# Calculus lll

### Calculus lll Syllabus

• Course Code: Math 250

Transcript:

Yes. Your transcript will come from the records office at United States University. They are regionally accredited and award semester credits.

Credits: 4 Semester

Transfer: 4 year degree applicable

Enrollment Schedule:

Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the self-paced courses as soon as they are able. Most students finish the lower level courses in 4 - 8 weeks. The upper level math classes, such as Calculus and above, usually take students 3-4 months. (Note: The 30-day extension cannot take your total course time six months beyond the date of enrollment. At the end of the six months, we must post a grade with the university.)

Required Textbook:

Yes, this course requires a textbook.

Proctored Final: Yes

#### Description

Presents a study of differentiation and integration of functions of several variables, parametric curves and surfaces, and the calculus of vector fields. Topics are inclusive of, but not limited to, multivariable vector functions, partial derivatives, directional derivatives, surfaces and hyper surfaces, parametric equations, multiple integrals using several different coordinate systems, line integrals, Green's Theorem, the Divergence Theorem and Stokes Theorem.
Prerequisite: Calculus ll with a grade of C or better.

#### Learning Outcomes

At the conclusion of this course, students should be able to:

1. Understand vector algebra and elementary differential vector calculus.
2. Perform and interpret geometrically partial differentiation and directional derivatives.
3. Find tangent planes and solve minimum/maximum problems with and without constraints.
4. Perform and interpret geometrically multiple integration using multiple coordinate systems.
5. Work with vector fields and vector integral theorems.
6. Demonstrate real-world problem solving skills. Analyze the problem and break it into parts, recognize the concepts applicable to the parts, recognize the relationship between the parts, write the concepts in proper algebraic representations, solve the problem in symbols, interpret the final results.

#### Methods of Evaluation:

Chapter quizzes 15%
Exams (3) 60%
Final 25%
(You must get at least 60% on this final in order to pass the class with a C or better.)

#### Homework Quizzes: 15%

Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and solving problems. Each lesson contains a set of homework problems, and you are required to do all the odd problems for each section. Work out each problem, and then check the solution manual for a detailed solution. Do not continue to the next problem until you understand your mistake. Once you feel comfortable with the homework set, take the homework quiz for that section. The homework quizzes are revised problems from the homework sets. You may take each quiz twice, and the higher of the two scores is used to calculate your quiz grade. Once you take a quiz, figure out what you did wrong on the problems that you missed and then try the quiz again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the test or the final. The struggle to figure out what you did wrong stores the mathematics into your long-term memory, and aids in building abstract thinking.

#### Chapter Tests: 60%

After you have completed a chapter, and understand everything in the lessons, homework sets and quizzes, take the chapter test. The chapter tests are revised problems from the quizzes. You may take each chapter test twice, and the higher of the two scores is used to calculate your chapter test grade. Once you take a chapter test, figure out what you did wrong on the problems that you missed and then try the chapter test again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the final.

#### Proctored Final: 25%

This course go towards a degree which means it must have a proctored final. Your college is accepting this course because it goes through a regionally accredited university, which tells them the class will have a proctored final, and the 60% rule will apply. Your college will not accept a class from a school that is not regionally accredited, because they know these standards won't be met.

The final exam must be proctored at college testing center or a Sylvan Learning Center. A valid driver's license or State ID must be shown at the testing center. An expired license or State ID will not be accepted. Use this link to help you find a college testing center or Sylvan Learning center near your home: Proctored Final

The final exam is a comprehensive final covering all of the chapters of the course. Other than scratch paper, you may view the "Authorized Materials" list for the final exam for each class.

• Students must obtain a 60% or better on the final exam in order to get a C or better in the class.
• Students that obtain a grade of an F on the final can receive at most a D in the class. Students that obtain a D on the final can receive at most a C in the class. Students that obtain a C on the final can receive at most a B in the class.

The 60% rule was set in place to protect the integrity of online math education by requiring a display of competency in exchange for a grade. All schools which are regionally accredited adhere to online standards. Your college is accepting this course because it goes through a regionally accredited university, which tells your college that standards have been met. Your college will not accept a class from a school that is not regionally accredited, because they know the standards won't be met.

