In this page you can find useful or otherwise interesting videos related to the topics covered in the course (special thanks Lauri Sääskilahti and Pekka Alestalo).

The order of the videos does not follow that of the lectures.

Note: The topics of the videos titled in blue are not included in the learning objectives of this course, but those who are more interested in the topic can find more interesting things to think about in them!

Contents

  • 1. Sequences
  • 2. Series
  • 3. Limit of a function and continuity
  • 4. Derivatives
  • 5. Taylor series and polynomials
  • 6. Inverse functions
  • 7. Integrals
  • 8. Integration methods
  • 9. Differential equations
  • A Complex numbers
  • B Other interesting things

1. Sequences

1.1 Basics on sequences
1.2 Convergence of sequences

2. Series (not required for the exam)

2.1 The n-th term divergence test
2.2 Ratio test
2.3 Comparison test
2.4 Integraalitesti
2.5 Conditional and absolute convergence
2.6 Cesaro sum

3. Limits of functions and continuity

3.1 Introduction to limits
3.2 Epsilon-delta definition of limits
3.3 Continuity

4. Derivatives

4.1 Infinitesimals (dx)
4.2 An intuitive approach to derivatives
4.3 Derivatives and the L'Hôpital's rule
4.4 L'Hôpital's rule
4.5 Chain rule
4.6 Linearization

5. Taylor series and Taylor polynomials

5.1 Taylor series
5.2 Taylor polynomial
5.3 Applications of Taylor approximation in physics

6. Inverse functions (mostly extra, not required)

6.1 Surjective and injective functions
6.2 Bijections and inverse functions
6.3 Inverse functions
6.4 Derivative of the inverse
6.5 Arcsin

7. Integrals

7.1 Riemann sums
7.2 Fundamental Theorem of Calculus
7.3 Integration: example
7.4 Area between curves
7.5 Volume of a solid
7.6 Improper integrals

8. Integration methods

8.1 Integration by parts

9. Differential equations

9.1 Visual introduction to differential equations
9.2 Introduction to differential equations
9.3 Separable differential equations
9.4 First order linear differential equations
9.5 Linear solutions to differential equations
9.6 Slope field
9.7 Euler's method
9.8 Second order linear differential equations
9.9 Second order linear differential equations
9.10 Applications of differential equations in physics

A Complex numbers

A1 Introduction to complex numbers
A2 Euler's formula

B Additional interesting things

B1 The sum of all natural numbers?
B2 What is e?
B3 The most beautiful formula in math
B4 Introduction to calculus
Last modified: Thursday, 22 September 2022, 9:36 PM