visual interpretations.
* Exercises: individual and collaborative problem-solving.
* Discussions: comparison of different methods and explanation of reasoning.
* Quizzes: short checks of understanding and core computational skills.
* Visualisation: selected use of graphs or computational tools to explore convergence and approximation.
Grading
Veronika is a Data Engineer specialising in data platforms and analytics architecture. She designs and builds end-to-end data platforms, including data pipelines, analytical infrastructure, and AI-assisted solutions, leveraging modern cloud technologies.
Alongside her work in the tech industry, teaching has always been an integral part of her professional journey. Her teaching philosophy is based on one simple idea: true learning begins with understanding. Rather than focusing on memorisation, she encourages students to build intuition, think critically, and understand the fundamental principles that remain valuable long after individual tools and technologies evolve.
See full profileApply for this course
Calculus 2
by Veronika Shukhman
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.