Course: Math 110 (4 credits): Techniques of Calculus I.

Prerequisite: MATH 022 or satisfactory performance on the mathematics proficiency examination.

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Overview

MATH 110 is an entry-level course in mathematics that introduces the student to skills associated with the application of calculus techniques to business and social science applications.  The course will review and/or enrich understanding of polynomial and exponential functions as well as introduce the concepts of derivatives and integration. Most topics will be explored analytically and graphically as they are applied to real life examples and problems.  The student will be expected to study the concepts and examples and be able to extend the skills and techniques to the solution of similar problems.

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Objectives

Upon successful completion of this course, the student should be able to:

1. Identify polynomial, rational, power, exponential, and logarithmic functions.
2. Calculate the domains of polynomial, rational, power, exponential, and logarithmic functions.
3. Calculate the sums, differences, products, quotients, and compositions of functions.
4. Model cost, revenue, profit, supply, and demand business functions.
5. Calculate equilibrium points within supply/demand markets and interpret the results.
6. Calculate or estimate finite/infinite limits of functions given by formulas, graphs, or tables.
7. Calculate one-sided limits of functions.
8. Determine whether a function given by a graph or formula is continuous at a given point or on a given interval.
9. Determine whether a function given by a graph or formula is differentiable at a given point or on a given interval.
10. Distinguish between average and instantaneous rate of change and interpret the definition of the derivative graphically.
11. Determine derivatives of some functions using the definition of derivative of a function.
12. Calculate derivatives of polynomial, rational, power, exponential, and logarithmic functions, and combinations of these functions.
13. Calculate derivatives of implicitly defined functions.
14. Apply the ideas and techniques of derivatives to related rate problems to include basic algebraic/geometric models and cost/average cost, revenue/average revenue, profit/average profit, supply, and demand models
15. Apply the ideas and techniques of derivatives to perform marginal analysis of basic economics models.
16. Apply the ideas and techniques of derivatives to calculate elasticity of basic economics models.
17. Apply the ideas and techniques of derivatives to finding extrema.
18. Apply the ideas and techniques of derivatives to graphing functions.
19. Apply the ideas and techniques of derivatives to optimization problems to include basic algebraic/geometric models and cost, revenue, profit, supply, and demand models.
20. Apply the ideas and techniques of derivatives to solve compound interest, continuous interest, effective interest rate, and present value business models.
21. Calculate the Riemann sum for a given function, partition and collection of evaluation points.
22. Describe a definite integral as the limit of a Riemann sum.
23. Determine anti-derivatives of basic algebraic functions.
24. Calculate values of definite integrals using anti-derivatives and areas.
25. Apply substitution techniques to integrate basic functions.
26. Apply the ideas of definite integrals to solve problems of areas.
27. Calculate the average value of business models using the definite integral.

Apply the ideas and techniques of the definite integral to evaluate consumer/producer surplus, future/present value of income streams, and annuity business models.

 

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Materials

Most World Campus courses require that students purchase materials (e.g., textbooks, specific software, etc.). To learn about how to order materials, please see the Course Materials page. You should check LionPATH approximately 3–4 weeks before the course begins for a list of required materials.

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Library Resources

Many of the University Libraries resources can be utilized from a distance. Through the Libraries website, you can

• access magazine, journal, and newspaper articles online using library databases;
• borrow materials and have them delivered to your doorstep—or even your desktop;
• get research help via email, chat, or phone using the Ask a Librarian service; and
• much more. 

You must have an active Penn State Access Account to take full advantage of the Libraries' resources and service.  The Off-Campus Users page has additional information about these free services.

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Technical Specifications

Technical Requirements

Operating System	Windows Vista, Windows 7, Windows 8*; Mac OS X 10.5 or higher *Windows 8 support excludes the tablet only RT version
Processor	2 GHz or higher
Memory	1 GB of RAM
Hard Drive Space	20 GB free disk space
Browser	We recommend the latest ANGEL-supported version of Firefox or Internet Explorer. To determine if your browser fits this criterion, and for advice on downloading a supported version, please refer to the following ITS knowledge base article: Supported Browsers and Recommended Computers. Note: Cookies, Java, and JavaScript must be enabled. Pop-up blockers should be configured to permit new windows from Penn State websites. Due to nonstandard handling of CSS, JavaScript and caching, older versions of Internet Explorer (such as IE 6 or earlier) do not work with our courses.
Plug-ins	Adobe Reader [Download from Adobe] Flash Player (v7.0 or later) [Download from Adobe]
Additional Software	Microsoft Office (2007 or later)
Internet Connection	Broadband (cable or DSL) connection required
Printer	Access to graphics-capable printer
DVD-ROM	Required
Sound Card, Microphone, and Speakers	Required
Monitor	Capable of at least 1024 x 768 resolution

If you need technical assistance at any point during the course, please contact the Service Desk.

