MS-A0111 - Differential and Integral Calculus 1, Lecture, 13.9.2021-27.10.2021

Topic outline

• Materials
  More material will be added here as the course proceeds. The videos do not cover all the course material; they only contain the main definitions and some examples.
  

  Short videos (with varying length):

  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)
      

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    Differential and Integral Calculus Book
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    Lecture Videos (2021) Page
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    Examples shown during the lectures.

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    Lecture notes, including copies of the lecture transcripts.

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    Lecture Videos (2020) Panopto Page

    Recorded lectures.

  • Select activity Activation

    Activation

  • Select activity Lecture 1 (Activation Quiz)

    

    Lecture 1 (Activation Quiz)

    Sequences, limits, functions. Not part of the continuous assessment, this is for activation only.

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    Lecture 2 (Activation Quiz)

    Derivative

  • Select activity Lecture 3 (Activation Quiz)

    

    Lecture 3 (Activation Quiz)

    Exponential, logarithms, trigonometric functions and their inverses.

  • Select activity Lecture 4 (Activation Quiz)

    

    Lecture 4 (Activation Quiz)

    Taylor polynomials.

  • Select activity Lecture 5 (Activation Quiz)

    

    Lecture 5 (Activation Quiz)

    The definite integral.

  • Select activity Lecture 6 (Activation Quiz)

    

    Lecture 6 (Activation Quiz)

    Numerical quadrature rules.

  • Select activity Lecture 7 (Activation Quiz)

    

    Lecture 7 (Activation Quiz)

    Techniques for integration: Method of substitution.

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    Lecture 8 (Activation Quiz)

    Integration by parts.

  • Select activity Lecture 9 (Activation Quiz)

    

    Lecture 9 (Activation Quiz)

    Ordinary differential equations.

  • Select activity Lecture 10 (Activation Quiz)

    

    Lecture 10 (Activation Quiz)

    Differential equations, including numerical methods.

  • Select activity Lecture 11 (Activation Quiz)

    

    Lecture 11 (Activation Quiz)

    2nd order ODE with constant coefficients.

  • Select activity Differential and Integral Calculus

    

    Differential and Integral Calculus Book
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    Lecture Transcripts (2021) Folder
  • Select activity Lecture Videos (2021)

    

    Lecture Videos (2021) Page
  • Select activity Lecture notes (2020)

    

    Lecture notes (2020) Folder

    Lecture notes, including copies of the lecture transcripts.