• This web page describes an activity within the Department of Mathematics at Ohio University, but is not an official university web page.
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# MATH 163A A01(04674), Fall 2009

## Introduction to Calculus

Catalog Description:
Presents a survey of basic concepts of calculus. For students who want an introduction to calculus, but do not need the depth of 263A-B-C. Note: Students cannot earn credit for both 163A and either of 263A of 266A.
Desired Learning Outcomes:
1. Understand the business terminology of demand, cost, price, revenue, and profit.
2. Use linear, polynomial, rational, algebraic, exponential and logarithmic functions in business applications.
3. Determine the limits of functions graphically, numerically, and analytically.
4. Recognize and determine infinite limits and limits at infinity.
5. Determine the continuity of functions at a point or on intervals.
6. Understand the interpretation of the derivative as the slope of a line tangent to a graph and as the rate of change of a dependent variable with respect to an independent variable, and determine the derivative of a function using the limit definition.
7. Use differentials in approximation problems.
8. Determine derivatives using the power rule, sum & difference rules, product rule, quotient rule, and chain rule.
9. Determine derivatives of Exponential and Logarithmic Functions
10. Understand the business terminology of marginal quantities, including marginal cost, marginal revenue, and marginal profit.
11. Determine higher order derivatives of a function.
12. Understand velocity as the derivative of position and acceleration as the 2nd derivative of position
13. Determine the absolute extrema of a continuous function on a closed interval.
14. Use the first and second derivatives to analyze and sketch the graph of a function, including determining intervals on which the graph is increasing, decreasing, constant, concave up, concave down, and finding relative extrema and inflection points.
15. Apply differential calculus to business applications.
Prerequisites:
C or better in MATH 113 or Placement level 2 or higher.
Instructor:
Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1259, 315-B Morton Hall.
Office hours: Monday 9-10am, Tuesday 9-10am, Thursday 3-4pm, and Friday 9-10am.
Web page:
http://www.ohiouniversityfaculty.com/mohlenka/20101/163A.
Class hours/ location:
MTuThF 8:10-9am in 126 Morton Hall.
Text:
Calculus for Business, Economics, Life Sciences, and Social Sciences, Eleventh Edition, by Barnett, Ziegler, and Byleen, Pearson/Prentice Hall, 2007; ISBN: 0-13-232818-6.
Homework:
Several problems from each section of the book are assigned. These problems will not be collected or graded, but you will need to do them in order to learn. Problems listed in [brackets] require a calculator.
Good Problems:
Six Good Problems are assigned, and will be collected and graded. These are homework problems that will be graded half on content and half on presentation. The idea is to practice writing mathematics regularly but in small pieces.
Tests:
There will be four mid-term tests, in class. Calculators are not permitted.
Final Exam:
The final exam is on Thursday, November 19, at 10:10 am in our regular classroom. Calculators are not permitted.
Each Good Problem is worth 1 unit, each test is worth 2 units, and the final is worth 4 units. Your lowest 2 units will be dropped and then your average is computed and a 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-.
Missed or Late work:
Only reasons given in advance of a missed test will be considered; otherwise a score of 0 will be given. Late Good Problems are penalized 5% for each 24 hour period or part thereof, excluding weekends and holidays. You can resubmit good problems to improve your score, but the late penalty will apply.
Attendance:
Attendance is assumed but is not counted in your grade. However, you should estimate that for each class you miss your average will decrease by one point due to the learning you missed. It is your responsibility to find out any announcements made in class.
You are strongly encouraged to work together on the homework. You can work together on the Good Problems, but you must acknowledge in writing what help you received and from whom. The tests and final exam must be your own work, and without the aid of notes, etc. Dishonesty will result in a zero on that work, and possible failure in the class and a report to the university judiciaries.
Supplemental Instruction:
SI "provides free, out-of-class study sessions led by an Ohio University undergraduate student who has already taken the course. Used throughout the U.S. and the world, the SI program has proven highly successful in increasing student achievement and retention." Check with the academic advancement center for more information and the schedule.
Special Needs:
If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let me know as soon as possible so that your learning needs may be appropriately met.
Learning Resources:
• The MATH 163 webpage http://www.math.ohiou.edu/courses/math163/ has supplemental handouts and drills.
• Wikipedia Mathematics Portal; Wikiversity Calculus topic
• ## Schedule

