Mathematics 182

182 CALCULUS II (4+1) 4 credits

Instructor  Course Section                    Time              Location
------------------------------------------------------------------------
Eric Olson  F02 Math 182 CALCULUS II          MTWRF 3:00-4:35am    AB634

Announcements

[11-Aug-11] Final Exam

             ∞     - |x - 1|
6.  Find    ∫     e           dx
             0

[10-Aug-11] Second Extra Credit

[09-Aug-11] First Extra Credit

[05-Aug-11] Fifth Quiz

[29-Jul-11] Fourth Quiz

[22-Jul-11] Midterm Exam

[15-Jul-11] Trigonometry Review

[15-Jul-11] Third Quiz

[14-Jul-11] Homework 2 Extended

[08-Jul-11] Second Quiz

[06-Jul-11] Cylindrical Shells

[01-Jul-11] First Quiz

                                    dx
7.  Solve the initial value problem -- = sin(2t+5) where x(0)=0.
                                    dt

Course Information

Instructor:

Eric Olson

email:

ejolson at unr edu

Office:

Monday, Tuesday, Wednesday and Friday 2pm DMS 238 and by appointment.

Homepage:

http://fractal.math.unr.edu/~ejolson/182/

Texts:

Hass, Weir and Thomas, University Calculus, Pearson, 2007

Grading

     5 Quizzes (drop 1)         8 points each
     1 Midterm                 38 points
     1 Final Exam              80 points
    24 Homework Assignments     2 points each
       Participation            2 points
    ------------------------------------------
                              200 points total

Calendar

Week 1 Jun 27:
    Chapters 5.5, 5.6, 5.7, 6.1
Week 2 Jul 04:
    Chapters 6.2, 6.3, 6.4, 7.1
Week 3 Jul 11:
    Chapters 7.2, 7.3, 7.4, 7.5
Week 4 Jul 18:
    Chapters 7.6, 7.7, 8.1, 8.2
Week 5 Jul 25:
    Chapters 8.3, 8.4, 8.5, 8.6
Week 6 Aug 01:
    Chapters 8.7, 8.8, 8.9, 8.10
Week 7 Aug 08:
    Review and Final

Homework

[30-Jun-11] Notes on Homework 1

Problem 5.5.13:

    integral sqrt(2+3*x) dx

If the answer is written
   
    (2/9)*sqrt(2+3*x)^3 + C
  
it is accepted, but if it is written
  
    (2/9)*sqrt((2+3*x)^3) + C
  
it is marked incorrect.

Problem 5.7.1:

   integrate 1/x dx from -9 to -4  
   simplify your answer
  
If the answer is written
  
   ln(4)-ln(9)     or    ln(4/9)
  
it is accepted, but if it is written
  
   2*ln(2/3)    or   -ln(9/4)
  
it is not accepted.

[12-Jul-11] Notes on Homework 2

Some of the problems in sections 6.3 and 6.4 contain integrals have either very complicated antiderivates or no antiderivative at all in terms of elementary functions. Our book discusses techniques to solve such problems in sections 7.5 and 7.6 which we will be covering this week. Until then the following Maple commands may help:

Problem 6.3.21:

Use a grapher to find the curve's length numerically.

                       Pi         5 Pi
    x = 2 sin y        -- <= y <= ----
                        6           6

(round to the nearest hundredth.)

To solve with Maple type

    restart;
    f:=2*sin(y);
    dfdy:=diff(f,y);
    L:=int(sqrt(dfdy^2+1),y=Pi/6..5*Pi/6);
    evalf(L);

Maple will respond with 3.012453716 which should be rounded to 3.01 
so the homework system will accept it.

Problem 6.3.38:

                                     1/3      2/3
Find the length of the curve f(x) = x    + 4 x    
where 0 <= x <= 1.  (Round to three decimal places as needed.)

To solve with Maple type

    restart;
    f:=x^(1/3)+4*x^(2/3);
    dfdx:=diff(f,x);
    L:=int(sqrt(dfdx^2+1),x=0..1);
    evalf(L);

Maple with respond with 5.118694873 which needs to be rounded to 5.119 
so the homework system will accept it.

Problem 6.4.1:

Set up an integral for the area of the surface generated by revolving
the curve
                       Pi         7 Pi
    y = tan x          -- <= x <= ----
                        5          16

about the x-axis.  Then find the area of the surface numerically.  (Do
not round until the final answer.  Then round to the nearest hundredth
as needed.)

To solve with Maple type

    restart;
    f:=tan(x);
    dfdx:=diff(f,x);
    A:=2*Pi*Int(f*sqrt(dfdx^2+1),x=Pi/5..7*Pi/16);
    evalf(A);

Note that in this case int is spelled with a capital as Int to prevent 
Maple from even trying to find an antiderivative.  Maple will respond
with 78.67832836 which needs to be rounded to 78.68 so the homework
system will accept it.

Problem 6.4.7:

Set up an integral for the area of the surface generated by revolving
the curve

    x = integral of 4 sin(t) dt from 0 to y

where 0 <= y <= Pi/4 about the y-axis.  

Graph the curve.

Use technology to find the surface area numerically.  (Round to two 
decimal places as needed.)

    restart;
    f:=int(4*sin(t),t=0..y);
    dfdy:=diff(f,y);
    A:=2*Pi*int(f*sqrt(dfdy^2+1),y=0..Pi/4);
    evalf(A);

Maple will respond with 4.767342002 which should be rounded to 4.77 so
the homework system will accept it.

Quizzes and Exams

• Quiz 1A, Quiz 1B solutions
• Quiz 2A, Quiz 2B solutions
• Quiz 3A, Quiz 3B solutions
• Exam 1A, Exam 1B solutions
• Quiz 4A, Quiz 4B solutions
• Quiz 5A, Quiz 5B solutions
• Final A

Maple Examples

[28-Jun-11] Three Different Antiderivatives of the Same Function (mws, mpl)

[30-Jun-11] Visualizing Volumes of Revolution (mws, mpl)

[06-Jul-11] Area of a Chopped Off Cone (mws, mpl) (macsyma)

[07-Jul-11] Arc Length of a Parametric Curve (mws, mpl)

[12-Jul-11] Arc Length and Surface Area (mws, mpl)

[13-Jul-11] Finding Antiderivatives (mws, mpl) (macsyma) (axiom)

[15-Jul-11] Trapezoid and Simpson's Method (mws, mpl)

[19-Jul-11] More on Trapezoid Method (mws, mpl)

[20-Jul-11] Minimization Problem with Maple (mws, mpl) (macsyma)

Final Exam

The final exam will be held on Thursday, August 11 from 3:00-4:35am in AB634.

Equal Opportunity Statement

Academic Conduct