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# Calculus 1

Organization Of Course: This a lecture-based course where students are encouraged to discuss lecture
topics, text material, Mathematica labs and assigned exercises.

Catalog Description: MATH-155 - CALCULUS I 4 credits
Topics include the straight line, conic sections, inequalities, functions and
graphs, including trigonometric, exponential and logarithmic functions; limits
and continuity; differentiation of algebraic and transcendental functions;
maxima/minima theory; related rates; differentials. Computer laboratories
illustrating key concepts are an essential part of the course.
PREREQUISITES: Math232, Math145, Placement Level MM107, or
Permission of Instructor

Attendance: Attendance is required. A student who misses 4 or more classes risks withdrawal
from the course. A student absent from class is responsible for all material
taught and for all procedural information discussed including any changes in
examination dates and assignments.

STCC POLICY ON DISRUPTIVE BEHAVIOR
"Behavior which disrupts the establishment or maintenance of the learning
environment may result in the student causing the behavior to be removed from
the classroom by the instructor. The student may be subject to further
disciplinary action..."

Please note that arriving late for class falls in this category. Please make every
effort to arrive at class on time excessive tardiness is equivalent to missing class
and will be dealt with likewise.

Evaluation: There will be four one-hour examinations and a cumulative final examination,
which will be valued as two hour examinations, administered in this course. The
labs will count as one test score. The final average will be computed based on
the best six of seven scores (note: lab grade will not be dropped).

Make-ups: There will be no make up exams without prior notice to the professor. The
makeup will be taken in the Math Center and you will not get the test back. You
will have to make an appointment with professor to discuss your grade.

Mathematica Labs: There are six labs to be turned in for the value of one test grade. This grade will
not be dropped.

Academic Dishonesty: If at any time during the semester there is any evidence of academic dishonesty
by students on an examination, then these students will be dismissed from the
course with an automatic grade of F and may be taken to the Dean of Students.

## Objectives/Competencies:

Objective 1: Analyze Functions and Relations.
Competencies:

1. Describe a region using set notation, interval notation, and on the Real number line.
2. Determine the length of a segment.
3. Determine the midpoint of a segment.
4. Determine the equation of a circle given its center and radius or diameter.
5. Determine the center and radius of a circle given its equation.
6. Find coterminal angles.
7. Convert between radian and degree measure.
8. Determine all six trigonometric functions for a given angle.
9. Evaluate a trig. function from a right triangle with one unknown side.
10. Evaluate trig. functions with and without using a calculator.
11. Solve trig. equations.
12. Determine period and amplitude of sine and cosine functions.
13. Graph sine and cosine functions with and without using a graphing utility.
14. Plot a relation and determine symmetry.
15. Define the properties of logarithmic functions.
16. Define the properties of exponential functions.
17. Sketch the graphs of logarithmic and exponential functions.
18. Evaluate a function and function formulas.
19. Find domain and range of a function.
20. Determine the region(s) over which a functions one-to-one.
21. Plot a function by analyzing shifts.
22. Plot a compound function.
23. Determine if a function is even or odd.

Objective 2: Evaluate Limits.
Competencies:

1. Estimate limits using a table.
2. Evaluate limits using direct substitution.
3. Evaluate limits using factoring.
4. Evaluate limits using rationalization.
5. Determine when a limit does not exist.

Objective 3: Discuss Continuity of a Function.
Competencies:

1. Determine point(s) of discontinuity of a function.
2. Give examples of why each part of the continuity definition is necessary.
3. Apply the Intermediate Value Theorem to find zeros of a function.
4. Find vertical and horizontal asymptotes for a rational function.

Objective 4: Differentiate
Competencies:

1. Apply definition to compute the derivative.
2. Apply the Power Rule.
3. Apply the Product Rule.
4. Apply the Quotient Rule.
5. Apply the Chain Rule.
6. Find the derivative of trigonometric forms.
7. Find the derivative of inverse trigonometric forms.
8. Find the derivative of exponential functions.
9. Find the derivative of logarithmic functions.
10. Compute the implicit derivative of a given function.

Objective 5: Apply the Derivative to Various Applied (Rate of Change) Problems.
Competencies:

1. Find the slope and equation of the line tangent to the graph of a function.
2. Compute the average rate of change of a function over an interval.
3. Given a position function, compute (instantaneous) velocity function.
4. Given a velocity function, compute the (instantaneous) acceleration function.
5. Solve applied problems in which quantities are changing with time.

