Week 5

Designing my Online Individual Project

Online MAT 1A (1st semester Calculus) course
I would like to design an online MAT 1A Calculus course at Riverside Community College.  We do not have any transferable math courses offered and taught online at RCC currently, so this design will be an original.  This course will be a 4 unit course that is transferable to the CSU and UC systems in place of the 1st part of the Calculus series.  The prerequisite for this course will be MAT 10 (Pre-Calculus) or placement into this course through the assessment exam.

The class will cover functions, limits, continuity, differentiation, inverse functions, applications of the derivative including maximum and minimum problems along with very basic integration.  Applications with the graphing calculator will also be explored in this course as well.  If the students are unable to purchase a graphing calculator, there are websites that allow the students to use a free version of an online graphing calculator.
http://www.coolmath.com/graphit/index.html

Calculus is typically taught through class lectures, discussions, and demonstrations of problems on the whiteboard.  Students in the class are given drill and practice problems in class in which everybody  should be arriving at the same answers.  Therefore, the material and content of the course will have more convergent answers, so the instructor and the students should be arriving at the same conclusions.

The main concern or problem in the first semester of calculus is defining the formal definition of a limit of a function and how to prove that the limit does actually exist.  This is done using the epsilon-delta definition and the students will go crazy over how to do this.  Another difficult section would be the application of the derivative functions in everyday life like with related rates and optimization problems.  One way to help clarify these topics might be to have some links to videos or animations that might help explain the problems rather than see the step by step process on the computer.
Here is an example of related rates:  
related rate
Another example using a U-tube video
related rate 2
Here is an example of optimization problems:
optimization 1

This online course should serve students who are working during the day when most of our calculus classes are offered and also allow students the freedom to take this class in a distant education format.  Another situation that might also be solved is the problem of conflicting Calculus with other science classes that require Calculus as a prerequisite or co-requisite to the course such as Chemistry and Physics.  Every semester we have problems deciding when we are going to offer our Calculus classes because we know that a majority of the students taking this course will also be enrolled in a science class as well.  The science courses have labs that do not make it feasible to offer those classes online, so the best solution would be to offer the Calculus class online.

Instructor Characteristics
The two instructors that I would choose for this online MAT 1A class would be either Sheila Pisa or Kathleen Saxon.  Both of these instructors have taught the MAT 1A class numerous times in the traditional format.  Saxon has the most experience with online education, teaching at least 2-3 online/hybrid courses every semester.  Pisa is one semester shy of completing her ED in Instructional Technology from Pepperdine University and has the most experience of anybody at RCC in the creation of new online classes from scratch.

Both of these instructors would provide excellent instructor and feedback to their students.  They both have similar teaching styles with demonstration, practice, drill and evaluation.  The main reason I would choose either of these instructors is because of their love for the use of technology in the classroom and their experience with online learning and education.  Both of these instructors have used CMS other than MyMathLab and are familiar with Camtasia so they can create their own videos to post online if needed.

Student Characteristics
The students in this class should be self-motivated.  My first thoughts would be that if the students are willing to take an online Calculus course, then they should be ready to work and learn.  They understand the importance of learning the material presented and how this knowledge will not only be useful this semester but in classes they plan to take in the future.  I would assume that most of the students would have experience with technology beyond just simple web browsing and email.  Perhaps some of the students might even be some of our online tutors in our online mathlab on campus.  Therefore, they would be experienced in using programs such as WebCT and MyMathLab.

For the student to student interaction, I would think that blogs or a discussion board might be the best solution.  That way all of the students can read other students postings and make comments to questions or solutions that are presented.

Course Goals
The course goals for this online Calculus class would be the same as the traditional course.
Students should be able to:

1. Calculate the limit of a function.
2. Determine the continuity of a function.
3. Find the derivatives of algebraic and transcendental functions.
4. Solve related rate problems.
5. Apply the absolute and relative extrema to curve sketching and optimization problems.
6. Use Newton's method to approximate the roots of a function.
7. Evaluate a definite integral using Riemann sums.

Course Objectives
These are the course objectives for the goals stated above.


      1.  Calculate the limit of a function.
           1.1  Given a transcendental function, correctly identify the limit of the function.
           1.1.1  The student will be able to calculate the limit of transcendental functions using the limit rules.
           1.2  Find the limit of linear and non-linear functions as the value approaches infinity.
           1.2.1  The student will be able to calculate the limit of linear and non-linear functions as the value approaches infinity using the limit rules.
           1.3  Find the limit of functions using the formal definition of the limit of a function.
           1.3.1  The student will be able to write out the formal definition using the epsilon-delta definition, thus proving that the limit exists and is equal to the calculated value.
           1.4  Find the limit of functions from the graph of the function.
           1.4.1  The student will be able to examine a graph and determine the value of the limit at any point on the graph.

