| Quiz #1: | 1. Verifying that a given function is a solution to a DE by substitution.
2. Finding the value of the constant in the general solution using the given initial condition. 3. Solving separable differential equations. 4. Applications of separable DE's: Newton's Law of Heating/Cooling, population growth, radioactive decay. |
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| Quiz #2: | 1. Solving first order linear DEs by the method of integrating factors.
2. Applications of first order linear DEs: Mixture tank problems. 3. Solving DEs by the method of substitution: Linear substitutions, homogeneous DEs, Bernoulli equations. |
| Quiz #3: | 1. Verifying that a given DE is exact and finding its implicit solution.
2. Verifying that two given functions y_1 and y_2 are solutions of a given second order linear homogeneous DE. Moreover, if initial conditions are given, finding constants c_1 and c_2 such that c_1y_1+c_2y_2 satisfies the given initial value problem (IVP). 3. Computing the Wronskian of two or three functions and using this to determine whether they are linearly independent or not on a given interval. |
| Quiz #4: | 1. Solving linear homogeneous equations with constant coefficients:
second order as well as higher order. 2. Solving linear non-homogeneous equations with constant coefficients (including the case where duplication occurs): second order as well as higher order. 3. Mechanical Vibrations: the free damped spring, the forced undamped spring. |
| Quiz #5: | 1. Computing Laplace transforms. 2. Computing inverse Laplace transforms via the 1st Translation Theorem and the method of partial fractions. 3. Solving initial value problems using Laplace transforms. 4. Computing Laplace transforms of step functions (2nd Translation Theorem). Note: For Quiz #5 (and for your final exam) you will have the table of Laplace transform given in "tools" appended to your quiz/exam. |