Mercer County Community College                                               Liberal Arts Division

 

MAT 111                                                              Calculus 1

 

TENTATIVE COURSE OUTLINE

 

Catalog Description:

 

This is the first course in the standard integrated calculus sequence.  Topics covered include differentiation and integration of algebraic and trigonometric functions.  Applications include curve sketching, related rates, maxima and minima, and approximations, and calculation of areas and volumes of revolution.  There is an emphasis on the theory of limits and continuity. 

 

Prerequisites:            MAT104 or MAT116 with minimum C grade

 

Required Materials:

            Text:    Calculus

                        Howard Anton, 7th edition

 

A graphing calculator is required.  TI – 83  will be used by the instructor and is therefore strongly recommended for the student

 

 

Instructor:  Richard Porter     

 

E-mail: porterr@mcc.ecu 

 

Web Page:    http://www.mcc.edu/~porterr

 

Office: LA 119  Extension 3826

 

Office Hours:  See Web Page

 

Grading:

 

Quizzes and Homework:      40%

Midterm:                                 20%

Final:                                       40%

 

Grade Scale:

90%-100%........A

80%-89.5%.......B

70%-79.5%.......C

60%-69.5%.......D

<59.5%.............F

 

 

Attendance: Perfect attendance is expected, and students are responsible for all material covered. Arriving late or leaving early will count as missing HALF a class. Any student missing the equivalent of 4 classes is not eligible to receive credit for the course. If a W grade is appropriate it will be given,  if not,  the student will receive an F. No excuse will be considered if it is not presented in writing and produced in advance when possible.

 

Make-ups: No make-ups are given for any reason. When valid excuses are produced in writing, work may be replaced by equivalent work from the final exam. One quiz can be missed without excuse.

 

Exams: There will be five tests at the testing center with no time limit, one timed in-class exams midterm and a timed final exam. Each exam is usually about 15 to 25 short answer questions. There are NO multiple choice questions, showing all work is required even for calculator problems, and partial credit is given for correct work shown on exam. No scrap paper, books, notes, formulas, or calculator programs may be used with the exam.

 

Quizzes: Students should expect to hand in homework every class, as this will make up part of the quiz grade. The rest of the quiz grade will be made of questions from the homework or lecture. For some quizzes, the homework may be used as reference for the quiz, so do your homework! Homework is not accepted late.

 

Academic Integrity: Students are encouraged to work together on homework. Students are expected to do their own work. Students who cheat will fail the course.

 

Classroom: Do not smoke or eat in class. No visitors (especially children) may attend. Disruptive students are expected to leave. Cell phones, beepers, and pagers can be disruptive and must be silent.

 

Grade: The midterm exam is worth 20% of your grade. The final is worth 40% of the grade, and a grade of 50% is required to pass this course. The remaining 20% of the grade is composed of tests, quizzes, and classroom participation.

 

 

Topics

Day

Date

Precalc

1

1/22/2003

Precalc

2

1/27/2003

Precalc

3

1/29/2003

2.1,2.2

4

2/3/2003

2.3,2.4

5

2/5/2003

2.5,2.6

6

2/10/2003

Review

7

2/12/2003

3.1

8

2/17/2003

3.1,3.2

9

2/19/2003

3.3,3.4

10

2/24/2003

3.5

11

2/26/2003

3.6,3.7

12

3/3/2003

3.8

13

3/5/2003

Review

14

3/10/2003

4.1,4.2

15

3/12/2003

4.3

16

3/24/2003

4.4

17

3/29/2003

4.5

18

3/31/2003

4.6

19

4/5/2003

Review

20

4/7/2003

Midterm

21

4/12/2003

5.1,5.2

22

4/14/2003

5.3

23

4/19/2003

5.4

24

4/21/2003

5.5

25

4/26/2003

5.6

26

4/28/2003

5.7

27

5/3/2003

5.8

28

5/5/2003

Review

29

5/10/2003

Review

30

5/12/2003

Chapter I       Functions     Classes: 1-3

 

At the conclusion of this Chapter the student should be able to:

 

1.         Define function and be able to determine the domain and range of various types of functions.

 

2.                  Sketch the graphs of functions on a graphing calculator choosing an appropriate viewing window and using aids to graphing such as symmetry, intercepts and translations or reflections of basic graphs.  Then interpret these graphs to answer questions about domain and range.

 

3.         Define and distinguish between discrete and continuous data.

 

4.                  Define the absolute value of "a" to be  =  and use this definition to solve equations and inequalities involving absolute value and to rewrite absolute value equations as piecewise functions.

 

5.                  Identify functions, perform arithmetic operations on functions, and define composite function, even and odd functions, constant functions, power functions, polynomial functions, rational functions, and algebraic functions.

 

6.                  Interpret position versus time and velocity versus time graphs.

 

7.                  Define slope of a line as m =  =  and slope = tan , where  = angle of inclination.

 

8.                  Recognize that parallel lines have equal slopes and perpendicular lines have slopes which are negative reciprocals.