      2.  Determine the continuity of a function.
           2.1  Determine and declare the 3 requirements for the formal definition of continuity of a function.
           2.1.1  The student will identify that the value of the function must exist at the point.
           2.1.2  The student will calculate the value of the limit using the limit rules at the point.
           2.1.3  The student will compare the results from the value of the function and the value of the limit of the function at the point in question and show that the two results are equal to each other, thus proving that the function is continuous at that point.

       3.  Find the derivatives of algebraic and transcendental functions.
            3.1  Define the derivative rules for algebraic functions
            3.1.1  The student will identify the power rule, sum, difference product and quotient rules for differentiation.
            3.1.2  The student will calculate the derivative of algebraic functions using the product and quotient rules of differentiation.
            3.2  The student will identify the derivative rules for transcendental functions.
            3.2.1  The student will calculate the derivative of transcendental functions using the product and quotient rules of differentiation.

         4.  Solve related rate problems.
             4.1  Identify the characteristic of the basic related rate problem.
             4.1.1  The student will identify the two rates and describe how they are related to each other.
             4.1.2  The student will calculate the missing component in the related rate problem by solving the formula for the missing term.

          5.  Apply the absolute and relative extrema to curve sketching and optimization problems.
              5.1  Describe the characteristics and differences between absolute and relative extrema.
              5.1.1  The student will calculate the absolute extrema of a continuous function on a closed interval.
              5.1.2  The student will calculate the relative extrema of a continuous function on a closed interval.
              5.2  Determine the characteristics of a typical optimization problem.
              5.2.1  Identify the closed intervals for the optimization probelm.
              5.2.2  Find the derivative of the function that describes the optimization problem.
              5.2.3  Correctly identify extraneous solutions and disregard those as possible solutions.

          6.  Use Newton's method to approximate the roots of a function.
              6.1  Understand the process of how Newton's method approximates the zero value of a function.
              6.1.1  The student will graph the function and graph the tangent lines approximating the zero values and their value approaches the target value.
              6.1.2  The student will calculate the approximate value of the target value by using Newton's formula and see how close this approximation is to the true value.

          7.  Evaluate a definite intergral using Riemann sums.
              7.1  Define the fundamental theorem of calculus.
              7.1.1  Use the fundamental theorem of calculus to find the area under a curve.
              7.2  Present application problems of using the definite interval of Riemann sums.
              7.2.1  The students will find the area under a curve.
              7.2.2  The students will apply the Mean Value Theorem to find the value of the definite integral.

Interactions
For the interactions in this course, I will focus on the first 4 course objectives.  They are as follows:

1. Calculate the limit of a function.
2. Determine the continuity of a function.
3. Find the derivatives of algebraic and transcendental functions.
4. Solve related rate problems.

 Calculate the limit of a function.
Student-Content Interaction:

• Student will read the mathematical definition of the limit of a function.
• Student will watch instructional videos of how the limit of a function is found using calculus.

Student-Instructor Interaction:

• Instructor will provide sample problems in which the students will download from the website.
• Student will work and solve limit problems.  Email the solutions only back to the instructor before deadline.
• If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes.

Student-Student Interaction:

• Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.
• Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.

Determine the continuity of a function.
Student-Content Interaction:

• Students will read the requirements for a continuous function. 
  

 Student-Instructor Interaction:

• The instructor will post various functions and the student will determine whether the functions are continuous or not continuous.  If the function is not continuous, the student must state why this is so.
• The instructor will post graphs of functions and the students will determine whether the functions are continuous or not continuous.  If the graph is not continuous, the student must state why this is so.

Student-Student Interaction:

• Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.
•  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.

Find the derivatives of algebraic and transcendental functions.
Student-Content Interaction:

• Students will read and learn the definition of the derivative of an algebraic and transcendental function.  
• Students will be able to prove the formal definition of the derivative of a function. 
  

Student-Instructor Interaction:

• The instructor will post sample functions in which the students will download from the website and work to find the derivative function.  If the derivative cannot be found, the student must state why.
• The students will email the solutions to the derivatives back to the instructor.
• If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes.

Student-Student Interaction:

• Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.
•  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.

Solve related rate problems.
Student-Content Interaction:

• Students will read and watch videos describing the characteristics of related rate problems.