#### Assessment:

A 90-100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.
B 80-89 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.
C 70-79 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.
D 60-69 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.
F 0-59 F Quality and quantity of work is below average and not sufficient to progress.

Instructional Process: In this course we will explore mathematical concepts, methods and applications from life issues, business and finance, social and environmental issues. Civic and social issues will be used as problems to apply the subject principles. Using the civic, social, and life related examples will help students understand the subject at a deeper level. After an introduction in each section, problems will be solved that start with the easiest examples and move slowly to the more advanced problems with Student Interactive Problems (SIP) in between. The SIPs are important! They give you a chance to slow down and make sure you understand the material. If you get the problem correct, continue on with the next example. If you get the problem wrong, you will be taken to a page that works out the problem in detail. The SIPs play a large part in storing the topics along with their procedures into your long-term memory. Each homework set contains applications for that lesson. These real life applications create a better understanding of math in our world and how it applies to every day life.

## Chapter 12

Vectors and The Geometry of Space

Lessons Homework
12.1 Three-Dimensional Coordinate System 12.1
12.2 Vectors 12.2
12.3 The Dot Product 12.3
12.4 The Cross Product 12.4
12.5 Lines and Planes in Space 12.5
12.6 Cylinders and Quadric Surfaces 12.6
Chapter 12 Quiz

## Chapter 13

Vector-Valued Functions and Motion in Space

Lessons Homework
13.1 Curves in Space and Their Tangents 13.1
13.2 Integrals of Vector Functions; Projectile Motion 13.2
13.3 Arc Length in Space 13.3
13.4 Curvature and Normal Vectors of a Curve 13.4
13.5 Tangential and Normal Components of Acceleration 13.5
13.6 Velocity and Acceleration in Polar Coordinates 13.6
Chapter 13 Quiz
Exam 1: Chapters 12 - 13

## Chapter 14

Partial Derivatives

Lessons Homework
14.1 Functions of Several Variables 14.1
14.2 Limits and Continuity in Higher Dimensions 14.2
14.3 Partial Derivatives 14.3
14.4 The Chain Rule 14.4
14.5 Directional Derivatives and Gradient Vectors 14.5
14.6 Tangent Planes and Differentials 14.6
14.7 Extreme Values and Saddle Points 14.7
14.8 Lagrange Multipliers 14.8
14.9 Taylor's Formula for Two Variables 14.9
14.10 Partial Derivatives with Constrained Variables 14.10
Chapter 14 Quiz

## Chapter 15

Multiple Integrals

Lessons Homework
15.1 Double and Iterated Integrals over Rectangular Regions 15.1
15.2 Double Integrals over General Regions 15.2
15.3 Area by Double Integration 15.3
15.4 Double Integrals in Polar Form 15.4
15.5 Triple Integrals in Rectangular Coordinates 15.5
15.6 Moments and Center of Mass 15.6
15.7 Triple Integrals in Cylindrical and Spherical Coordinates 15.7
15.8 Substitutions in Multiple Integrals 15.8
Chapter 15 Quiz
Exam 2: Chapters 14 - 15

## Chapter 16

Integration in Vector Fields

Lessons Homework
16.1 Line Integrals 16.1
16.2 Vector Fields and Linea Integrals: Work, Circulation, and Flux 16.2
16.3 Path Independence, Conservative Fields, and Potential Functions 16.3
16.4 Green's Theorem in the Plane 16.4
16.5 Surfaces and Area 16.5
16.6 Surface Integrals 16.6
16.7 Stoke's Theorem 16.7
16.8 The Divergence Theorem and a Unified Theory 16.8
Chapter 16 Quiz

## Chapter 17

Second-Order Differential Equations

Lessons Homework
17.1 Second-Order Linear Equations 17.1
17.2 Nonhomogeneous Linear Equations 17.2
17.3 Applications 17.3
Chapter 17 Quiz
Exam 3: Chapters 16 - 17
 Final for Calculus lll

#### Time on Task:

This course is online and your participation at home is imperative. A minimum of 8 - 10 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirty-day extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.

#### Schedule:

Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able.

