Math 223, Section 101

Syllabus

Textbook: A. Givental: Linear Algebra and Differential Equations.

This is the syllabus which lists all topics covered in this course,
and for which you are responsible on the final exam.
(Updated, Dec. 6, 2009.)

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Part I.   Geometry in the Plane.
(11 lectures and 3 homework assignments)

1.1.  (2 lectures) Vectors.
1.2.  (3 lectures) Analytic geometry.
1.3.  (4 lectures) Linear transformations and matrices.
1.5.1, 1.5.2  (2 lectures) Eigenvalues.

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Part II.   Linear Algebra.
(11 lectures and 3 homework assignments)

1.4.  (2 lectures) Complex numbers.
1.5.3.  (2 lecture) Normal forms.
Additional topic.  (2 lectures) Discrete dynamical systems: see the notes here .
3.2.  (3 lectures) Matrices and Determinants.
3.4.1  (2 lectures) Gaussian elimination.

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Part III.   Quadratic Forms, Eigenvalues.
(12 lectures and 4 homework assignments)

3.3.  (4 lectures) Vectors and Linear systems.
3.4.2.  (2 lectures) Applications of Gaussian elimination.
3.5.  (3 lectures) Quadratic forms. Omit Sections 3.5.2 (least squares) and 3.5.5 (small oscillations).
3.6.  (3 lectures) Eigenvalues. Omit Section 3.6.3 (higher order ODE), but include 3.6.2 Linear ODE.
See also Section 2.1.2 and the Summary of Dynamical Systems here .
From the Summary of Dynamical Systems, you are responsible for Corollary 2, Remark 3, Formula 5, Theorem 5, Corollary 6 and Remark 7.

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