Objective 6: Compute the Extreme Values of a Function.
Competencies:

1. Compute the critical number(s) of a function.
2. Determine region(s) over which a function is increasing/decreasing.
3. Apply First Derivative Test to classify critical number(s) as being associated with relative max/min.
4. Apply Second Derivative Test to classify critical number(s) as being associated with relative max/min.

Objective 7: Discuss Concavity of a Given Function.
Competencies:

1. Compute point(s) of inflection for a given function.
2. Determine region(s) over which a function is concave up/down.

Objective 8: Sketch Curves using Calculus Techniques.
Competencies:

1. Compute domain and range.
2. Compute x-intercept(s) and y-intercept(s).
3. Determine symmetry.
4. Find any point(s) of discontinuity.
5. Compute vertical and horizontal asymptote(s).
6. Find point(s) of nondifferentiability.
7. Compute relative extrema.
8. Discuss concavity.
9. Compute point(s) of inflection.
10. Determine behavior over the extent using limits at infinity.

Objective 9: Solve Optimization Problems.
Competencies:

1. Find absolute max/min of a function.
2. Solve applied max/min problems.

## Course Outline

Chapter 1 Preparation of Calculus
Appendix D - Precalculus Review

1.1 Graphs and Models
1.2 Linear Models and Rates of Change
1.3 Functions and Their Graphs
1.5 Inverse functions
1.6 Exponential and Logarithmic functions

Chapter 2 Limits and Their Properties
2.2 Finding Limits Graphically and Numerically
2.3 Evaluating Limits Analytically
2.4 Continuity and One-Sided Limits
2.5 Infinite Limits

Chapter 3 Differentiation
1.1 Derivative and Tangent Line Problem
3.2 Basic Differentiation Rules and Rates of Change
3.3 Product and Quotient Rules and Higher-Order
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivative of Inverse Functions
3.7 Related Rates
3.8 Newton’s Method

Chapter 4 Applications of Differentiation
4.1 Extrema on a Interval
4.2 Rolle’s Theorem and Mean Value Theorem
4.3 Increasing and Deceasing Functions and The First Derivative Test
4.4 Concavity and The Second Derivative Test
4.5 Limits at Infinity
4.6 Curve Sketching
4.7 Optimization Problems
4.8 Differentials

**Chapter 5 Integration
5.1 Antiderviatives and Indefinite Integration
5.2 Area
5.3 Riemann Sums and Definite Integrals
5.4 Fundamental Theorem of Calculus

** Time-permitting.

## Suggested Homework Problems

 Section Page Problems Appendix D TBA 1.1 8 1- 5, 7, 9, 11, 19, 21, 43, 47, 53, 61- 67 odd, 81, 83 1.2 16 1- 19 odd, 23- 59 odd, 59, 61, 63, 65, 83 1.3 27 1- 45 odd, 57, 59, 61, 63, 81, 83, 95, 97, 99 1.5 44 1,5, 9,11, 29-39 odd, 89-95 odd, 107-131 odd 1.6 54 1, 3, 5, 7, 15, 25, 27, 31, 33, 35, 37, 39, 45, 49, 53. 61, 65, 71-89 odd Exam 1 2.2 74 5, 9, 11-27 odd, 2.3 87 1-81 odd 2.4 98 1-19 odd, 29, 31, 37, 41, 51, 53, 55, 63, 65, 91 2.5 108 1-51 odd, 65 Exam 2 3.1 123 1-17 odd, 33, 37, 39, 59, 71, 81, 83, 85 3.2 136 1-61 odd, 3.3 147 1-35 odd, 41-57 odd, 69, 71, 101, 103 3.4 161 1-31 odd, 49, 51, 55-91 odd, 117, 119, 123, 131 3.5 171 1, 5, 7, 13, 17, 25, 31, 33, 35 3.6 179 3, 11, 13, 17, 19-45 odd 3.7 187 1, 3, 7, 15, 19, 27, 31 3.8 195 1, 3 Exam 3 4.1 209 1-17 odd, 21, 23, 25, 41, 43, 63, 65 4.2 216 1, 9, 11, 37, 43, 45 4.3 226 1-35 odd, 63, 67 4.4 235 1-21 odd, 29, 33, 37, 41, 67, 69 4.5 245 1-7 odd, 17-41 odd, 63, 65, 67 4.6 255 1-13 odd 4.7 265 3, 5, 11, 19, 21, 27 4.8 276 1, 7, 11, 17, 31, 33 Exam 4 Final Exam