 Week Complete Sections 1 12.1 - 12.3 2 12.4 - 12.6 3 13.1 - 13.3 4 13.4 - 13.6 5 14.1 - 14.3 6 14.4 - 14.5 7 14.6 - 14.7 8 14.8 - 14.9 9 14.10 - 15.1 10 15.2 - 15.3 11 15.4 - 15.5 12 15.6 - 15.7 13 15.8 - 16.2 14 16.3 - 16.5 15 16.6 - 16.7 16 16.8 - 17.1 17 17.2 - 17.3 Final Exam

## Conduct Code:

#### Code of Ethics:

Regulations and rules are necessary to implement for classroom as well as online course behavior. Students are expected to practice honesty, integrity and respect at all times. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct. Cheating is forbidden of any form will result in an F in the class.

#### Respectful communications:

When contacting Omega Math or Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, harassing, or bullying via telephone, email, or otherwise will be considered a disrespectful communication and will result in a formal warning.

We reserve the right to refuse service. If we receive multiple disrespectful communications from person(s) representing the student, or the student themselves, the student will be excluded from taking future courses at Westcott Courses/Omega Math.

#### Examples of academic misconduct:

Cheating: Any form of cheating will result in an F in the class. If there is an associated college attached to the course, that college will be notified of the F due to cheating and they will determine any disciplinary action.

Any form of collaboration or use of unauthorized materials during a quiz or an exam is forbidden.

By signing up for a course, you are legally signing a contract that states that the person who is named taking this course is the actual individual doing the course work and all examinations. You also agree that for courses that require proctored testing, that your final will be taken at a college testing center, a Sylvan Learning center, and the individual signed up for this course will be the one taking the test. Failure to do so will be considered a breach of contract.

Other forms of cheating include receiving or providing un-permitted assistance on an exam or quiz; taking an exam for another student; using unauthorized materials during an exam; altering an exam and submitting it for re-grading; failing to stop working on the exam when the time is up; providing false excuses to postpone due dates; fabricating data or references, claiming that Westcott Courses/Omega Math lost your test and or quiz scores. This includes hiring someone to take the tests and quizzes for you.

#### Unauthorized collaboration:

Working with others on graded course work without specific permission of the instructor, including homework assignments, programs, quizzes and tests, is considered a form of cheating.

#### Important Notes:

This syllabus is subject to change and / or revision during the academic year. Students with documented learning disabilities should notify our office upon enrollment, as well as make sure we let the testing center know extended time is permitted. Valid documentation involves educational testing and a diagnosis from a college, licensed clinical psychologist or psychiatrist.

• Course Code: MATU 8005

Transcript:

Yes. Your transcript will come from the records office at Brandman University. They are regionally accredited and award Proffessional Development Units (PDU).

Credits: 4 Professional Development Units (PDU)

Transfer:

Since Professional Development units (PDU) are not academic credits, they typically cannot be used towards graduation of an undergraduate degree. However, the course may be able to be used as a prerequisite at some schools and/or graduate programs. Since graduate programs usually just need to verify the course has been taken, PDUs are usually acceptable. Ask your counselor for pre-approval by sending him/her the Course Description on Brandman's Site. The course can also be used to learn the material and then receive credit at your college using Credit by Examination. (K-12 use)

Enrollment Schedule:

Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the self-paced courses as soon as they are able. Most students finish the lower level courses in 4 - 8 weeks. The upper level math classes, such as Calculus and above, usually take students 3-4 months. (Note: The 30-day extension cannot take your total course time six months beyond the date of enrollment. At the end of the six months, we must post a grade with the university.)

Required Textbook:

Yes, this course requires a textbook.

Proctored Final: No

#### Description

Presents a study of differentiation and integration of functions of several variables, parametric curves and surfaces, and the calculus of vector fields. Topics are inclusive of, but not limited to, multivariable vector functions, partial derivatives, directional derivatives, surfaces and hyper surfaces, parametric equations, multiple integrals using several different coordinate systems, line integrals, Green's Theorem, the Divergence Theorem and Stokes Theorem.
Prerequisite: Calculus ll with a grade of C or better.

