--| home
| research
| txt
| code
| teach
| specialfunctionswiki
| timescalewiki
| hyperspacewiki
| links |--
Syllabus: [pdf] [tex]

Honors syllabus: [pdf] [tex]

__Exams__

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

**Exam 2**: [pdf] [tex]

**Exam 3**: [pdf] [tex]

__Homework__

**Homework 1** (*due 22 January*) (solution) (honors homework: [pdf] [tex]): Section 1.1: #4, 6, 8, 11; Section 1.2: #70, 72, 76, 77, 88, 90, 92, 98, 100, 102, and the following problems:

*Problem A*: Compute the average value of the function over the given interval from problems #76 and #77.

*Problem B*: Use the method in the video to estimate $\displaystyle\int_0^{5} e^{-x^2} \mathrm{d}x$ with a rectangle width of $\Delta x = 0.01$. Compare this value to the actual value found from WolframAlpha.

*Problem C*: Use the method in the video to estimate $\displaystyle\int_0^{5} \sin(t^2) \mathrm{d}t$ with a rectangle width of $\Delta x = 0.01$. Compare this value to the actual value found from WolframAlpha.

**Homework 2** (*due 28 January*) (solution) (honors homework: [pdf] [tex]): Section 1.3: #148, 150, 154, 170, 172, 175, 181, 182; Section 1.5: #262, 264, 266, 272, 274, 276, 281, 282, 292, 294; Section 1.6: #320, 322, 328, 330, 356, 360

**Homework 3** (*due 4 February*) (solution) (honors homework: none this week): Section 2.1: #2, 4, 6, 7, 10, 15, 23; Section 2.2: #74, 77, 79, 82, 83, 86, 90, 91, 99, 101

**Homework 4** (*due 13 February*) (solution) (honors homework: [pdf] [tex]): Section 2.3: #120, 122, 124, 125, 131, 132; Section 2.5: #218, 222, 224, 226, 229, 231

**Homework 5** (*due 22 February*) (solution) (honors homework: [pdf] [tex]): Section 3.1: #6, 10, 12, 14, 20, 21, 22, 38, 42; Section 3.2: #80, 82, 84, 86, 90, 91, 98, 104, 106

**Homework 6** (*due 27 February*) (honors homework: none) (solution): Section 3.3: #134, 135, 136, 137, 138, 139, 141, 142, 148, 151

**Homework 7** (*due 4 March*) (honors homework: [pdf] [tex]) (solution): Section 3.4: #196, 197, 198, 199; Section 3.7: #356, 357, 358, 362, 366, 370, 374, 382

and the following three problems:

**Problem A**: Compute $\displaystyle\int \dfrac{2x+1}{x^2+4x+4}$.

**Problem B**: Compute $\displaystyle\int \dfrac{x-1}{(x+1)(x^2+9)}$.

**Problem C**: Compute $\displaystyle\int \dfrac{1}{(x^2+36)(x^2+4)}$.

**Homework 8** (*due 27 March*) (honors homework: [pdf] [tex]) (solution): Section 5.1: #2, 3, 7, 8, 14, 17, 23, 26, 27, 28; Section 5.2: #67, 70, 72, 73

**Homework 9** (*due 3 April*) (honors homework: [pdf] [tex]) (solution): Section 5.2: #84, 85, 88, 90, 94, 95, 98, 102, 103, 104; Section 5.3: #138, 139, 141, 142, 146, 152, 153, 155, 156, 158, 160, 161, 165, 169, 170

**Problem A**: Compute $\displaystyle\sum_{n=0}^{\infty} \dfrac{1}{n^2+3n+2}$.

**Homework 10** (*due 10 April*) (honors homework: none) (solution): Section 5.4: #197, 198, 202, 203, 209, 211, 212, 215, 224, 227, 234

**Homework 11** (*due 15 April*) (honors homework: none) (solution): Section 5.5: #250, 251, 252, 254, 261, 263, 265, 282, 283, 304; Section 5.6: #318, 320, 321, 322, 325, 326, 328, 330, 332, 334, 346

**Homework 12** (*due 3 May*) (honors homework: here) (solution): Section 6.1: #13, 14, 15, 16, 18, 19, 23, 24, 33, 35; Section 6.2: #87, 90, 91, 102 (only first sentence), 109; Section 6.3: #116, 119, 120

__Quizzes__

**Quiz 1** (*due 25 January*) (solution): Compute $\displaystyle\int_{\frac{\pi}{2}}^{\pi} \cos^2(\theta)\sin(\theta) \mathrm{d}\theta$.

**Quiz 2** (*due 15 February*): Compute $\displaystyle\int \sin^2(x) \mathrm{d}x$.

**Quiz 3** (*due 25 February*): Integrate $\displaystyle\int \dfrac{1}{(x-7)(2x+1)} \mathrm{d}x$.

**Quiz 4** (*due 27 February*): Integrate $\displaystyle\int \dfrac{1}{(x^2+1)(x^2+4)} \mathrm{d}x$.

**Quiz 5** (*due 19 March*) (solution): Write the first 5 terms of the sequence defined by $\left\{ \begin{array}{ll}
a_{n+1} = a_n + a_{n-1} \\
a_0=2, a_1=1.
\end{array} \right.$

**Quiz 6** (*due 20 March*) (solution): Compute the limit $\displaystyle\lim_{n \rightarrow \infty} \dfrac{n^2+3n+1}{5n^2-7n}$.

**Quiz 7** (*due 26 March*) (solution): Compute $\displaystyle\sum_{n=0}^{\infty} \left( -\dfrac{1}{7} \right)^n$.

**Quiz 8** (*due 8 April*) (solution): Does the series $\displaystyle\sum_{n=0}^{\infty} \dfrac{1}{3^n+n}$ converge or diverge? Explain why or why not.

**Quiz 9** (*due 29 April*): Find the Taylor series, centered at $x=0$, of $\cos(x)$.

__Notes__

Some series for practice (solutions can be found in the Fall 2017 EXAM 4 solution and the Spring 2017 EXAM 4 solutions here)

8 April, alternating harmonic series

8 April, alternating reciprocal of squares

Example 2, 1 April

Example 1, 1 April

Spreadsheet 1 (20 March 2019)

Spreadsheet 2 (20 March 2019)

Spreadsheet 3 (20 March 2019)

__External links__