MA131-040  MW(Th)F 11.45-12.35

     Class-room: SAS Hall 2229

    Instructor: Mette S Olufsen

    Office: SAS 3216

   
Phone Number: 919-515-2678
    E-mail address: msolufse@ncsu.edu

Office Hours: By appointment

Documents:

    1.   Syllabus
    2.   Supplement
    3.   Difference equations biological examples
    4.   Excel example 1 DE (money and acetaminophen)

Homework (https://www.webassign.net/ncsu/login.html)

    1.     Due 8/23 (Wednesday)
           
Optional:
            Intro to WebAssign
            Intro to Symbolic Questions
            Symbolic Questions (Part 2)

   2.     
Due 8/23 (Wednesday)
           
Paper Homework (discussed in class):
            A: What is the interest of your bank account and how frequent it is compounded?
            B: Is there a fee associated with your account?

            C: Assume your interest rate of XX% is compounded yearly (even if it is not) and use the yearly fee YY.
            Assume that you deposit $1,000 in your account and that you withdraw $100 per year.
            How long before your account will reach a 0 balance?

          

    3.     Due 8/25 (Friday)
            Electronic Webassign: Difference Equations (I)
            Paper Homework:
           
A: The solution to the finite difference equation yn+1 = a yn + b is given by  yn = b/(1-a) + (y0 - b/(1-a)) a^n
                 To show that this solution is correct we used the trick
                 1 + a + a^2 + ... + a^n-1 = (1 - a^n)/(1 - a)
                 In class we showed that this was valid for n=1 and n=2. Show that the formula is valid for n=3

            B: For the population of NC, plot actual population from 1920 to 2016 (google NC population) vs the one predicted.
                Assume population growth is 1.4% and 5,000 people immigrate each year. In 1920 the population was 2,588 million.

            C: Problems 32 (parts a and b) pages 98-99 in Documents 3  [The problems follow examples 2 (page 87) and 4 (page 89)]

            D: Repeat C but for a drug of  your choice. Give a source explaining values you used for the drug you chose.
                 If you cannot find these make up numbers.


    4   Due 9/1 (Friday)
           
Electronic Webassign:
Mini homework on difference equations

                                                   Difference equations II (problem 1)

            Paper Homework:
            Section 10.3 (supplement): 1-19 (odd problems), 22, 24.
           

            Section 10.5 (supplement): 3, 5, 6, 7, 11.


    3.     Due 9/7 (Thursday)
            Electronic Webassign: Derivatives and tangent lines


   
4.    Due 9/22 (Friday)

           Paper Homework:
           Section  1.5 (book): 15, 17, 19, 21, 23
       
          Use the power law and the formal definition to calculate the derivative of f(x) = sqrt (3x)
          Recall: f'(x) = lim_(h->0) [ f(x+h) - f(x) ] / h



   5.    Due 9/27 (Wednesday)

           Electronic Webassign:
          
Limits, continuity, and differentiability
           Derivatives II

   6.    Due 10/2 (Monday)
         Electronic Webassign: Mini homework: Product, Quotient and Chain rules
        
Electronic Webassign: Applications of derivatives

         Paper Homework:   Section 1.8 problems 4, 7, 15, 17, 18, 21,  22

FUTURE HOMEWORK

    5.  Due

                                         Section 3.1 problems 67, 68 [Challenge extra credit]
                                         Section 3.2 problem 50, 55   [Challenge extra credit]


    6.  Due
      
  Paper Homework:  Section 2.3 problems 17, 19, 21, 23, 25, 27, 29, 31
      
                             
    7.  Due 
         Paper Homework:  Section 8.3 problems 1-19 odd problems, and problem 23 & 25


   8.  Due 
        Electronic Webassign: Optimization       
   

       
Paper Homework:   Section 2.5 problems 11, 12, 16
                                         Section 2.6 problems 20, 23, 27


   9.  Due
          Electronic Webassign: More rules for differentiation
  

  
10.  Due
  
      
Electronic Webassign: Mini homework - Exponential functions
         Electronic Webassign: Mini homework - Rules of logarithms
         Electronic Webassign: Exponential and logarithm functions
         Electronic Webassign: Applications: Exponential and Logarithmic functions