#### Learning Outcomes

At the conclusion of this course, students should be able to:

1. Understand vector algebra and elementary differential vector calculus
2. Perform and interpret geometrically partial differentiation and directional derivatives.
3. Find tangent planes and solve minimum/maximum problems with and without constraints.
4. Perform and interpret geometrically multiple integration using multiple coordinate systems.
5. Work with vector fields and vector integral theorems.
6. Demonstrate real-world problem solving skills: analyze the problem and break it into parts, recognize the concepts applicable to the parts, recognize the relationship between the parts, write the concepts in proper algebraic representations, solve the problem in symbols, interpret the final results.

#### Methods of Evaluation:

Homework quizzes 15%
Chapter tests 60%
Final 25%
(You must get at least 60% on this final in order to pass the class with a C or better.)

#### Homework Quizzes: 15%

Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and solving problems. Each lesson contains a set of homework problems, and you are required to do all the odd problems for each section. Work out each problem, and then check the solution manual for a detailed solution. Do not continue to the next problem until you understand your mistake. Once you feel comfortable with the homework set, take the homework quiz for that section. The homework quizzes are revised problems from the homework sets. You may take each quiz twice, and the higher of the two scores is used to calculate your quiz grade. Once you take a quiz, figure out what you did wrong on the problems that you missed and then try the quiz again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the test or the final. The struggle to figure out what you did wrong stores the mathematics into your long-term memory, and aids in building abstract thinking.

#### Chapter Tests: 60%

After you have completed a chapter, and understand everything in the lessons, homework sets and quizzes, take the chapter test. The chapter tests are revised problems from the quizzes. You may take each chapter test twice, and the higher of the two scores is used to calculate your chapter test grade. Once you take a chapter test, figure out what you did wrong on the problems that you missed and then try the chapter test again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the final.

#### Assessment:

A 90-100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.
B 80-89 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.
C 70-79 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.
D 60-69 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.
F 0-59 F Quality and quantity of work is below average and not sufficient to progress.

Instructional Process: In this course we will explore mathematical concepts, methods and applications from life issues, business and finance, social and environmental issues. Civic and social issues will be used as problems to apply the subject principles. Using the civic, social, and life related examples will help students understand the subject at a deeper level. After an introduction in each section, problems will be solved that start with the easiest examples and move slowly to the more advanced problems with Student Interactive Problems (SIP) in between. The SIPs are important! They give you a chance to slow down and make sure you understand the material. If you get the problem correct, continue on with the next example. If you get the problem wrong, you will be taken to a page that works out the problem in detail. The SIPs play a large part in storing the topics along with their procedures into your long-term memory. Each homework set contains applications for that lesson. These real life applications create a better understanding of math in our world and how it applies to every day life.

## Chapter 12

Vectors and The Geometry of Space

Lessons Homework HW Quiz
12.1 Three-Dimensional Coordinate System 12.1 12.1
12.2 Vectors 12.2 12.2
12.3 The Dot Product 12.3 12.3
12.4 The Cross Product 12.4 12.4
12.5 Lines and Planes in Space 12.5 12.5
12.6 Cylinders and Quadric Surfaces 12.6 12.6
Chapter 12 Test

## Chapter 13

Vector-Valued Functions and Motion in Space

Lessons Homework HW Quiz
13.1 Curves in Space and Their Tangents 13.1 13.1
13.2 Integrals of Vector Functions; Projectile Motion 13.2 13.2
13.3 Arc Length in Space 13.3 13.3
13.4 Curvature and Normal Vectors of a Curve 13.4 13.4
13.5 Tangential and Normal Components of Acceleration 13.5 13.5
13.6 Velocity and Acceleration in Polar Coordinates 13.6 13.6
Chapter 13 Test

## Chapter 14

Partial Derivatives

Lessons Homework HW Quiz
14.1 Functions of Several Variables 14.1 14.1
14.2 Limits and Continuity in Higher Dimensions 14.2 14.2
14.3 Partial Derivatives 14.3 14.3
14.4 The Chain Rule 14.4 14.4
14.5 Directional Derivatives and Gradient Vectors 14.5 14.5
14.6 Tangent Planes and Differentials 14.6 14.6
14.7 Extreme Values and Saddle Points 14.7 14.7
14.8 Lagrange Multipliers 14.8 14.8
14.9 Taylor's Formula for Two Variables 14.9 14.9
14.10 Partial Derivatives with Constrained Variables 14.10 14.10
Chapter 14 Test

