Math 5A Course Description
Math 5A is the second course of a two quarter sequence in Differential
Equations and Linear Algebra. The text is Farlowe, et al.
'Differential Equations and Linear Algebra.'
In differential equations, the emphasis is divided between quantitative
and qualitative aspects
- The emphasis is on the simplest cases of methods for closed form
solutions with e.g. Undetermined Coefficients. Because of this, we
emphasize accuracy of solutions. Students should be taught to verify
that their answer really does solve the ODE.
- The phase plane, equilibrium points and their stability are
important.
In linear algebra, proofs of theorems and large scale hand computations
are de-emphasized in order to tie the material more closely to the
application at hand: systems of linear differential equations. Again,
this means we emphasize the accuracy of those calculations which are
done. Students should verify that, for example, eigenvectors really
are correct.
5A covers three and a half chapters in the text. Times given below
are very approximate and do not include exams; we have not yet taught
this version of the syllabus.
Appendix CN Complex numbers (~ 1 lecture) Students need to know
exp(x+iy) = exp(x)(cos(y) + i sin(y)).
Chapters & Topics
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| 4. |
2nd Order Linear ODEs (~ 2.5 weeks)
Section 4.6 is mostly optional, except the conversion from 2nd order ODEs to first order
systems of ODEs, which provides the connection to chapter 6.
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| 5. |
Linear Transformations (~ 2.5 weeks)
In Section 5.3 'Eigenvalues and Eigenvectors' you might want to
motivate the abstract definition of eigenvector by looking ahead to
Section 6.2, p.333 and 334.
Section 5.4 'Diagonalization' contains a subsection 'The Right Point of View for DEs' which provides the
connection between the linear algebra theory and the (inhomogeneous) linear system of ODEs application.
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| 6. |
Linear Systems of DEs (~ 2.5 weeks)
Section 6.4 'Decoupling a linear DE system' connects up with chapter 5 as mentioned above.
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| 7. |
Nonlinear Systems (~ 1 week)
Cover only 7.1 Nonlinear Systems and 7.2 Linearization.
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