KASKASKIA COLLEGE

MATH 166 CALCULUS AND ANALYTIC GEOMETRY

INSTRUCTOR: ERIC HOFELICH

Office Hours:  TBA

OFFICE LOCATION: ST. – 116

OFFICE PHONE: 545-3359

PLACEMENT REQUIREMENTS:  Math 135; High School Trigonometry or Permission of Instructor

COURSE DESCRIPTION: First course in Calculus and Analytic Geometry. This course will consider:  limits and their properties; differentiation and applications; integration; logarithmic, exponential, and other transcendental functions

TEXTBOOK: Calculus, by Larson, Hostetler, Edwards (8th edition, 2006)

EVALUATION: Five 50-minute exams will be given during the semester. 100 pts. Each.

                          Test 1  Chapter 1 Limits and Their Properties
                          Test 2  Chapter 2  Differentiation
                          Test 3  Chapter 3 Applications of Differentiation
                         
Test 4  Chapter 4 Integration
                         
Test 5  Chapter 5 Logarithmic, Exponential, and other Transcendental Functions.

Homework and announced/unannounced quizzes 100 pts.

The lowest of the first four exam scores may be dropped

Thus, TOTAL POINTS FOR THE CLASS would be 500 pts.

Grades will be assigned as follows:

450 – 500 A, 400 – 449 B, 350 – 399 C, 300 – 349 D, below 300 F

CHEATING POLICY: If caught cheating in any way, the student will receive an F for the final grade.

ATTENDANCE POLICY: To be successful in a math course, attendance would be very important, almost critical. If more than two weeks of classes are missed without a valid excuse ( death in family, hospitalization, nuclear blast, etc.) I reserve the right to withdraw you from class with an F. If you know in advance that you cannot attend class on a certain day, you may possibly get my prior approval. There are no make-up exams or quizzes. If you come to class late, you will not receive extra time for exams or quizzes.

 

 Math 166 Calculus and Analytic Geometry I Learning Outcomes

After successful completion of Math 166 a student should be able to perform the following at a 70% success rate (C or better):

1.      Find limits graphically and numerically

2.      Determine if a limit exists and evaluate limits analytically of polynomial, rational, radical, trigonometric, and composite functions

3.      Use the formal definition of a limit to prove its existence

4.      Find the derivative of a function by using the limit process

5.      Use the derivative to find the slope at a point on the graph

6.      Find the derivative of a function by applying basic differentiation rules such as the product rule and quotient rule

7.      Find the derivative of trigonometric functions

8.      Find the derivative of a composite function by applying the chain rule

9.      Find higher-order derivatives

10.  Use implicit differentiation to find the rate of change of a function

11.  Apply the extreme value theorem to find extrema on an closed interval

12.  Apply Rolle's Theorem and the Mean Value Theorem to find relative extrema on an open interval

13.  Use the first derivative test to find relative extrema and intervals for which the function is increasing or decreasing

14.  Use the second derivative test to determine concavity of a function and points of inflection

15.  Use Newton's Method for approximating the zeroes of a function

16.  Apply the basic integration rules to find the anti-derivative of a function

17.  Find upper and lower sums for a region

18.  Use the Fundamental Theorem of Integral Calculus to find the area under a curve

19.  Determine the area under a curve by applying the Mean Value Theorem for integrals

20.  Find the average value of a function on a closed interval

21.  Use the Second Theorem of Integral Calculus

22.  Integrate by substitution or by using the change of variable technique

23.  Find the derivative of a function by using logarithmic differentiation

24.  Find the derivative or integral of a natural logarithmic or exponential function

25.  Find the partial or general solution to differential equations

26.  Find integrals of inverse trigonometric functions

27.  Find the derivative or integral of hyperbolic functions

If Chapter 6 material is covered:

28.  Find the area of a region between two curves

29.  Find the volume of solids of revolution by applying the disk method, shell method , and washer method