## Chapter 15

Multiple Integrals

Lessons Homework HW Quiz
15.1 Double and Iterated Integrals over Rectangular Regions 15.1 15.1
15.2 Double Integrals over General Regions 15.2 15.2
15.3 Area by Double Integration 15.3 15.3
15.4 Double Integrals in Polar Form 15.4 15.4
15.5 Triple Integrals in Rectangular Coordinates 15.5 15.5
15.6 Moments and Center of Mass 15.6 15.6
15.7 Triple Integrals in Cylindrical and Spherical Coordinates 15.7 15.7
15.8 Substitutions in Multiple Integrals 15.8 15.8
Chapter 15 Test

## Chapter 16

Integration in Vector Fields

Lessons Homework HW Quiz
16.1 Line Integrals 16.1 16.1
16.2 Vector Fields and Linea Integrals: Work, Circulation, and Flux 16.2 16.2
16.3 Path Independence, Conservative Fields, and Potential Functions 16.3 16.3
16.4 Green's Theorem in the Plane 16.4 16.4
16.5 Surfaces and Area 16.5 16.5
16.6 Surface Integrals 16.6 16.6
16.7 Stoke's Theorem 16.7 16.7
16.8 The Divergence Theorem and a Unified Theory 16.8 16.8
Chapter 16 Test

## Chapter 17

Second-Order Differential Equations

Lessons Homework HW Quiz
17.1 Second-Order Linear Equations 17.1 17.1
17.2 Nonhomogeneous Linear Equations 17.2 17.2
17.3 Applications 17.3 17.3
Chapter 17 Test
 Final for Calculus lll

#### Time on Task:

This course is online and your participation at home is imperative. A minimum of 8 - 10 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirty-day extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.

#### Schedule:

Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able.

 Week Complete Sections 1 12.1 - 12.3 2 12.4 - 12.6 3 13.1 - 13.3 4 13.4 - 13.6 5 14.1 - 14.3 6 14.4 - 14.5 7 14.6 - 14.7 8 14.8 - 14.9 9 14.10 - 15.1 10 15.2 - 15.3 11 15.4 - 15.5 12 15.6 - 15.7 13 15.8 - 16.2 14 16.3 - 16.5 15 16.6 - 16.7 16 16.8 - 17.1 17 17.2 - 17.3 Final Exam

## Conduct Code:

#### Code of Ethics:

Regulations and rules are necessary to implement for classroom as well as online course behavior. Students are expected to practice honesty, integrity and respect at all times. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct. Cheating is forbidden of any form will result in an F in the class.

#### Respectful communications:

When contacting Omega Math or Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, harassing, or bullying via telephone, email, or otherwise will be considered a disrespectful communication and will result in a formal warning.

We reserve the right to refuse service. If we receive multiple disrespectful communications from person(s) representing the student, or the student themselves, the student will be excluded from taking future courses at Westcott Courses/Omega Math.

#### Examples of academic misconduct:

Cheating: Any form of cheating will result in an F in the class. If there is an associated college attached to the course, that college will be notified of the F due to cheating and they will determine any disciplinary action.

Any form of collaboration or use of unauthorized materials during a quiz or an exam is forbidden.

By signing up for a course, you are legally signing a contract that states that the person who is named taking this course is the actual individual doing the course work and all examinations. You also agree that for courses that require proctored testing, that your final will be taken at a college testing center, a Sylvan Learning center, and the individual signed up for this course will be the one taking the test. Failure to do so will be considered a breach of contract.

Other forms of cheating include receiving or providing un-permitted assistance on an exam or quiz; taking an exam for another student; using unauthorized materials during an exam; altering an exam and submitting it for re-grading; failing to stop working on the exam when the time is up; providing false excuses to postpone due dates; fabricating data or references, claiming that Westcott Courses/Omega Math lost your test and or quiz scores. This includes hiring someone to take the tests and quizzes for you.

#### Unauthorized collaboration:

Working with others on graded course work without specific permission of the instructor, including homework assignments, programs, quizzes and tests, is considered a form of cheating.

#### Important Notes:

This syllabus is subject to change and / or revision during the academic year. Students with documented learning disabilities should notify our office upon enrollment, as well as make sure we let the testing center know extended time is permitted. Valid documentation involves educational testing and a diagnosis from a college, licensed clinical psychologist or psychiatrist.

