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Syllabus: [pdf] [tex]

__Exams__

**Exam 1**: [pdf] [tex]

**Exam 2**:

**Exam 3**:

__Homework__

**Homework 1** (*due 23 January*) (solution): p.10: #1, 3 (explain why), 4, 7, 9, 15, 16; ~~p.15: #2, 4, 6 ~~

**Homework 2** (*due 28 January*) (solution): p.15: #2 (just draw slope field and nullcline(s) -- software is ok to use), 4, 6; p. 19: #1, 3, 4b, 4c, 9, 11; p. 26: #1a, 1b, 1c

**Homework 3** (*due 4 February*) (solution): p. 26: #1d, 1h, 4a; p.32: #1, 3; p.34: #2, 4; p.41: #1, 2a, 2b, 3a, 3d

**Homework 4** (*due 11 February*) (solution): p.41: #2d, 2e; p.90: #1a, 1b, 1c, 1d, 2 (do only 1a and 1c for #2), 3 (do only 1b and 1d for #3); p.94: #1a, 1b, 1c, 1d, 2 (do only 1a and 1c for #2); p.111: #2a, 2b, 2c

**Homework 5** (*due 20 February*) (solution): p.120: #1c (it should be $t^2x''+3tx'+x=0$ -- there is a typo), 1e, 1f; p.124: #1a, 1e

**Homework 6** (*due 25 February*) (solution): p.144: #3, 8a, 8b, 9a, 9c, 9d, 9j; p.156: #1, 6a, 6c, 6d,

**Homework 7** (*due 4 March*) (solution): p.144: #8c, 8f, 9b, 9f; p.156: #6b, 6e, 14; p.162: #1b, 1c, 6, 7; p.173: #1, 2, 3

**Homework 8** (*due 27 March*): p.190: #3a, 3c, 3d; p.198: #1~~, 2a, 3, 5, 6, 8~~

__Quizzes__

**Quiz 1** (*due 16 January*): (solution) Given $v(t)=Ve^{-\frac{kt}{m}}$, show that $v$ solves the initial value problem $\left\{ \begin{array}{ll}
-kv = mv' \\
v(0)=V
\end{array} \right.$

**Quiz 2** (*due 23 January*): (solution) Show that $x(t)=\dfrac{e^{2t}-1}{e^{2t}+1}$ solves $\left\{ \begin{array}{ll}
x'&=1-x^2\\
x(0)&=0
\end{array} \right.$.

**Quiz 3** (*due 25 January*): (solution) Solve the initial value problem $\left\{ \begin{array}{ll}
x' = 2t \\
x(0)=5.
\end{array} \right.$

**Quiz 4**

**Quiz 5** (*due 22 February*): Compute the Laplace transform of $\mathscr{L}\{t^2\}(s)$ from the definition of $\mathscr{L}$.

**Quiz 6** (*due 20 March*) (solution): Solve $\left\{ \begin{array}{ll}
x' = -y \\
y'=x \\
x(0)=1, y(0)=0.
\end{array} \right.$

**Quiz 7** (*due 25 March*): Find the inverse of the matrix $A = \begin{bmatrix} 3&0 \\ 1&10\end{bmatrix}$ and show that it works properly by computing $AA^{-1}$.

__Notes__

__External links__

Slope field calculator

Desmos (general purpose plotting)