MTH 125      COURSE OUTLINE             Spring 2007

 

INSTRUCTOR:   K.W.NICHOLSON                                email:  nnicholson@cacc.cc.al.us

OFFICE HOURS: POSTED ON DOOR OF RM 224       Ph 256-215-4336 or 4343

                                                                                               webpage located at:  http://caccphysics.cacc.cc.al.us

TEXT:     Stewart's "Essential Calculus"

 

TOPICS COVERED:  Functions, derivatives, curve sketching, max & min word problems, integration of polynomial, trig  and  exponential functions.  (Essentially, Chapters 1 through 5)

 

PURPOSE OF THIS COURSE:

           Til now most of your math has dealt with static situations and functions.  Calculus introduces the math of dynamic situations. This course will develop the symbols and language of math that will enable you to solve some really interesting problems.    Your objective should be to become familiar enough with differentiation and integration that it becomes part of your vocabulary and your thinking.

 

EVALUATION:

Item

Date

Discussion

4-100 point tests

Jan 25, Feb 15, Mar 8, April 5

No make up tests will be given.  A missed test will be replaced by 1/2 of your final exam score.

 

1-200 point Final Exam

May 1, 10:30 - 12:30

Final will be comprehensive.

DDFD's -100 pts total

daily

These will be straight forward drill on differentiation & integration formulas

 

The above total, excluding bonus points, is 700, (plus a few points, depending on miscellaneous assignments), and your accumulative total will be divided by that amount to calculate your final average.

 

  90 - 100 = A, 80 - 89 = B, 70 - 79 = C, 60 - 69 = D, 0 - 59 = F

 

NOTES: 

l.  Final percentage will be rounded UP, i.e., a final percent of 79.00000001 will be rounded up to 80.

2.  You should keep all returned papers.  You should also keep track of the ratio (your accumulative total)/(The accumulative total possible to date) as the quarter progresses.   If this average is not above 70 by midterm, you should consider dropping the course to avoid a bad grade.

 

3.  If you stop attending this class without obtaining a drop slip from student services the registrar will give you a grade of F in this course.

 

4.  Words of wisdom regarding Math homework.

            I hear........ and I forget,

            I see..........and I remember,

            I do...........and I understand.
1.  Review some basic essentials in Algebra.

          

     (a + b)n is never equal to an + bn for any n,  so    (a + b)2 = a2 + 2ab + b2, not a2 + b2.

                      

     And since n_a = (a)1/n,  = (a + b)1/n, so

    

     = (a + b)1/2 is never a1/2 + b1/2 .

 

Never cancel the same thing from top and bottom of a fraction.  Instead you divide numerator and denominator by the same factor, thereby reducing that factor to 1 on both top and bottom.

 

Rules for exponents.

 

anam = am+n, so 3234 = 36, not 96.

 

(ab)n = anbn so (x3y4)2 = x6y8, but what is (x3 + y4)2 ?

              1

a-n =   an 

Special products

 

x2 - y2 = (x-y)(x+y)

x3 + y3 = (x+y)(x2-xy+y2)

x3 - y3 = (x-y)(x2+xy+y2)

x2 + 2ax + a2 = (x+a)2

 

Analytical geometry

 

Points in the xy plane, distance and midpoint formulas.

A line and its essential components.

Slopes of parallel and perpendicular lines.

A circle and its essential components.

 

Course Overview.

 

1.  Discuss the definition of functions and limits.

 

2.  Discuss the true meaning of a derivative, to get an idea of its usefulness, and learn the differentiation formulas that make differentiation a powerful, easy to use tool that permeates all of science, and increasingly, business as well.

3. Practice using derivatives to graph functions, and solve applied problems.

 

4.  Learn what an integral is, what it means, and what exactly was "the discovery of the Calculus", that made Newton and Leibniz so famous. 
Notation & Vocabulary by section

1.1

Function

Function notation

Domain & Range

vertical line test

increasing & decreasing fcts.

 

1.2

Polynomials

degree of polynomials

quadratic functions

transformations Pg 17

composition of functions

RBD  or "No. 1 Pet Peeve"  A trig function without an argument has no meaning!

 

1.3

Limits concept

Definition:   if and only if left and right limits = L

 

1.4

Limit Laws  1 - 7  Pg 35

Plus the general form of 6   functions

Direct Substitution Property Pg 37  Says all polynomials, rational functions, & trig functions have limits everywhere they exist.

RBD - bottom of Pg 38 - Says it is ok to "alter" the expression using algebra in order to try to find a limit.

Also note worthy - Squeeze thm.

 

1.5 

Define Continuity

IVT - Pg 52

Infinite Limits - VA's

Limits at infinity - HA's

 

2.1

pt - slope form of linear equation

Define- tangent line

Define  - slope of a  curve at a point

Definition of a derivative

           Conceptually

           Graphically

           Algebraically

2.2 

Differentiable Functions

Know where functions NOT differentiable Pg 89

f"(x) & f"'(x)

f(4)(x)

 

2.3 - 2.6  Differentiation Formulas

Implicit Differentiation

 

2.7  Steps to solve Related Rates Problems Pg 129

 

2.8  Differentials

 

3.1

Exponential functions

e = ?

 

3.2

Define Inverse of a function

Notation f-1(x)   RBD  -Know what it is NOT!

Define Log Functions  Pg 154

Define  Natural Log Function Pg 155

Laws of Logs  Pg 155 & 157

 

RBD eln x = x

ln ex = x

ln e = 1

ln 1 = 0

 

3.3

Derivative formulas for log and exponential functions

Logarithmic Differentiation

 

3.5 

Define Inverse Trig functions

Notation  sin-1 x = ?  Know what it is NOT!