   11.  Due
 
       Paper Homework:         PDF (emailed)
                                               Section 5.4 problem 11, 12

   12.  Due
 
      Electronic Webassign  Mini-homework Antiderivatives
       
        Paper Homework: Section 6.1 problems 19-28 (odd), 47, 48, 55, 56, 60        
        Paper Homework: Section 8.3 problems 35-44 (odd)        
 
  13.  Due
         Electronic Webassign: Area under curves, Riemann sums
         Electronic Webassign: Integrals and areas under curves (note for these problems reduce functions before you integrate)
         Electronic Webassign:   Solids of revolution
   
         Paper Homework:
Section 6.3 problems 51, 52 (use excel spreadsheet)
                                       Section 6.4 problem 45, 46

          Glass volume (solid of revolution)
          Find a cone-shaped glass and calculate and measure the volume of the glass.
          Use the equation

                    V = int_a^b  pi ( g(x) )^2 dx

          Hint: you need to measure the height of the glass and radius in both ends to find g(x) = c1 x + c2 as well as a and b.

   14. Due
         Electronic Webassign:   Further integration
         Paper Homework:         
Section 9.2 problems 3, 11, 15,  23
                                                Section 9.3 problems 3, 11, 17
 
        ALL OLD HOMEWORK IS DUE WEDNESDAY DEC 6th


Tests  
     Test 1    -  Friday 9/8

     Test 2    -  Friday 9/29

     Test 3    -  Friday 10/27
     Test 4    -  Monday 11/20



Review
   
Part I (differentiation)
    Differentiation:
        1.3 Derivative and limits (the power rule), problems 1-32, 49-56
        1.4 Limits and the derivative, problems 7-28, 61-72
        1.6 Rules for differentiation (constant multiple, sum, and general power rule), problems 1-37
        1.7 More about derivatives (2nd order derivative), problems 1-30, 33
        3.1 Product and quotient rules, problems 1-28, 41-46,  53-65, 67-68
        3.2 Chain rule (and general power rule), problems 1-50, 55
        4.3 Differentiation of exponential functions, problems 1-31, 35-39
        4.5 Differentiation of logarithm functions, problems 1-30
        8.3 Differentiation and integration of sin and cos (differentiation), problems 1-34, 47, 51-52 (includes both differentiation and integration)

        Curve sketching:
        2.2 The first- and second-derivative rules, problems 1-44 (mostly graphical)
        2.3 The first- and second-derivative test and curve sketching, problems 1-32, 44
        2.4 Curve sketching, problems 1-30

        Distance, velocity, and acceleration:
        1.8 Distance, velocity, acceleration, problems 1-4, 7, 10-17, 21, 32
        Section 8.3 on differentiating sin and cosine also have some problems on distance, velocity, and acceleration

        Optimization:
        Know formulas for area, surface area, volume, and circumference for basic shapes including circles, spheres, cylinders, rectangles, boxes etc.
        2.5 Optimization problems, problems 1-14, 17-25
        2.6 Further optimization problems (biological), problems 11-14, 16, 19-23, 25, 27, 28

    Part II (integration)
        Integration techniques:
        6.1 Antidifferentiation no bounds (power and exponential functions), problems 1-46, 55-60
        6.2 The definite integral, problems 1-22, 31-34 (distance, vel, acc),  39 (population), 42-44 (exp functions)
       
8.3 Integration of sin(t) and cos(t), problems 35-46, 47-48, 51-52
        9.1 Integration by substitution, problems (no bounds) 1-36, 39-52
        9.2 Integration by parts, problems 1-36
        9.3 Definite integrals  (substitution and integration by parts), problems 1-23
        9.6 Improper integrals, problems 1-47
       

        Area under curves:
        6.3 Definite integrals and area under a graph and Riemann sums, problems 1-48
        6.4 Areas in the xy-plane, problems 1-31, 37-39, 43-46

        Solids of revolution:
        6.5 Applications of the definite integral (part that has to do with solids of revolution), problems 29-42
       
 

Final  
       Final (comprehensive),  MONDAY 12/11 8.00 - 11.00 am SAS 2229
.
       For the final you may bring calculator and two sheet with notes.