**Office Hours**: Thursday 12:30 – 1:30pm in SH 6432u

**Math Lab Hours**: Wednesdays 12:00 – 2:00pm in SH 1607

You may also email me at vtkala@math.ucsb.edu for a short appointment.

Free tutoring is available at the Math Lab in SH 1607. They are open M-F 12-5pm. Go early and often to get free help on your homework!

March 13:

- Solutions to Final Practice Questions
- #15 is a system with complex eigenvalues, the solution here shows in detail what happens if you expand BOTH
**v**_1 e^{\lambda t} and**v**_2^{\lambda t}

- #15 is a system with complex eigenvalues, the solution here shows in detail what happens if you expand BOTH

March 7:

- Final Review
- Typo in example, eigenvalue is -1 (not 1)

- Final Practice Questions
- Typo on #3, dy/dx should be replaced with dx
- Typo on #7(a), should be y” – 2y’ + y = 0, not y” – 2y’ + y’ = 0
- Typo on #8(d), replace x’s with t’s

March 5:

- Quiz 8 (Homogeneous system of linear equations with constant coefficients)
- Quiz 7 (Variation of Parameters)
- Quiz 6 (Undetermined Coefficients, Variation of Parameters)
- Quiz 5 (Homogeneous linear equations with constant coefficients)

March 3:

- Factoring Cubic Polynomials
- Typo in the second equation, should be x^2 + b_2 x + b_3, not x^2 + b_2 c + b_3

- Review of long division of polynomials:

March 1:

February 2:

- Solutions to Midterm Practice Questions
*Corrections to solutions*:- On #6, when plugging in the initial value we should instead have
*e*ln*e – e*=*C*, so*C*= 0 - On #8b, we should have negatives exponents since
*r*= -1 - On #8c, replace
*y*with*u*,*x*with*t* - On #8d, replace
*y*with*r*,*x*with*s* - On #9b, there should be a negative term in front of the integral. The Wronskian should instead by
*W*=*c*exp(*x*-2ln*x*) = ce^x/x^2

- On #6, when plugging in the initial value we should instead have

January 31:

- Midterm Review (updated with notes on Existence and Uniqueness Theorem, the Wronskian, Reduction of Order)
- Midterm Practice Questions
- Solutions available at the link above

- Quiz 4 (Homogeneous linear equations with constant coefficients)

January 21:

- Quiz 3 (Exact Equations)
- Quiz 2 (Separable and First Order Linear Equations)
- Solutions
*Correction to solutions:*- On #2, there should be a factor of 1/2 in front of the natural log term

- Quiz 1 (Review Quiz)
- Solutions
*Correction to solutions*:- On #2b, there should be a negative sign (-) in front of the sine term