# 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

## Documents:

1.   Syllabus

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) [If handed in by Thursday you will get them back Friday before the test]
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
Section 3.1 problems 13, 15, 19, 25

Section 3.2 problems 11, 13, 17, 19

7.  Due 10/13 (Friday)
Paper Homework:  Section 2.3 problems 17, 27, 30, 32 (for all problems sketch the graph)
Section 2.5 problems 12 (volume), 16 (cost),  23 (area),
Section 2.6 problems 20 (area), 23 (Oxygen), 27 (surface area)

8.  Due 10/16 (Monday)
Webassign:
Optimization

9.  Due 10/20 (Friday)

Paper Homework:  Section 8.3 problems 1-19 odd problems, and problem 23 & 25

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

10.  Due 11/06 (Monday)
Paper Homework:         PDF (file)
Section 5.4 problem 11, 12

11.  Due 11/10 (Friday)

Electronic Webassign  Mini-homework Antiderivatives

12.  Due 11/13 (Monday)

Paper Homework: Section 6.1 problems 19-28 (odd), 47, 48, 55, 56, 60
Paper Homework: Section 6.2 problems 3, 5, 7, 13, 19, 21
Paper Homework: Section 9.1 problems 1- 52 (every other odd problem 15,9,13,17....)
Paper Homework: Section 9.2 problems 1-37 (every other odd problem 1,5,9,13,17...)

13.  Due 11/20 (Monday)
Electronic Webassign: Integrals and areas under curves (note for these problems reduce functions before you integrate)

If handed in before the test it will be graded - this type of problem will be on the test

Paper Homework: Section 6.4 problem 45, 46
Paper Homework:
Section 9.3 problems 3, 11, 17

14.
Due 12/1 (Friday)
Electronic Webassign: Area under curves, Riemann sums
Electronic Webassign: Solids of revolution
Electronic Webassign: Further integration

Paper Homework: Section 6.3 problems 51, 52 (use excel spreadsheet)
Section 6.5 problems 33, 35
Extra credit:
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.

ALL OLD HOMEWORK IS DUE WEDNESDAY DEC 6th

Tests
Test 1    -  Friday 9/8
[solution]
Test 2    -  Friday 9/29      [solution]

Test 3    -  Friday 10/27    [solution]
Test 4    -  Friday 11/27    [solution]

Review

Part 0  (difference equations)
10.1 Introduction, problems 7-14, 17-21, 23-24
10.3 Graphing, problems 1-22
10.5 Modeling with difference equations, problems 1-13

Differentiation:

1.3 Derivative and limits (the power rule), problems 1-32, 49-56
1.3 Tangent line equation, problems 33-48
1.4 Limits, problems 7-28, 61-66
1.4 Use limits to calculate the derivative, problems 37-48
1.6 Rules for differentiation (constant multiple, sum, and general power rule), problems 1-38
1.7 More about derivatives (2nd order derivative), problems 1-30
3.1 Product and quotient rules, problems 1-44
3.2 Chain rule (and general power rule), problems 1-49
4.3 Differentiation of exponential functions, problems 1-32, 37-41
4.5 Differentiation of logarithm functions, problems 1-30
8.3 Differentiation and integration of sin and cos (differentiation), problems 1-34, 47,47-52 (includes both differentiation and integration)

Curve sketching:

2.2 The first- and second-derivative rules
2.3 The first- and second-derivative test and curve sketching, problems 1-44
2.4 Curve sketching, problems 1-30

Distance, velocity, and acceleration:
1.8 Distance, velocity, acceleration, problems 1-22
4.3 Exponential functions (velocity problem 37-41)

Optimization:

Know formulas for area, surface area, volume, and circumference for basic shapes including circles, spheres, cylinders, rectangles, and boxes.
2.5 Optimization problems, problems 1-31
2.6 Further optimization problems (biological), problems 11-14, 16-28

Part II (integration)
Integration techniques:

6.1 Anti-differentiation no bounds (power and exponential functions), problems 1-36, 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) 1-34, 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 21-46

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 7-26, 31, 37-40, 43-46

Applications of the definite integral:
6.5 Average value, problems  1-10
6.5 Solids of revolution, problems 27-36

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.