Math104
Calculus-1
Faculty
Alexey Vasiliev
Senior Researcher at Space Research Institute, Moscow
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 the first step in calculus, often referred to as “the mathematics of change”. If one needs to describe and study something that varies in time or space, the use of calculus cannot be avoided. In the class we’ll go through notions of function limits and continuity to the central concept of function derivative. We’ll learn how to calculate derivatives of various functions and how to use them to analyze function behavior. At the end of the course, we’ll get to understand the idea of definite integral and antiderivative. Numerous examples will be studied, demonstrating the importance and usefulness of calculus in various scientific and practical problems.
Learning highlights
- The objective of the course is to get acquainted with basic notions and ideas of calculus: function limits, continuity of functions, derivatives, notion of a definite integral and antiderivatives.
- We’ll learn to find function limits, calculate derivatives of various functions, analyze behavior of functions using methods of calculus.
- We’ll study numerous examples demonstrating the usefulness of calculus in problems of mathematics, physics and real life.
Course outline
15 classes
Session 1
Limits of functions
Session 2
Continuous functions, “squeeze” theorem
Session 3
Derivative: motivation and definition, simple cases
Session 4
Rules of differentiation 1
Session 5
Rules of differentiation 2
Session 6
Review and Midterm 1
Session 7
Local extrema; Rolle’s and the mean value theorems
Session 8
Increasing and decreasing functions; concavity and the second derivative
Session 9
Examples and problem solving
Session 10
Examples and problem solving
Session 11
Review and Midterm 2
Session 12
Definite integral: motivation and main ideas. Newton-Leibnitz theorem
Session 13
Problem Solving
Session 14
Problem Solving
Session 15
Final test
Methodology
Each three-hour session will consist partly of a lecture given by the professor and partly of a practical session, where students will try to solve problems (related to the subject of the day) under the professor's supervision. There will also be some classroom discussion. In order to further improve understanding of the material, homework will be assigned after every session. There will be two interim tests after each of the first two weeks, and a final test at the end of the module.
Grading
In 1987, Alexei Vasiliev graduated from the Physics Department of Moscow State University and joined Moscow Space Research Institute as a PhD student. After obtaining his PhD in theoretical physics in 1991, he worked on problems of nonlinear chaotic dynamics in various fields of physics, like hydrodynamics, classical mechanics, celestial mechanics, and plasma physics. In 2012 he obtained his Second doctoral degree in theoretical and mathematical physics. Alexei Vasiliev worked as PI or investigator in numerous international projects; he authored more than 70 scientific publications. He also teaches at Moscow Institute of Physics and Technology and at New Economic School.
See full profileApply for this course
Calculus-1
by Alexey Vasiliev
Total hours
45 Hours
Dates
Nov 28 - Dec 16, 2022
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.