Student-Instructor Interaction:

• The instructor will post sample related rate problems for the students to download from the website.  The students will identify the two rates and present how the rates are related to each other.
• The students will proceed to solve the problems and email the solutions back to the instructor. 
• If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes.

Student-Student Interaction:

• Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.
•  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.

Course Level Design

Session  1 Introduction to the class. Review of the syllabus. Discuss the proctored exams.	Student-Content:  Podcast presentation of the instructor’s background and what is expected from the class.  The presentation and the syllabus will describe in detail what exactly is expected from the first week. Student-Instructor:  Students will email the instructor their preferred email address that they check most frequently.  The students will create a blog site and email the instructor the address for their site.  Student will also need to let the instructor know if they cannot make it to the mathlab for their proctored exams.  If not, the students must let the instructor know who their proctor will be and provide an email address for the proctor. Student-Student:  Students will create a blog site The students will describe a little bit of themselves and tell why they are taking this class and what they hope to learn from this class.
Session  2 Review of Pre-Calculus material. Introduction to limits. 1.       Calculate the limit of a function. 1.1  Given a transcendental function, correctly identify the limit of the function.	Student-Content:  Podcast presentation of how the limit is found.  Also, the textbook’s description of the definition of the limit of function. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Student will work and solve limit problems.  Email the solutions  back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  3 1.       Calculate the limit of a function.          1.1  Given a transcendental function,      correctly identify the limit of the function.            1.1.1  The student will be able to calculate the limit of transcendental functions using the limit rules.            1.2  Find the limit of linear and non-linear functions as the value approaches infinity.            1.2.1  The student will be able to calculate the limit of linear and non-linear functions as the value approaches infinity using the limit rules.	Student-Content:  Podcast presentation of how the limit is found.  Also the textbook’s description of the definition of the limit, how the rules apply and how to find the limit as the function values approach infinity or negative infinity. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Student will work and solve limit problems.  Email the solutions  back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  4 1.       Calculate the limit of a function.           1.3  Find the limit of functions using the formal definition of the limit of a function.            1.3.1  The student will be able to write out the formal definition using the epsilon-delta definition, thus proving that the limit exists and is equal to the calculated value.            1.4  Find the limit of functions from the graph of the function.            1.4.1  The student will be able to examine a graph and determine the value of the limit at any point on the graph.	Student-Content:  Podcast presentation of how the limit is found using the formal definition of epsilon delta.  Also the textbook’s description of the definition of the limit, how to determine the limit from the graph of a function and how to draw the graph of a function given the equation. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Student will work and solve limit problems and write out the formal definition of proofs to limit functions.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  5 2.       Determine the continuity of a function.            2.1  Determine and declare the 3 requirements for the formal definition of continuity of a function.            2.1.1  The student will identify that the value of the function must exist at the point.            2.1.2  The student will calculate the value of the limit using the limit rules at the point.            2.1.3  The student will compare the results from the value of the function and the value of the limit of the function at the point in question and show that the two results are equal to each other, thus proving that the function is continuous at that point.	Student-Content:  Podcast presentation of how continuity is determined.  Also the textbook’s description of the 3 requirements before a function is determined to be continuous. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Student will work on continuity of function problems and determine whether given functions are continuous or not.  If not, the students must provide reason and which requirement is not satisfied for the conditions.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  6   3.  Find the derivatives of algebraic and transcendental functions.             3.1  Define the derivative rules for algebraic functions             3.1.1  The student will identify the power rule, sum, difference product and quotient rules for differentiation.	Student-Content:  Podcast presentation of how derivatives of functions are determined.  Also the textbook’s description of the rules for differentiation of functions. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will work on differentiation of functions using the rules presented in the podcast.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  7 3.  Find the derivatives of algebraic and transcendental functions.            3.1.2  The student will calculate the derivative of algebraic functions using the product and quotient rules of differentiation.             3.2  The student will identify the derivative rules for transcendental functions.             3.2.1  The student will calculate the derivative of transcendental functions using the product and quotient rules of differentiation.	Student-Content:  Podcast presentation of how derivatives of functions are determined.  Also the textbook’s description of the rules for differentiation of functions. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will work on differentiation of functions using the rules presented in the podcast.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  8 4.  Solve related rate problems.              4.1  Identify the characteristic of the basic related rate problem. Midterm Exam week covering the first 7 sessions. Students will either take the midterm in the mathlab or find an approved proctor for their exam.	Student-Content:  Podcast presentation of the basic characteristics of related rate problems.  Review some examples of the typical basic types of related rate problems often found in Calculus.   