Course of Study Applied Calculus II, Mth 272

Distance Learning Option

• Course Title, Number and Description

• The nature of the course

• Broad goals      

• Specific objectives

• Requirement of communication

• Getting Started in the Course

• Text and Other Instructional Materials

• Areas to be Covered

• Instructional methods

• Grading policy

Course Title, Number and Description, Required Prerequisite Knowledge

Required Prerequisite Knowledge:  To succeed in this course a student must have good mastery of Precalculus and first-semester Calculus.

• Thorough knowledge of linear, quadratic, power, exponential, logarithmic and trigonometric functions and linear combinations, products, quotients and composites of these functions.  Knowledge should include graphing by shifting and stretching transformations as well as characteristics of first and second derivative, and optimization using first- and second-derivative tests.
• Definition and application of limits, continuity and differentiability.
• Calculation of rates of change and application of the concept of rate of change, relationship with integral and derivative.
• Introductory-level knowledge of the definition of an integral and the fundamental theorem of calculus.
• Ability to sketch graphs of derivatives or antiderivatives, given the graph of a function.
• Application of the above to solve a wide variety of theoretical and real-world problems.

The nature of the course

This course is offered via the Internet and via distributed DVD's in an asynchronous mode. The student will receive instructional information and assignments via these modes and will respond to assignments by submitting work through web forms.

The student must have standard access to the Internet and must have the ability to access the content on the DVD's.  The material on the DVD's is accessible using a variety of media players (e.g., Windows Media Player). 

The instructor is available via web forms (to which students will be introduced at the very beginning of the course), and will normally respond by the end of the day following your submission (and more typically on the same day) with answers to properly posed questions, feedback on your efforts, and other information. Exceptions may occur in the event of Internet problems or other technical events. 

Broad goals and Purpose of the Course

The student will

• Use the concepts of the derivative, the differential and differential equations to relate quantities to rates of change for exponential and logarithmic functions.
• Demonstrate the basic techniques for calculating integrals.
• Apply integration to real-world problems related to the study of business, economics, management, and the social and life sciences.
• Extend techniques and applications of integration and differentiation to functions of several variables.

Specific objectives

Each assigned task and problem constitutes a specific objective, which is to complete that problem or task and understand as fully as possible its relationship to the stated goals of the assignment and to other concepts, problems and situations encountered in the course.

1 person in 1000 has the combination of aptitude and learning style capable of doing it otherwise, but for the rest of us, solving problems is the only way to learn the material in this course.

Ability to perform the tasks listed below provide a good foundation for the task.

Each assigned problem constitutes a specific objective, which is to solve the problem and to use it as a means of synthesizing the student's understanding of the subject. Objectives may be partially categorized as follows:

• Understand exponential and logarithmic functions and their derivatives and their applications, and apply the techniques of differentiation to these functions as appropriate.
• Know and be able to apply the rules for integrating power functions, polynomials, exponential functions and logarithmic functions.
• Know and be able to apply the techniques of integration by substitution and integration by parts.
• Be able to apply integration to solving a wide variety of problems involving sums and averages.
• Be able to identify and sketch the various quadric surfaces and relate these surfaces to their defining equations.
• Know how to find values of functions of two or more variables, and to find partial derivatives and tangent lines for such functions.
• Apply the techniques necessary to find relative and absolute maxima and minima for functions of two variables.
• Apply the theory of functions of two variables to determine the equations for linear and quadratic regression lines.
• Evaluate double integrals and change the order of integration for a given double integral.
• Use double integrals to find the areas of region in the plane bounded by given functions.

Assignment-specific objectives are included in the Assignments Table for the course.  Organized by modules, those objectives are as follows:

Requirement of communication

Regular communication is required of the student. This includes turning in assignments in a timely fashion and responding in a timely manner to feedback on these assignments. Any deviation of more than three days from the chosen schedule of the course must be approved in advance by the instructor. Exceptions will of course be made in the event of documented illness or other unexpected emergencies, but the instructor should be informed of such situations within a reasonable time of occurrence.

