Teaching Calculus

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  • Nikolay Brodskiy
  • Alexander Brodsky

Lecture 2012.01.17 What Is Multivariable Calculus?

YouTube Playlist

Image Title Description Files Demonstrations
Part 01 What is Calculus? Notes
Video Transcript
 
Part 02 An example of nonlinear problem and how to solve it using Calculus. Newton's method. Notes Video Transcript  
Part 03 Another example of using Calculus in solving nonlinear problems. Calculus helps us to do useful approximatons. Notes Video Transcript   
Part 04 Using Calculus we locally approximate a nonlinear function with linear one and then study properties of the linear approximation. Notes Video Transcript   
Part 05 How to study global properties of a function? Case 1: we know all the derivatives of the function at a given point -- Taylor series. Notes Video Transcript   
Part 06 How to study global properties of a function? Case 2: we know the first derivative of the function at all points -- integral. Notes Video Transcript   
Part 07 What is differentiation in terms of Taylor series. Notes Video Transcript   
Part 08 Calculus helps us to reduce a nonlinear problem to linear one. But do you know how to solve multivariable linear problems? Notes Video Transcript   
Part 09 Introducing multivariable functions. Notes Video Transcript   
Part 10 What does it mean to be linear? Three points of view: Algebra, Geometry, Physics. Notes Video Transcript   
Part 11 Limitations and advantages of geometric, physical, and algebraic points of view. Notes Video Transcript   
Part 12 Why am I following this way in teaching Calculus? Notes Video Transcript