MS-A0111 - Differential and Integral Calculus 1, Lecture, 5.9.2022-19.10.2022

Osion kuvaus

• Materials
  The textbook is Adams, Essex: Calculus, A Complete Course, 7th Ed, Pearson. 

  As usual in higher education, only parts of the book will be covered. However, the book is useful also in Calculus 2 and 3.

  
  

  Additional material

  • Lecture notes will be provided here.
  • Below you can find html notes from previous implementations of the course.
  • Below you can find great video lectures recorded by Harri Hakula in 2021. Please note that the current implementation of the course will essentially have the same structure as in 2021, but there will be slight differences.
  • Very nice YouTube channel with animated math: https://www.youtube.com/c/3blue1brown/featured
  • You are invited to use a web browser and find your own favorite material. One of the nice things about calculus is that, being used in every branch of science, you will find thousands of videos and lecture notes about every single topic of the course. 
  • The following videos by Pekka Alestalo do not cover all the course material but they can be very helpful. They only contain the main definitions and some examples.

  1. Sequences (25:01)
     
  2. Series (35:43; please skip blackboard cleaning from 10:00 to 13:45 :)
     
  3. Continuity (33:09)
     
  4. Derivative (30:11)
     
  5. Taylor polynomials and series Part 1: Taylor (35:50), Part 2: Power series (23:24)
     
  6. Elementary functions Part 1: Inverse (18:49); Part 2: Inverse trig. (18:58); Part 3: exp and ln (21:34)
     
  7. The concept of area in the plane (14:22)
     
  8. Integral Part 1: Definition (32:06); Part 2: Applications (13:12); Part 3: Improper integrals (10:58); Part 4: Methods of integration (41:51)
     
  9. ODE of the 1st order  Part 1: Separable (24:55); Part 2: Linear (14:24)
     
  10. ODE of the 2nd order Part 1: General theory (14:46); Part 2: Homogeneous case (18:46); Part 3: Non-homogeneous case (21:25)
      

  • Valitse aktiviteetti Differential and Integral Calculus

    

    Differential and Integral Calculus Kirja
  • Valitse aktiviteetti Lecture Videos by Harri Hakula (2021)

    

    Lecture Videos by Harri Hakula (2021) Sivu

    Videos of the lectures by Harri Hakula in the 2021 implementation of the course

  • Valitse aktiviteetti Useful videos

    

    Useful videos Sivu

    YouTube videos on the course contents, in which you may find, among other things, examples (with solutions) or additional information.

  • Valitse aktiviteetti Practice exam

    

    Practice exam Tiedosto PDF
  • Valitse aktiviteetti Formulas available on October's exam sheet

    

    Formulas available on October's exam sheet Tiedosto PDF
  • Valitse aktiviteetti Solutions to practice exam

    

    Solutions to practice exam Tiedosto JPG
  • Valitse aktiviteetti October 2022 exam

    

    October 2022 exam Tiedosto PDF
  • Valitse aktiviteetti Solutions to October 2022 exam

    

    Solutions to October 2022 exam Tiedosto PDF

    EDIT: December 11, fixed typo in the solution of Problem 5.