• Course Code: None

Transcript:

A certificate of completion is issued from Omega Math. This course under the non-credit option does not go through one of our partner universities; thus, a transcript is not included with the course.

Credits: 0

Certificate of Completion: Yes

Transfer:

If you would like to take this class for personal enrichment, the non-credit course is the exact same class as the credit course; it is just less expensive since it is not sent through our partner university for credit. If you want to transfer the course to your college, you will need to enroll under the semester credit option. If you would like pre-approval from your school, please send your counselor or registrar's office the link to this page. The non-credit courses can also be used to learn the material and then receive credit at a home college using Credit by Examination. (K-12 use)

Enrollment Schedule:

Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the self-paced courses as soon as they are able. Most students finish the lower level courses in 4 - 8 weeks. The upper level math classes, such as Calculus and above, usually take students 3-4 months. (Note: The 30-day extension cannot take your total course time six months beyond the date of enrollment. At the end of the six months, we must post a grade with the university.)

Required Textbook:

Yes, this course requires a textbook.

Proctored Final: No

#### Description

Presents a study of differentiation and integration of functions of several variables, parametric curves and surfaces, and the calculus of vector fields. Topics are inclusive of, but not limited to, multivariable vector functions, partial derivatives, directional derivatives, surfaces and hyper surfaces, parametric equations, multiple integrals using several different coordinate systems, line integrals, Green's Theorem, the Divergence Theorem and Stokes Theorem.
Prerequisite: Calculus ll with a grade of C or better.

#### Learning Outcomes

At the conclusion of this course, students should be able to:

1. Understand vector algebra and elementary differential vector calculus
2. Perform and interpret geometrically partial differentiation and directional derivatives.
3. Find tangent planes and solve minimum/maximum problems with and without constraints.
4. Perform and interpret geometrically multiple integration using multiple coordinate systems.
5. Work with vector fields and vector integral theorems.
6. Demonstrate real-world problem solving skills: analyze the problem and break it into parts, recognize the concepts applicable to the parts, recognize the relationship between the parts, write the concepts in proper algebraic representations, solve the problem in symbols, interpret the final results.

#### Methods of Evaluation:

Homework quizzes 15%
Chapter tests 60%
Final 25%
(You must get at least 60% on this final in order to pass the class with a C or better.)

#### Homework Quizzes: 15%

Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and solving problems. Each lesson contains a set of homework problems, and you are required to do all the odd problems for each section. Work out each problem, and then check the solution manual for a detailed solution. Do not continue to the next problem until you understand your mistake. Once you feel comfortable with the homework set, take the homework quiz for that section. The homework quizzes are revised problems from the homework sets. You may take each quiz twice, and the higher of the two scores is used to calculate your quiz grade. Once you take a quiz, figure out what you did wrong on the problems that you missed and then try the quiz again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the test or the final. The struggle to figure out what you did wrong stores the mathematics into your long-term memory, and aids in building abstract thinking.

#### Chapter Tests: 60%

After you have completed a chapter, and understand everything in the lessons, homework sets and quizzes, take the chapter test. The chapter tests are revised problems from the quizzes. You may take each chapter test twice, and the higher of the two scores is used to calculate your chapter test grade. Once you take a chapter test, figure out what you did wrong on the problems that you missed and then try the chapter test again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the final.

#### Assessment:

A 90-100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.
B 80-89 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.
C 70-79 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.
D 60-69 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.
F 0-59 F Quality and quantity of work is below average and not sufficient to progress.

Instructional Process: In this course we will explore mathematical concepts, methods and applications from life issues, business and finance, social and environmental issues. Civic and social issues will be used as problems to apply the subject principles. Using the civic, social, and life related examples will help students understand the subject at a deeper level. After an introduction in each section, problems will be solved that start with the easiest examples and move slowly to the more advanced problems with Student Interactive Problems (SIP) in between. The SIPs are important! They give you a chance to slow down and make sure you understand the material. If you get the problem correct, continue on with the next example. If you get the problem wrong, you will be taken to a page that works out the problem in detail. The SIPs play a large part in storing the topics along with their procedures into your long-term memory. Each homework set contains applications for that lesson. These real life applications create a better understanding of math in our world and how it applies to every day life.