For registration, advising, disability services, help with materials, exams, general problem solving, visit World Campus Student Services!

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Arranging a Proctor

You will need to secure a proctor in order to take exams in this course. A proctor will not automatically be assigned to you; rather, you must make the necessary contacts to secure a professional who will serve in this capacity.

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Course Schedule

Lesson 0: Algebra Readiness
Readings:	None
Assignments:	Algebra Readiness Quiz Chapter 1 - Self Assessment Download Methematica Player Review Elluminate Live schedule and download software

Lesson 1: Course Overview; Concepts of Functions
Readings:	Chapter 2, section 2.1 and 2.2
Assignments:	Self-assessments Practice Homework Problems: Section 2.1: 1-13 odd, 21-33 odd, 49-55 Section 2.2: 1-23 odd, 25-34, 47, 51, 52

Lesson 2: Algebra of Functions and Mathematical Modeling
Readings:	Chapter 2, section 2.3
Assignments:	Self-assessments Practice Homework Problems: Section 2.3: 1-7 odd, 9-14, 51, 53, 56, 66, 67, 74, 75, 78

Lesson 3: Intuitive/Graphical and Tabular Ideas of Limit; Formal Limit Notation and "Properties;" and Limit Concept of the Derivative
Readings:	Chapter 2, section 2.4, 2.5, and 2.6
Assignments:	Self-assessments Practice Homework Problems: Section 2.4: 1-8, 17-22, 23-39 odd, 49-62, 73-80 Section 2.5: 1-6, 9-14, 21-35 odd, 39, 44, 51, 52 Section 2.6: 9-21 odd, 30, 34-36, 45-50

Lesson 4: Basic Rules for Calculating Derivatives; Product and Quotient Rules and Chain Rule
Readings:	Chapter 3, section 3.1, 3.2, and 3.3
Assignments:	Self-assessments Practice Homework Problems: Section 3.1: 1-36 odd, 37, 38, 41-46 Section 3.2: 1-29 odd, 35-41 odd, 46 Section 3.3: 1-53 odd, 61-64

Lesson 5: Marginal Functions; Product and Quotient Rules and Chain Rule
Readings:	Chapter 3, section 3.4 and 3.5
Assignments:	Self-assessments Practice Homework Problems: Section 3.4: 3-17 odd, 23-33 odd Section 3.5: 1-14 odd, 30

Lesson 6: Implicit Differentiation; Related Rates
Readings:	Chapter 3, section 3.6
Assignments:	Self-assessments Practice Homework Problems: Section 3.6: 1-17 odd, 31, 33, 41, 42, 56, 59, 60, 61

Exam 1
Assignments:	Complete Exam 1 in Angel

Lesson 7: Applications of 1st and 2nd derivatives
Readings:	Chapter 4, Sections 4.1, 4.2, and 4.3
Assignments:	Self-assessments Practice Homework Problems: Section 4.1: 1-8, 11-33 odd, 35-41, 43-46, 47-63 odd Section 4.2: 1-12, 21-67 odd Section 4.3: 1-10, 11-27 odd, 37-43 odd, 49-53, 56, 62

Lesson 8: Optimization
Readings:	Chapter 4, section 4.4 and 4.5
Assignments:	Self-assessments Practice Homework Problems: Section 4.4: 1-8, 9-27 odd, 40, 42, 46-51 Section 4.5: 1, 3, 4, 5, 6, 7, 8, 10, 12, 28

Lesson 9: Exponential and Log Functions – Differentiation
Readings:	Chapter 5, section 5.1, 5.2, 5.4, and 5.5
Assignments:	Self-assessments Practice Homework Problems: Section 5.1: 1-25 odd Section 5.2: 1-27 odd, 35-42 odd, 54 Section 5.4: 1-45 odd, 46, 60, 61 Section 5.5: 1-55 odd

Lesson 10: Compound Interest and Applications
Readings:	Chapter 5, section 5.3 and 5.6
Assignments:	Self-assessments Practice Homework Problems: Section 5.3: 1-23 odd Section 5.6: 7-13 odd, 19, 23

Exam 2
Assignments:	Complete Exam 2 in Angel

Lesson 11: Anti-derivatives and Basic Integration; Area, the Definite Integral
Time frame:	April 13 – April 19, 2009
Assignments:	Self-assessments Practice Homework Problems: Section 6.1: 1-57 odd, 67, 68 Section 6.2: 1-43 odd, 51 Section 6.2: 5, 7, 13, 15

Lesson 12:The FTC and Applications from Lesson 11; Review for Final Exam
Readings:	Chapter 6, section 6.4, 6.5, 6.6 and 6.7
Assignments:	Self-assessments Practice Homework Problems: Section 6.4: 1-39 odd, 41-43 Section 6.5: 1-27 odd, 29-37 ODD, 53 Section 6.6: 1-37 odd Section 6.7: 1-9, 11-13, 16-18

Final Proctored Exam

 

Please refer to the University Grading Policy for Undergraduate Courses for additional information about University grading policies. Note: If you are planning to graduate this semester, please communicate your intent to graduate to your instructor. This will alert your instructor to the need to submit your final grade in time to meet the published graduation deadlines. For more information about graduation policies and deadlines, please go to the Graduation Information on the My Penn State Online Student Portal.