The Good Problems and Tests are fixed, but we may not cover sections on exactly the days shown.
Week Date Section Homework Wikipedia Good Problem/ Test
0 prerequisiteAppendix A: Basic Algebra Review Elementary algebra
prerequisiteChapter 1: A Library of Elementary Functions
prerequisite1-111,21,23,25,33, 34,35,36,39,41, 65,67Linear equation
prerequisite1-217,23,25,35ab[cd],37, 49,51,53,57,59, 61,69,77Line (geometry)
1 Chapter 2: Functions and Graphs
Tue Sep 82-135,37,39,45,47, 49,51,67,69,70, 93,97,99,103,105, 109 Function (mathematics)
Thu Sep 102-23,5,7,9,11, 17,19,21,23,25, 30,31,32,33,34, 35,37,39,47,49, 51,53,61,63a,65, 67Graph of a function
Fri Sep 112-39,13,15,19,21, 23,25,[31],[41],45, 47,51,52,57,59, 61,63Polynomial Good Problem 1: Mathematical Autobiography, using Layout
2Mon Sep 142-41,3,5,7,16, 17,19,21,23,25, 27,29,31,33,43, 45,47,49,51,61, 65,67,73,75 Exponential function
Tue Sep 152-52,3,5,9,11, 13,15,17,19,21, 23,31,33,35,37, 39,41,43,45,47, 49,51,61,63,[71], [73],[77],87,[91],[93], [95],99,100a[b]cd,[104] Inverse function; Logarithm
Thu Sep 17Review
Fri Sep 18study guideTest 1 on 1-1, 1-2, 2-1, 2-2, 2-3, 2-4, 2-5
3 Chapter 3: Limits and the Derivative
Mon Sep 213-13,4,5,7,17, 21,35,37,41,45, 47,49,55,57,59, 63,71 Limit (mathematics); One-sided limit; Limit of a function
Thu Sep 243-21,3,5,7,9, 10,15,19,21,25, 27,29,31,33,35, 49,53,63,65,71, 75Continuous function
Fri Sep 253-31,2,3,4,5, 6,7,8,9,11, 13,15,21,23,25, 27,31,33,35,37, 39,49,57,59,61, 63,69 AsymptoteGood Problem 2: Section 3-1 #66, using Graphs
4Mon Sep 283-41,5,7,13,17, 19,21,27,29,31, 32,33,34,35,36, 37,38,39,41,45, 46,57,59,61 Derivative
Tue Sep 29
Thu Oct 1Review
Fri Oct 2study guideTest 2 on 3-1, 3-2, 3-3, 3-4
5Mon Oct 53-51,3,7,9,11, 15,17,23,25,29, 31,33,35,37,39, 41,43,45,47,51, 55,65,67,75,77, 79,83,89Calculus with polynomials
Tue Oct 63-61,3,7,11,13, 15,19,21,37,41, 43,45,47Differential of a function
Thu Oct 83-71,3,5,9,11, 13 Marginal concepts; Marginal cost; Marginal revenue
Fri Oct 94-1[1],[3],[5],[11],[13], [17],[19],[21],[25],[27], [33],[35],[37],[39] e (mathematical constant); Compound interest Good Problem 3: Section 3-5 #52, using Flow
6Mon Oct 124-21,3,7,11,13, 15,17,19,21,23, 25,27,29,31,33, 35,37,41,51,53 (drop deadline with WP/WF)
Tue Oct 134-31,3,5,9,11, 17,23,25,27,35, 39,47,51,53,55, 57,59,61,67,77, 83,87Product rule; Quotient rule
Thu Oct 15
Fri Oct 164-423,27,29,31,33, 35,37,39,41,45, 47,49,51,57,61, 63,67,71,79,83, 89,93,[97],[99] Chain rule Good Problem 4: Section 4-3 #82, using Logic
7Mon Oct 194-53,7,9,13,17, 19,25,29,31,43, 47Implicit function
Tue Oct 20
Thu Oct 22Review
Fri Oct 23study guideTest 3 on 3-5, 3-6, 3-7, 4-1, 4-2, 4-3, 4-4, 4-5
8Mon Oct 264-61,3,7,9,11, 13,17,19,21,31 Related rates
Tue Oct 27
Chapter 5: Graphing and Optimization
Thu Oct 295-11,3,5,6,7, 9,11,13,15,17, 21,23,25,27,29, 33,51,53,55,57, 59,61,63,65,67, 69,71,73,77,79, 91,101 Monotonic function; Critical point (mathematics); First derivative test; Fermat's theorem (stationary points)
Fri Oct 305-21,3,5,7,9, 11,13,15,16,18 19,21,25,29,31, 33,37,45,51,55, 59,61,71,73,79, 81,89Second derivative test; Inflection point; Concave function Good Problem 5: Section 4-6 #18, using Intros
9Mon Nov 25-41,3,5,7,9, 11,15,17,21,23, 24,25,43,57,59, 65,75,83
Tue Nov 3
Thu Nov 5Review
Fri Nov 6study guideTest 4 on 4-6, 5-1, 5-2, 5-4
10Mon Nov 95-51,3,5,7,11, 15,17,19,21,23, 27,29,33,35,37, 51,57,59,61 Maxima and minima; Extreme value theorem
Tue Nov 10
Thu Nov 125-61,3,5,7,9, 11,13ab,23,25,30, 31,37
Fri Nov 13 Good Problem 6: Section 5-5 #56, using Symbols
11Mon Nov 16Review
Thu Nov 19 study guide Final Exam at 10:10am, in our classroom

Martin J. Mohlenkamp