 

9.                  Use the various forms of a linear equation

 

a)  double intercept form

b)     point slope form y - y1 = m(x - x1)

c)      slope intercept form y = mx + b

d)     standard form Ax + By + C = 0

 

10.             Define and graph the six trigonometric functions and find arc length "s" on a circle using radian measure.

 

11.             Graph any trigonometric equation or parametric equations on the graphing calculator.  For trig equations, determine amplitude, period, frequency, and phase shift if possible.

 

 

Chapter 2      Limits             Classes: 4 - 8

 

At the conclusion of this Chapter the student should be able to:

 

1.                  Determine one-sided and two-sided limits of various functions from their graphs.

 

2.                  Determine infinite limits and limits at  from graphs.

 

3.                  Use various theorems on limits to calculate limits of functions algebraically.

 

4.                  Use the delta-epsilon definition of limit to determine delta when given epsilon, or to prove the truth of a given limit.

 

5.                  Define continuity and be able to determine points of discontinuity, if they exist, for given functions.  Be able to describe discontinuity points as removable or nonremovable discontinuity.

 

6.                  Determine vertical and horizontal asymptotes if they exist, for given functions.

 

7.                  Explain how limits at specific values of "x" or at infinity can fail to exist.

 

8.                  State and use the Intermediate Value Theorem to approximate roots.

 

9.                  Find limits and determine points of discontinuity of trigonometric functions using  and

 

10.             State and use the Squeezing Theorem to find limits.

 

 

Chapter 3      The Derivative         Classes: 9 -14

 

At the conclusion of this Chapter the student should be able to:

 

1.                  Determine average versus instantaneous velocity using the slope of the secant line through two points and the slope of the tangent line through a given point on the position function.

 

2.                  Calculate the instantaneous rate of change of y with respect to x and distinguish this from the average rate of change of y with respect to x for a given function.

 

3.                  Define the derivative f ' (x) or  or y' to be  and be able to find the derivative and the equation of the tangent line to y = f(x) at a given point x = a.

 

4.                  Use the theorems on techniques of differentiation to differentiate constant functions, polynomials, products, and quotients of functions.

 

5.                  Find higher derivatives y ", y ''', etc. of given functions.

 

6.                  Find derivatives of trigonometric functions.

 

7.                  Use the chain rule to find derivatives of composite functions.

 

8.                  Use differentials to approximate changes in function values, and to find the local linear approximation of f at x0 using f(x)  f(x0) +f '(x0) (x - x0).

 

9.                  Find the propagated error, relative error, and percentage error in applications problems caused by given errors in measurements.

 

10.             Find dy for a given function.

 

 

Chapter 4      Exponential and Logarithmic Functions         Classes: 15 - 21

 

At the conclusion of this Chapter the student should be able to:

 

1.                  Define inverse functions and given a function, find its inverse, if it has one, and find the domain and range of the inverse.

 

2.                  Use the horizontal line test to determine if a function is one to one and therefore has an inverse.

 

3.                  Graph a function and its inverse on the same axis system along with the reflection line y = x on a graphing calculator.

 

4.                  Use the derivative to find an interval on which f(x) is increasing or decreasing and therefore has an inverse on this interval.

 

5.                  Restrict the domain to make a function one to one or invertible.

 

6.                  Determine the continuity and differentiability of the inverse of a given function.

 

7.                  Define and graph on graphing calculators exponential functions and logarithmic functions and determine their domain and range.

 

8.                  State and use the algebraic properties of logarithms to solve exponential and logarithmic equations.

 

9.                  Use the change of base formula for logarithms.

 

10.             Perform implicit differentiation.

 

11.             Differentiate exponential and logarithmic functions and use logarithmic differentiation when applicable.

 

12.             Differentiate, graph, and evaluate inverse trigonometric functions and find their domain and range.

 

13.             Use differentiation with respect to time t to solve related rate problems.

 

14.             Use L' Hopital's Rule to evaluate limits of indeterminate form , if possible.

 

15.             Analyze other indeterminate forms such as 0 , , 00, , 1to see if they can be rewritten and L' Hopital's Rule can be applied to find the limit.

 

 

Chapter 5      The Derivative in Graphing and Applications Classes 22 - 29 lecture hours)

 

At the conclusion of this Chapter the student should be able to:

 

1.                  Determine intervals where a function is increasing, decreasing, or constant by analyzing its first derivative.

 

2.                  Use the second derivative to determine where a function is concave up or concave down.

 

3.                  Define and locate points of inflection for a function.

 

4.                  Define and locate relative maxima and relative minima using the first and second derivative tests.

 

5.                  Define and locate critical points and stationary points, if any, for a function.

 

6.                  Graph polynomial functions, rational functions, equations with vertical tangent lines or cusps.

 

 

 

 

7.                  Maximization or minimization of a function

 

a.                  relative maxima or minima

b.                  absolute maxima or minima

c.                  Extreme Value Theorem

 

8.                  Marginal analysis of profit, revenue, and cost.

 

9.                  Rectilinear motion.

 

10.             Solutions to equations of the form f(x) = 0 that may have irrational roots using Newton's Method.

 

11.             State Rolle’s Theorem and the Mean-Value Theorem, and use the theorems to solve problems.

 

Review Class 30.