# Calculus ll

Presents a continuing study of integration techniques, applications to physics and engineering, improper integrals, transcendental functions, first order differential equations, series and sequences, parametric equations and polar coordinates. Each topic is taught geometrically, numerically, and algebraically.
Prerequisite: Calculus l with a grade of C or better.

## Chapter 5

Integration

Lessons Homework
5.1   Area and Estimating with Finite Sums 5.1
5.2   Sigma Notation and Limits of Finite Sums 5.2
5.3   The Definite Integral 5.3
5.4   The Fundamental Theorem of Calculus 5.4
5.5   Indefinite Integrals and the Substitution Method 5.5
5.6   Substitution and Area Between Curves 5.6
Chapter 5 Quiz

## Chapter 6

Applications of Definite Integrals

Lessons Homework
6.1   Volumes Using Cross-Sections 6.1
6.2   Volumes Using Cylindrical Shells 6.2
6.3   Arc Length 6.3
6.4   Areas of Surfaces of Revolution 6.4
6.5   Work and Fluid Forces 6.5
6.6   Moments and Centers of Mass 6.6
Chapter 6 Quiz
Chapter 5-6 Exam

## Chapter 7

Transcendental Functions

Lessons Homework
7.1   Inverse Functions and Their Derivatives 7.1
7.2   Natural Logarithms 7.2
7.3   Exponential Functions 7.3
7.4   Exponential Change and Separable Differential Equations 7.4
7.5   Indeterminate Forms and L'Hopital's Rule 7.5
7.6   Inverse Trigonometric Functions 7.6
7.7   Hyperbolic Functions 7.7
7.8   Relative Rates of Growth 7.8
Chapter 7 Quiz

## Chapter 8

Techniques of Integration

Lessons Homework
8.1   Integration by Parts 8.1
8.2   Trigonometric Integrals 8.2
8.3   Trigonometric Substitution 8.3
8.4   Integration of Rational Functions by Partial Fractions 8.4
8.5   Integral Tables and Computer Algebra Systems 8.5
8.6   Numerical Integration 8.6
8.7   Improper Integrals 8.7
Chapter 8 Quiz
Chapter 7-8 Exam

## Chapter 9

First Order Differential Equations

Lessons Homework
9.1   Solutions, Slope-Fields, and Euler's Method 9.1
9.2   First-Order Linear Equations 9.2
9.3   Applications 9.3
Chapter 9 Quiz

## Chapter 10

Infinite Series and Sequences

Lessons Homework
10.1   Sequences 10.1
10.2   Infinite Series 10.2
10.3   The Integral Test 10.3
10.4   Comparison Test 10.4
10.5   The Ratio and Root Test 10.5
10.6   Alternating Series, Conditional and Absolute Convergence 10.6
10.7   Power Series 10.7
10.8   Taylor and Maclaurin Series 10.8
10.9   Convergence of Taylor Series 10.9
10.10   The Binomial Series and Applications of Taylor Series 10.10
Chapter 10 Quiz
Chapter 9-10.6 Exam

## Chapter 11

Parametric Equations and Polar Coordinates

Lessons Homework
11.1   Parametrizations of Plane Curves 11.1
11.2   Calculus with Parametric Curves 11.2
11.3   Polar Coordinates 11.3
11.4   Graphing in Polar Coordinates 11.4
11.5   Areas and Lengths in Polar Coordinates 11.5
11.6   Conic Sections 11.6
11.7   Conics in Polar Coordinates 11.7
Chapter 11 Quiz
Chapter 10.7-11 Exam
 Final for Calculus ll (Paper Based Test)

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 5.1 - 5.3 2 5.4 - 5.6 3 6.1 - 6.3 4 6.4 - 6.6 5 7.1 - 7.3 6 7.4 - 7.6 7 7.7 - 7.8 8 8.1 - 8.3 9 8.4 - 8.6 10 8.7 - 9.2 11 9.3 - 10.2 12 10.3 - 10.4 13 10.5 - 10.6 14 10.7 - 10.9 15 10.10 - 11.1 16 11.2 - 11.4 17 11.5 - 11.7 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.

#### Grading information and proctored final policies:

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 8004

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 continuing study of integration techniques, applications to physics and engineering, improper integrals, transcendental functions, first order differential equations, series and sequences, parametric equations and polar coordinates. Each topic is taught geometrically, numerically, and algebraically.
Prerequisite: Calculus l with a grade of C or better.

