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Syllabus: [pdf] [tex]

__Previous course materials__

Spring 2018 (Fairmont)

Fall 2017 (Fairmont)

Fall 2016 (Fairmont)

Spring 2011 (Marshall)

Spring 2010 (Marshall)

__Exams__

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

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

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

__Homework__

**Homework 1** (due 22 August) (solution): Section 2.2: #6, 7, 8, 9, 10, 15, 22, 26, 27; Section 2.5: #6, 7, 8, 9 (ok to use quadratic formula), 38, 39, 40, 41; Section 3.5: #27, 29, 30

**Homework 2** (due 27 August) (solution): Section 7.1: #24, 25, 27, 28, 31, 32, 34, 35, 38, 39, 40, 43; Section 7.2: #6, 7, 11, 12, 17, 18, 19, 20, 30, 31, 35, 36~~, 48, 49, 50, 51, 53~~

**Homework 3** (due 5 September) (solution): Section 7.2: #48, 49, 50, 51, 53; Section 7.3: #10, 12, 19, 20, 21, 24, 29, 30, 31, 32, 43, 44, 45, 46, 52, 53, 70, 71, 80, 81, 87, 88; Section 7.4: #10, 11, 12, 19, 20, 21, 38, 72, 75

**Homework 4** (due 10 September) (solution): Section 8.1: #10, 12, 18, 20; Section 8.2: #23

**Homework 5** (due 19 September) (solution): Section 8.1: #8, 14, 19; Section 8.2: #25, 29, 33 (note: on all graphing problems, plotting 1 whole period is ok, you need to label "everything" as was done in class)

**Homework 6** (due 24 September) (solution): Section 8.3: #8, 9, 11, 13, 18, 20, 25, 26, 28, 29, 32, 35, 37, 40, ~~53, 54, 55, 57, 59, 62~~

**Homework 7** (due 1 October) (solution): Section 8.3: #48, 49, 50, 51, 53, 54, 59, 62; Section 9.1: #11, 12, 15, ~~20, 21, 22, 29, 30, 32, 33, and the following problems: ~~**Problem A**: Establish the identity $\dfrac{1-\sin^2(x)}{\cos(x)}=\cos(x)$; **Problem B**: Establish the identity $\dfrac{\sin^2(x)}{\cos(x)}=\sec(x)-\cos(x)$.; **Problem C** Establish the identity $\dfrac{\cos(x)}{\sin(x)\cot(x)}=1$.

**Homework 8** (due 8 October) (solution): Section 9.1: #20, 21, 22, 29, 30, 32, 33, and the following problems: **Problem A**: Establish the identity $\dfrac{1-\sin^2(x)}{\cos(x)}=\cos(x)$; **Problem B**: Establish the identity $\dfrac{\sin^2(x)}{\cos(x)}=\sec(x)-\cos(x)$.; **Problem C** Establish the identity $\dfrac{\cos(x)}{\sin(x)\cot(x)}=1$.

**Homework 9** (due 17 October) (solution): Section 9.2: #5, 7, ~~11, 12, 14, 16, 18, 20, 22, 23, 24, 47~~; Section 9.3: #~~5, 7, 11~~, 13, 15, 19~~, 21, 23, 24, 27, 28, 33~~

**Homework 10** (due 22 October) (solution): Section 9.2: #11, 12, 14, 16, 18, 20, 22, 23, 24, ~~47, 51~~; Section 9.3: #5, 7, 11, 21, 23, 24, 27, 28, 33, ~~34, 37, 39, 40, 55, 58, and the following additional problems: ~~

**Problem A**: Compute $\cos\left(\sin^{-1}\left(\dfrac{1}{4} \right) + \tan^{-1} \left( -\dfrac{1}{7} \right) \right)$.

**Problem B**: The so-called Chebyshev polynomials (of the second kind), denoted by $U_n(x)$, are a special set of polynomials defined by the formula
$$U_n(x)=\dfrac{\sin\Big((n+1) \cos^{-1}(x)\Big)}{\sin(\cos^{-1}(x))}.$$
Compute $U_1(x)$ and $U_2(x)$.

(*hint: to find, for example, $U_2(x)$, set $n=2$ in the definition and then expand using the sum identity for sine and the double angle identity for sine, as appropriate*)

**Homework 11** (due 29 October) (solution): Section 9.2: #47, 48, 51; Section 9.3: #34, 37, 39, 40, 55, 58, 59; and the following additional problems:

**Problem A**: Compute $\cos\left(\sin^{-1}\left(\dfrac{1}{4} \right) + \tan^{-1} \left( -\dfrac{1}{7} \right) \right)$.

**Problem B**: The so-called Chebyshev polynomials (of the second kind), denoted by $U_n(x)$, are a special set of polynomials defined by the formula
$$U_n(x)=\dfrac{\sin\Big((n+1) \cos^{-1}(x)\Big)}{\sin(\cos^{-1}(x))}.$$
Compute $U_1(x)$ and $U_2(x)$.

(*hint: to find, for example, $U_2(x)$, set $n=2$ in the definition and then expand using the sum identity for sine and the double angle identity for sine, as appropriate*)

**Homework 12** (due 7 November) (solution): Section 9.5: #4, 6, 7, 16, 17, 19, 22, 24, 25, 36; Section 10.1: #11, 12, 14, 15, 20, 21, 23; Section 10.2: #13, 15, 16, 22, 23, 24, 25

**Homework 13** (due 12 November) (solution): Section 10.3: #7, 8, 10, 11, 12, 14, 17, 20; Section 10.4: #19, 37; Section 10.8: #9, 11, 17, ~~18, 29, 31, 33, 34, 58, 62, 63~~

**Homework 14** (due 28 November) (solution): Section 10.8: #18, 29, 31, 33, 34, 58, 62, 63

__Quizzes__

Quiz 1

Quiz 2

Quiz 3

Quiz 4

Quiz 5

Quiz 6

Quiz 7

Quiz 8

Quiz 9

Quiz 10

Quiz 11

__Notes__

Video lecture for Section 2.2

Video lecture for Section 2.5

Video lecture for Section 3.5