Section 15 - Integral calculus
The topic of integral calculus has been broken down into the following sections:
Setting the scene: But Why is a sphere's surface area four times its shadow?
Wondering where to start with your discussion of Calculus? Well, why not start with something you know - the surface area of a sphere - and the add on something your about to learning about - limits/approximations.
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3blue1brown: The essence of calculus
3blue1brown is created by Grant Sanderson who aims to animate maths. This involves providing excellent animations of the concepts as well as bring greater meaning to the content he delivers. In this particular playlist, "the goal is to make calculus feel like something that you yourself could have discovered". Each video is between 10 and 20 minutes long, and well worth the time to watch. Enjoy!
■ Warning! The videos created by 3blue1brown are not tailored to the VCE Mathematical Methods course. Students are encouraged to use these videos to deepen their understanding of concepts and not as a complete compilation of the study design requirements. |
Chapter 1: Essence of calculus
Chapter 2: derivatives paradox
Chapter 3: Geometry of derivatives
CHAPTER 4: VISUALISING THE "RULES"
CHAPTER 5: DERIVATIVES OF EXPONENTIALS
Chapter 6: Implicit differentiation
This video is not relevant to VCE Methods; however, it is well worth a watch for Specialist Mathematics.
Chapter 7: Limits
Chapter 8: Integrals
Chapter 9: Area and slope?
Chapter 10: Higher order derivatives
Chapter 12: Taylor series
Chapter 12: Another view of calculus
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