## Chapter 12

Vectors and The Geometry of Space

Lessons Homework HW Quiz
12.1 Three-Dimensional Coordinate System 12.1 12.1
12.2 Vectors 12.2 12.2
12.3 The Dot Product 12.3 12.3
12.4 The Cross Product 12.4 12.4
12.5 Lines and Planes in Space 12.5 12.5
12.6 Cylinders and Quadric Surfaces 12.6 12.6
Chapter 12 Test

## Chapter 13

Vector-Valued Functions and Motion in Space

Lessons Homework HW Quiz
13.1 Curves in Space and Their Tangents 13.1 13.1
13.2 Integrals of Vector Functions; Projectile Motion 13.2 13.2
13.3 Arc Length in Space 13.3 13.3
13.4 Curvature and Normal Vectors of a Curve 13.4 13.4
13.5 Tangential and Normal Components of Acceleration 13.5 13.5
13.6 Velocity and Acceleration in Polar Coordinates 13.6 13.6
Chapter 13 Test

## Chapter 14

Partial Derivatives

Lessons Homework HW Quiz
14.1 Functions of Several Variables 14.1 14.1
14.2 Limits and Continuity in Higher Dimensions 14.2 14.2
14.3 Partial Derivatives 14.3 14.3
14.4 The Chain Rule 14.4 14.4
14.5 Directional Derivatives and Gradient Vectors 14.5 14.5
14.6 Tangent Planes and Differentials 14.6 14.6
14.7 Extreme Values and Saddle Points 14.7 14.7
14.8 Lagrange Multipliers 14.8 14.8
14.9 Taylor's Formula for Two Variables 14.9 14.9
14.10 Partial Derivatives with Constrained Variables 14.10 14.10
Chapter 14 Test

## Chapter 15

Multiple Integrals

Lessons Homework HW Quiz
15.1 Double and Iterated Integrals over Rectangular Regions 15.1 15.1
15.2 Double Integrals over General Regions 15.2 15.2
15.3 Area by Double Integration 15.3 15.3
15.4 Double Integrals in Polar Form 15.4 15.4
15.5 Triple Integrals in Rectangular Coordinates 15.5 15.5
15.6 Moments and Center of Mass 15.6 15.6
15.7 Triple Integrals in Cylindrical and Spherical Coordinates 15.7 15.7
15.8 Substitutions in Multiple Integrals 15.8 15.8
Chapter 15 Test

## Chapter 16

Integration in Vector Fields

Lessons Homework HW Quiz
16.1 Line Integrals 16.1 16.1
16.2 Vector Fields and Linea Integrals: Work, Circulation, and Flux 16.2 16.2
16.3 Path Independence, Conservative Fields, and Potential Functions 16.3 16.3
16.4 Green's Theorem in the Plane 16.4 16.4
16.5 Surfaces and Area 16.5 16.5
16.6 Surface Integrals 16.6 16.6
16.7 Stoke's Theorem 16.7 16.7
16.8 The Divergence Theorem and a Unified Theory 16.8 16.8
Chapter 16 Test

## Chapter 17

Second-Order Differential Equations

Lessons Homework HW Quiz
17.1 Second-Order Linear Equations 17.1 17.1
17.2 Nonhomogeneous Linear Equations 17.2 17.2
17.3 Applications 17.3 17.3
Chapter 17 Test
 Final for Calculus lll

#### Time on Task:

This course is online and your participation at home is imperative. A minimum of 8 - 10 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirty-day extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.

#### Schedule:

Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able.

 Week Complete Sections 1 12.1 - 12.3 2 12.4 - 12.6 3 13.1 - 13.3 4 13.4 - 13.6 5 14.1 - 14.3 6 14.4 - 14.5 7 14.6 - 14.7 8 14.8 - 14.9 9 14.10 - 15.1 10 15.2 - 15.3 11 15.4 - 15.5 12 15.6 - 15.7 13 15.8 - 16.2 14 16.3 - 16.5 15 16.6 - 16.7 16 16.8 - 17.1 17 17.2 - 17.3 Final Exam

## Conduct Code:

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