After registering for the course you will get an email, sent to your VCCS email account, with instructions for Orientation and Startup.  This process will constitute appropriately the first week's assignments for your course (about the first half of the week during the shorter summer term), and will show you the basic navigation of the website including how to communicate, submit work, locate assignments and due dates, and more.

Text and Other Instructional Materials

The text is specified in Textbook Information, which the student will have encountered prior to arriving at this page.  Any student who has not noted Textbook Information is advised to review all information to be sure no other essential details have been missed.

Areas to be Covered

Units to be covered:

Chapters 6-11 inclusive, plus supplementary material posted by instructor.

Chapter Topics:

Chapter 6:  Constructing Antiderivatives

Chapter 7:  Integration

Chapter 8:  Using the Integral

Chapter 9:  Series

Chapter 10:  Approximating Functions

Chapter 12: Differential Equations

Specific information regarding assignments and areas covered is included on the homepage.

Instructional methods

Students will complete and submit the assignments specified on the homepage.

The instructor will respond in a timely fashion to any work submitted, making suggestions where improvement is needed and posing questions designed to enhance the student's learning experience. The student will be required to respond to all critiques, except those designated otherwise.

Questions posed by students and the instructor's responses will be posted to a site, specified in at the beginning of the course, for the student's review.

Students may on occasion be asked to critique work done by other students.  Full student anonymity will be preserved, with no reference  to the identity of any party in this exchange.

The instructor is available via web forms (to which you will be introduced at the very beginning of the course), and will normally respond by the end of the day following your submission (and more typically on the same day) with answers to properly posed questions, feedback on your efforts, and other information. Exceptions may occur in the event of Internet problems or other technical events. 

Use of email:  Prior to registration and receipt of initial instructions students my use Email to communicate with the instructor.  However email is much less reliable than web forms, and after registration and receipt of initial instructions anything sent through email should first be sent using the appropriate form.

Grading policy

Three tests and a final exam will be administered.  The final examination will given the same weight as a regular test; however, if it is to the advantage of the student this final examination will be given double the weight of a regular test. 

A student's portfolio, consisting of instructor responses to assigned work and/or daily quizzes, will at the end of the term be assigned a grade.  A student who completes all assigned work in the prescribed manner can expect to make an A on this aspect of the course. The average of grades assigned on this work will count as 1/4 of a test grade. If this average is higher than the average on other tests, it will be counted as 1/2 of a test grade.

Raw test scores will be normalized to the following scale, according to the difficulty of the test, as specified in advance of each test by the instructor:

A: 90 - 100

B: 80 - 90

C: 70 - 80

D: 60 - 70

F: Less than 60.

The final grade will be a weighted average according to the above guidelines. A summary of the weighting is as follows:

Test #1:  Weight .5 or 1.0, to the advantage of the student

Test #2: Weight 1.0

Test #3: Weight 1.0

Comprehensive Final Exam: Weight 1.0 or 2.0, to the advantage of the student

Assignment/Quiz Grade Average: Weight .25 or .5, to the advantage of the student.

The table below summarized the calculation of course grades:

assessment	weighting	contribution to total score
test 1	1	test score * 1
test 2	1	test score * 1
test 3	1	test score * 1
test 4	1	test score * 1
portfolio	1/4 <= p_weight <= 1/2	portfolio score * p_weight
	total of weightings	total of contributions
Final average = total of contributions / total of weightings

Criteria for Grading of Tests:

Tests will consist of problems designed to measure the level of your achievement of the course goals. 

Each problem is graded on a 10-point scale, with the following guidelines:

• 10 points will be earned for a correct solution which documents the details of the entire solution process, including all reasoning.
• At least 7 points will be earned for a solution which follows a valid reasoning process and is substantially correct, but with some errors in detail.
• 5 points will be given for any reasonable attempt at a solution.
• Some credit will be given for any attempt relevant to the solution.
• 0 points will be earned for any solution, whether correct or not, which does not document the reasoning and the solution process.
• If a problem consists of two or more distinct parts, credit will be pro-rated accordingly.