MATH10222: Calculus and Applications -- Part 1: ODEs

Corrections:

• Minor clarification to the Existence and Uniqueness statement 1.3.5 in Chapter 1. [Thanks to David Ward for spotting this!].
• In the four-step-procedure that explains the overall procedure for the solution of a linear 2nd order ODE at the end of section 3.1 of Chapter 4 , I kept switching between x and t as the independent variable. [Thanks again to David Ward for spotting this!].
• A factor of 2 was missing in the expression multiplying the x term in the discussion of the case when a is a double root of the characteristic polynomial in section 3.2.2 in Chapter 4. [And, yet again, thanks to David Ward!].
• Replaced "rubber string" by "spring" in Question 1 of Example Sheet 5. This is necessary because a rubber string would not be able to resist the compressive force generated when the mug moves upwards. (In the actual experiment, the presence of gravity ensures that at t=0, when the mug is in its initial equilibrium position, its weight is exactly balanced by the tensile force in the stretched rubber string. A moderate upward motion of the mug during the oscillation therefore reduces the (positive) tension in the rubber string but does not compress it.) [Thanks to Rich Hewitt for suggesting that I clarify this.]

If you spot any other problems, please contact me by email (M.Heil@maths.man.ac.uk) or catch me after the lecture. Thanks.