#### Learning Outcomes

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

1. Integrate a wide variety of elementary functions using one of many (or a combination of) several integration techniques.
2. Understand some of the applications of integration, including areas, volumes, work, arc length, surface area, and center of mass.
3. Understand parametric equations, polar coordinates, and their applications.
4. Understand the difference between a sequence and series and be able to test for convergence.
5. Calculate power series and Taylor series.
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 5

Integration

Lessons Homework HW Quiz
5.1   Area and Estimating with Finite Sums 5.1 5.1
5.2   Sigma Notation and Limits of Finite Sums 5.2 5.2
5.3   The Definite Integral 5.3 5.3
5.4   The Fundamental Theorem of Calculus 5.4 5.4
5.5   Indefinite Integrals and the Substitution Method 5.5 5.5
5.6   Substitution and Area Between Curves 5.6 5.6
Chapter 5 Test

## Chapter 6

Applications of Definite Integrals

Lessons Homework HW Quiz
6.1   Volumes Using Cross-Sections 6.1 6.1
6.2   Volumes Using Cylindrical Shells 6.2 6.2
6.3   Arc Length 6.3 6.3
6.4   Areas of Surfaces of Revolution 6.4 6.4
6.5   Work and Fluid Forces 6.5 6.5
6.6   Moments and Centers of Mass 6.6 6.6
Chapter 6 Test

## Chapter 7

Transcendental Functions

Lessons Homework HW Quiz
7.1   Inverse Functions and Their Derivatives 7.1 7.1
7.2   Natural Logarithms 7.2 7.2
7.3   Exponential Functions 7.3 7.3
7.4   Exponential Change and Separable Differential Equations 7.4 7.4
7.5   Indeterminate Forms and L'Hopital's Rule 7.5 7.5
7.6   Inverse Trigonometric Functions 7.6 7.6
7.7   Hyperbolic Functions 7.7 7.7
7.8   Relative Rates of Growth 7.8 7.8
Chapter 7 Test

## Chapter 8

Techniques of Integration

Lessons Homework HW Quiz
8.1   Integration by Parts 8.1 8.1
8.2   Trigonometric Integrals 8.2 8.2
8.3   Trigonometric Substitution 8.3 8.3
8.4   Integration of Rational Functions by Partial Fractions 8.4 8.4
8.5   Integral Tables and Computer Algebra Systems 8.5 8.5
8.6   Numerical Integration 8.6 8.6
8.7   Improper Integrals 8.7 8.7
Chapter 8 Test

## Chapter 9

First Order Differential Equations

Lessons Homework HW Quiz
9.1   Solutions, Slope-Fields, and Euler's Method 9.1 9.1
9.2   First-Order Linear Equations 9.2 9.2
9.3   Applications 9.3 9.3
Chapter 9 Test

## Chapter 10

Infinite Series and Sequences

Lessons Homework HW Quiz
10.1   Sequences 10.1 10.1
10.2   Infinite Series 10.2 10.2
10.3   The Integral Test 10.3 10.3
10.4   Comparison Test 10.4 10.4
10.5   The Ratio and Root Test 10.5 10.5
10.6   Alternating Series, Conditional and Absolute Convergence 10.6 10.6
10.7   Power Series 10.7 10.7
10.8   Taylor and Maclaurin Series 10.8 10.8
10.9   Convergence of Taylor Series 10.9 10.9
10.10   The Binomial Series and Applications of Taylor Series 10.10 10.10
Chapter 10 Test

## Chapter 11

Parametric Equations and Polar Coordinates

Lessons Homework HW Quiz
11.1   Parametrizations of Plane Curves 11.1 11.1
11.2   Calculus with Parametric Curves 11.2 11.2
11.3   Polar Coordinates 11.3 11.3
11.4   Graphing in Polar Coordinates 11.4 11.4
11.5   Areas and Lengths in Polar Coordinates 11.5 11.5
11.6   Conic Sections 11.6 11.6
11.7   Conics in Polar Coordinates 11.7 11.7
Chapter 11 Test
 Final for Calculus ll

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 5.1 - 5.3 2 5.4 - 5.6 3 6.1 - 6.3 4 6.4 - 6.6 5 7.1 - 7.3 6 7.4 - 7.6 7 7.7 - 7.8 8 8.1 - 8.3 9 8.4 - 8.6 10 8.7 - 9.2 11 9.3 - 10.2 12 10.3 - 10.4 13 10.5 - 10.6 14 10.7 - 10.9 15 10.10 - 11.1 16 11.2 - 11.4 17 11.5 - 11.7 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.

