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pg 15: @ example of linear approx. to non-linear map; Leibniz's notation;
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More Applications of 2x2 Matrices - Wild Linear Algebra A
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- 1 CONTENT SUMMARY: pg 1: @ a bit of review; matrix/vector multiplication; define a mapping/function/transformation; A linear transformation;
- 2 pg 2: @ proof of transformation linearity;
- 3 pg 3: @05:25 rule implied by knowledge of linearity; mapped base vectors; area dilation factor @;
- 4 pg 4: @ determining how the basis vectors transform; The columns of the transformation matrix are the transformations of the basis vectors;
- 5 pg 5: @ examples;
- 6 pg 6: @ example continued; rotations; unit circle; rotation matrix;
- 7 pg 7: @ rotations by 30degree's, 45degree's, 60degree's
- 8 pg 8: @ some trig identities; exercise 3.1
- 9 pg 9: @ Rational parametrization; alternate rotation matrix; exercise
- 10 pg 10: @ reflection
- 11 pg 11: @ reflection continued; Composition of linear transformations
- 12 pg 12: @ example: rotation/reflection composition
- 13 pg 13: @ example continued;
- 14 pg 14: @ Linear approximations to non-linear maps; globally nonlinear/locally approx._linear; differential calculus mentioned;
- 15 pg 15: @ example of linear approx. to non-linear map; Leibniz's notation;
- 16 pg 16: @50:28 example continued; the derivative matrix at a point; Lesson derivatives are linear transformations @ ;
- 17 pg 17: @ exercises 7.3-4 ;
- 18 pg 18: @ exercises 7.5-7 ; THANKS to EmptySpaceEnterprise