Formal instruction will end on the last day of class. Provided that you have an active Penn State Access Account user ID and password, you will continue to be able to access the course materials for one year, starting from the end date of the academic semester in which the course was offered (with the exception of library reserves and other external resources that may have a shorter archival period). After one year, you might be able to access the course based on the policies of the program or department offering the course material, up to a maximum of three years from the end date of the academic semester in which the course was offered. For more information, please review the University Course Archival Policy.

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Course Requirements and Grading

The World Campus follows the same grading system as the Penn State resident program. The grades of A, B, C, D, and F indicate the following qualities of academic performance:

A = (Excellent) Indicates exceptional achievement
B = (Good) Indicates extensive achievement
C = (Satisfactory) Indicates acceptable achievement
D = (Poor) Indicates only minimal achievement
F = (Failure) Indicates inadequate achievement necessitating a repetition of the course in order to secure credit

2 Midterm Exams in Angel (un-proctored, 50 points each)	100 points
12 Weekly Lessons (50 points each, best 10)	500 points
1 Final Exam in Angel (proctored)	400 points
Total	1000 points

Grading Scale

Grade	%-Score	Points
A, A-	90 – 100	896 – 1000
B+, B, B-	80 – 89	796 – 895
C+, C	70 – 79	696 – 795
D	60 – 69	596 – 695
F	0 – 59	0 – 595

 

If, for reasons beyond the student's control, a student is prevented from completing a course within the prescribed time, the grade in that course may be deferred with the concurrence of the instructor. The symbol DF appears on the student's transcript until the course has been completed. Non-emergency permission for filing a deferred grade must be requested by the student before the beginning of the final examination period. In an emergency situation, an instructor can approve a deferred grade after the final exam period has started. Under emergency conditions during which the instructor is unavailable, authorization is required from one of the following: the dean of the college in which the candidate is enrolled; the executive director of the Division of Undergraduate Studies if the student is enrolled in that division or is a provisional student; or the campus chancellor of the student's associated Penn State campus.

For additional information please refer to the Deferring a Grade page.

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Academic Integrity

According to Penn State policy G-9: Academic Integrity , an academic integrity violation is “an intentional, unintentional, or attempted violation of course or assessment policies to gain an academic advantage or to advantage or disadvantage another student academically.” Unless your instructor tells you otherwise, you must complete all course work entirely on your own, using only sources that have been permitted by your instructor, and you may not assist other students with papers, quizzes, exams, or other assessments. If your instructor allows you to use ideas, images, or word phrases created by another person (e.g., from Course Hero or Chegg) or by generative technology, such as ChatGPT, you must identify their source. You may not submit false or fabricated information, use the same academic work for credit in multiple courses, or share instructional content. Students with questions about academic integrity should ask their instructor before submitting work.

Students facing allegations of academic misconduct may not drop/withdraw from the affected course unless they are cleared of wrongdoing (see G-9: Academic Integrity ). Attempted drops will be prevented or reversed, and students will be expected to complete course work and meet course deadlines. Students who are found responsible for academic integrity violations face academic outcomes, which can be severe, and put themselves at jeopardy for other outcomes which may include ineligibility for Dean’s List, pass/fail elections, and grade forgiveness. Students may also face consequences from their home/major program and/or The Schreyer Honors College.

How Academic Integrity Violations Are Handled
World Campus students are expected to act with civility and personal integrity; respect other students' dignity, rights, and property; and help create and maintain an environment in which all can succeed through the fruits of their own efforts. An environment of academic integrity is requisite to respect for oneself and others, as well as a civil community.

In cases where academic integrity is questioned, the Policy on Academic Integrity indicates that procedure requires an instructor to inform the student of the allegation. Procedures allow a student to accept or contest a charge. If a student chooses to contest a charge, the case will then be managed by the respective college or campus Academic Integrity Committee. If that committee recommends an administrative sanction (Formal Warning, Conduct Probation, Suspension, Expulsion), the claim will be referred to the Office of Student Accountability and Conflict Response.

All Penn State colleges abide by this Penn State policy, but review procedures may vary by college when academic dishonesty is suspected. Information about Penn State's academic integrity policy and college review procedures is included in the information that students receive upon enrolling in a course. To obtain that information in advance of enrolling in a course, please contact us by going to the Contacts & Help page .