#### Grading information and proctored final policies:

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 continuing study of integration techniques, applications to physics and engineering, improper integrals, transcendental functions, first order differential equations, series and sequences, parametric equations and polar coordinates. Each topic is taught geometrically, numerically, and algebraically.
Prerequisite: Calculus l with a grade of C or better.

#### Learning Outcomes

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

1. Integrate a wide variety of elementary functions using one of many (or a combination of) several integration techniques.
2. Understand some of the applications of integration, including areas, volumes, work, arc length, surface area, and center of mass.
3. Understand parametric equations, polar coordinates, and their applications.
4. Understand the difference between a sequence and series and be able to test for convergence.
5. Calculate power series and Taylor series.
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 5

Integration

Lessons Homework HW Quiz
5.1   Area and Estimating with Finite Sums 5.1 5.1
5.2   Sigma Notation and Limits of Finite Sums 5.2 5.2
5.3   The Definite Integral 5.3 5.3
5.4   The Fundamental Theorem of Calculus 5.4 5.4
5.5   Indefinite Integrals and the Substitution Method 5.5 5.5
5.6   Substitution and Area Between Curves 5.6 5.6
Chapter 5 Test

## Chapter 6

Applications of Definite Integrals

Lessons Homework HW Quiz
6.1   Volumes Using Cross-Sections 6.1 6.1
6.2   Volumes Using Cylindrical Shells 6.2 6.2
6.3   Arc Length 6.3 6.3
6.4   Areas of Surfaces of Revolution 6.4 6.4
6.5   Work and Fluid Forces 6.5 6.5
6.6   Moments and Centers of Mass 6.6 6.6
Chapter 6 Test

## Chapter 7

Transcendental Functions

Lessons Homework HW Quiz
7.1   Inverse Functions and Their Derivatives 7.1 7.1
7.2   Natural Logarithms 7.2 7.2
7.3   Exponential Functions 7.3 7.3
7.4   Exponential Change and Separable Differential Equations 7.4 7.4
7.5   Indeterminate Forms and L'Hopital's Rule 7.5 7.5
7.6   Inverse Trigonometric Functions 7.6 7.6
7.7   Hyperbolic Functions 7.7 7.7
7.8   Relative Rates of Growth 7.8 7.8
Chapter 7 Test

## Chapter 8

Techniques of Integration

Lessons Homework HW Quiz
8.1   Integration by Parts 8.1 8.1
8.2   Trigonometric Integrals 8.2 8.2
8.3   Trigonometric Substitution 8.3 8.3
8.4   Integration of Rational Functions by Partial Fractions 8.4 8.4
8.5   Integral Tables and Computer Algebra Systems 8.5 8.5
8.6   Numerical Integration 8.6 8.6
8.7   Improper Integrals 8.7 8.7
Chapter 8 Test

## Chapter 9

First Order Differential Equations

Lessons Homework HW Quiz
9.1   Solutions, Slope-Fields, and Euler's Method 9.1 9.1
9.2   First-Order Linear Equations 9.2 9.2
9.3   Applications 9.3 9.3
Chapter 9 Test

## Chapter 10

Infinite Series and Sequences

Lessons Homework HW Quiz
10.1   Sequences 10.1 10.1
10.2   Infinite Series 10.2 10.2
10.3   The Integral Test 10.3 10.3
10.4   Comparison Test 10.4 10.4
10.5   The Ratio and Root Test 10.5 10.5
10.6   Alternating Series, Conditional and Absolute Convergence 10.6 10.6
10.7   Power Series 10.7 10.7
10.8   Taylor and Maclaurin Series 10.8 10.8
10.9   Convergence of Taylor Series 10.9 10.9
10.10   The Binomial Series and Applications of Taylor Series 10.10 10.10
Chapter 10 Test

## Chapter 11

Parametric Equations and Polar Coordinates

Lessons Homework HW Quiz
11.1   Parametrizations of Plane Curves 11.1 11.1
11.2   Calculus with Parametric Curves 11.2 11.2
11.3   Polar Coordinates 11.3 11.3
11.4   Graphing in Polar Coordinates 11.4 11.4
11.5   Areas and Lengths in Polar Coordinates 11.5 11.5
11.6   Conic Sections 11.6 11.6
11.7   Conics in Polar Coordinates 11.7 11.7
Chapter 11 Test
 Final for Calculus ll