 

3.7

L'Hopital's Rule

Determined Forms

Indeterminant Forms

 

4.1  Steps to solve Max & Min Problems

 

4.2  MVT

4.3  How to determine Concavity

4.4   Steps to Curve Sketching

4..5  Steps to solving Optimization Problems  (Applied Max & Min Problems)

 

4.7  Define Antiderivatives

 

5.1  Define Integration

 

Finding Area under a curve

 

5.2  Definition of a Definite Integral

           Properties of Integrals Pg 270

 

5.3  The FTC

 

5.4 

More Precise FTC

MVT for Integration 

5.5  Integration by substitution (or change of variable)
THE BIG PICTURE

 

Class time:   Tuesday & Thursday  10:50 - 12:35

Assignment Notation: 

Should - Means problems you should do.

Must - Means problems that will be on the tests.

Dare (D) - Means 5 pt Bonus problems due at beginning of next class period.

Double Dare (DD) - Means 10 Pt Bonus problems due at beginning of next class period.

DAILY          SCHEDULE

Date

Topic

Stewart Homework assignment

T Jan 9

Sections 1.1 & 1.2Background info

 

Sect.1.1  Should:  9 - 22

Must:  37 - 40

 

Sect. 1.2  Should 1 - 14. 21 - 34

Must:  37 - 43,  45 - 51

Th 1-11

Experiment 1:  Where do functions come from?

Day 2 We meet in Physics Lab BS 214

T 1-16

1.3  Limit Concepts

1.4  Laws of Limits

Sect. 1.3  Should:  1,3,4,5,6,7,9,11

Sect. 1.4  Should:  1,2,7,8,9,

Must:  11 - 17

Th 1 -18

1.5  Continuity

1.6  Infinite Limits - Vertical Asymptotes

Limits at Infinity - Horizontal Asymptotes

Sect. 1.5  Shouild:  3, 5, 13, 15

Sect. 1.6  Should:  19 - 31, except 23, 27

Must:  1,5,7,13,15

Dare:  23, 27, 29

T 1-23

2.1  Drill on equations of lines

Derivatives, definitions of derivatives

Sect. 2.1  Should:  9,10.15,16,17

Th 1 - 25

Test 1

2.2  Differentiable Functions & Not Diff.

 

Sect. 2.2  Must: 3,5,7,27 - 30, 33 

T 1 - 30

2.3  Differentiation Formulas I

Sect. 2.3  Should:  57

Must:  1 - 26, 29 - 32, 51, 52

Dare:  59, 60

Th Feb 1

2.4  Product Rule & Quotient Rule

Sect. 2.4  Should:  2

Must:  3 - 30

Dare:  41, 49

T Feb 6

2.5  Chain Rule:

Sect. 2.5  Should 1 - 5, 55

Must:  7 - 40, 57

Th 2 - 8

2.6  Implicit Differentiation

Sect. 2.6  Must:  3 - 13, 17,19,23,25

Dare 15 & 16

Double Dare:  44

T 2 - 13

 

 

Th 2 -15

Test 2

2.7  Related Rates

 

Sect. 2.7:  Should:  13, 15, 17

Must 1 - 12

Dare:  22, 25, 26

T 2 -20

2.7  Continued

 

Th 2 -22

2.8  Differentials

Sect. 2.8  Should:  11 - 14

Must:  17, 18

Dare:  24

T 2 -27

3.1  Exponential Functions

Sect. 3.1  Should:  1 - 13

Must:  15, 16

Dare:  17, 23

Th 3-1

3.2  Inverses of Functions, log functions

Sect. 3.2  Must:  21,23,25, 43 - 53, 61-64

T 3 - 6

3.3  Derivatives of Log & Exp Functions

Sect. 3.3  Must 1 - 42, 45 - 54

Dare:  55, 56, 57

Double Dare:  58

Th 3- 8

Test 3

3.5  Inverse Trig Functions

Sect. 3.5  Should:  35 - 38

Must 1-10, 16 - 28

Dare:  39

T 3-13

3.7  L'Hopital's Rule

Sect.  3.7  Must:  1 - 36

Dare:  46

Th 3-15

4.1  Max & Min

Sect. 4.1  Must:  3 - 11, 15, 17, 18, 19, 20, 22, 23, 25, 37, 39

Dare:  35, 36

 

 

 

T 3-27

4.2  MVT

4.3  Concavity

Sect. 4.2  Should:  1,3,11,13

Sect. 4.3  Should:  9, 15, 17, 19

Must  1,3,5,23,25,33,35,36

Th 3-29

4.4  Curve Sketching

Sect. 4.4  Must 1 - 16

T 4- 3

4.5  Optimization Problems

Sect.  4.5  Must:  3,5,7,9,13

Dare:  19

Th 4-5

Test 4

Finish 4.5

 

T 4-10

5.1  Area

5.2  Definite Integrals, Properties of Integrals

Sect. 5.1  Should:  1,5,7

Dare:  12

Sect. 5.2  Instr:  Do 20 & 21

Th 4 - 12

5.3  The FTC

Sect.  5.3  Should:  48 - 58, 61

Must:  1 - 30, 41 - 44

T 4 - 17

5.4  More FTC

Sect. 5.4  Must:  5,7,9,15,17

Th 4 - 19

Sect. 5.5  Integration by Substitution

Sect.  5.5  Must:  1 - 50, 57

T 4 - 24

Review for Final

 

Th 4 - 26

Review for Final

 

T 5 - 1

Final Exam  10:30-12:30