# UCSB Winter 2016: Math 4B

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}

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 elne – e = C, so = 0
• On #8b, we should have negatives exponents since = -1
• On #8c, replace y with ux with t
• On #8d, replace y with rx with s
• On #9b, there should be a negative term in front of the integral. The Wronskian should instead by c exp(x-2lnx) = ce^x/x^2

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