Also review the textbook’s examples of related rate problems and the characteristics that all related rate problems have in common. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will identify the basic rates, how they are related and which formula they should differentiate.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  9 4.  Solve related rate problems.              4.1.1  The student will identify the two rates and describe how they are related to each other.                4.1.2  The student will calculate the missing component in the related rate problem by solving the formula for the missing term.	Student-Content:  Podcast presentation of the basic characteristics of related rate problems.  Review some examples of the typical basic types of related rate problems often found in Calculus.   Also review the textbook’s examples of related rate problems and the characteristics that all related rate problems have in common. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will identify the basic rates, how they are related and which formula they should differentiate.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  10 5.  Apply the absolute and relative extrema to curve sketching and optimization problems.               5.1  Describe the characteristics and differences between absolute and relative extrema.               5.1.1  The student will calculate the absolute extrema of a continuous function on a closed interval.               5.1.2  The student will calculate the relative extrema of a continuous function on a closed interval.	Student-Content:  Podcast presentation of the basic characteristics of absolute and relative extrema problems.  Discuss the differences between absolute and relative extrema.  Define a closed interval.  Also review the textbook’s examples of absolute and relative extrema problems. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will identify absolute and relative extrema characteristics.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  11 5.  Apply the absolute and relative extrema to curve sketching and optimization problems.               5.2  Determine the characteristics of a typical optimization problem.               5.2.1  Identify the closed intervals for the optimization probelm.               5.2.2  Find the derivative of the function that describes the optimization problem.               5.2.3  Correctly identify extraneous solutions and disregard those as possible solutions.	Student-Content:  Podcast presentation of the basic characteristics of optimization problems.  Discuss the typical types of optimization problems and the importance of optimization in everyday life.  Also review the textbook’s examples of optimization problems. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will solve optimization problems.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  12 6.  Use Newton's method to approximate the roots of a function.                 6.1  Understand the process of how Newton's method approximates the zero value of a function.	Student-Content:  Podcast presentation of the basic characteristics of Newton’s Method.  Discuss the purpose and show some examples of how this method can be used to solve calculus related problems.  Also review the textbook’s examples of Newton’s Method problems. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will solve Newton’s Method problems.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  13 6.  Use Newton's method to approximate the roots of a function.              6.1.1  The student will graph the function and graph the tangent lines approximating the zero values and their value approaches the target value.               6.1.2  The student will calculate the approximate value of the target value by using Newton's formula and see how close this approximation is to the true value.	Student-Content:  Podcast presentation of the basic characteristics of Newton’s Method.  Show the graphing method of how Newton’s Method would provide an approximation for the true value.  Show some examples of how this method can be used to solve calculus related problems.  Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will solve Newton’s Method problems by graphing.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  14 7.  Evaluate a definite intergral using Riemann sums.               7.1  Define the fundamental theorem of calculus.               7.1.1  Use the fundamental theorem of calculus to find the area under a curve.	Student-Content:  Podcast presentation of the basic characteristics of the definite integral.  Define the fundamental theorem of calculus and show how this theorem can be used to find the area under a curve.  Also review the textbook’s examples of Riemann sums. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will use the fundamental theorem of calculus to solve problems.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  15 7.  Evaluate a definite intergral using Riemann sums.               7.2  Present application problems of using the definite interval of Riemann sums.               7.2.1  The students will find the area under a curve.               7.2.2  The students will apply the Mean Value Theorem to find the value of the definite integral.	Student-Content:  Podcast presentation of the basic characteristics of the definite integral.  Define the fundamental theorem of calculus and show how this theorem can be used to find the area under a curve.  Also review the textbook’s examples of Riemann sums. Student-Instructor:  Instructor will provide sample problems in which the students will download from the website.  Students will use the fundamental theorem of calculus to solve problems.  Email the solutions back to the instructor before deadline.  If any of the solutions are not correct, the instructor will notify the student and the student will have until the deadline to correct any mistakes. Student-Student:  Students may interact and ask other students in the class for help with homework problems that they missed.  All interaction will take place through a discussion board or blog so that the instructor can see that a process of solving is followed and not just giving out the answers.  Each solution that students are able to provide for the entire class will count as a participation point.  Therefore, it will benefit the students to work on the assignments as early as possible so they can verify their solutions are correct.
Session  16 Final exam covering all 15 sessions. Students will either take the final exam in the mathlab or find an approved proctor for their exam.	Student-Content:  Final exam will either be provided in the mathlab computer by protected passwords on MyMathLab or the approved proctor will type in the password for the student. Student-Instructor:  Once the student has completed the exam, a score will be assigned and that score will be sent electronically to the instructor for grades. Student-Student:  none.