Syllabus

NORTH CENTRAL TEXAS COLLEGE

COURSE SYLLABUS

 

 

Course Title:

Calculus II (Online)

Course Prefix & Number: 

MATH 2414

Section Number: 

310

Semester/Year:

Spring 2019

Semester Credit Hours:

4

Lecture Hours:

48

Lab Hours:

 

Course Description (NCTC Catalog): Differentiation and integration of transcendental functions; parametric equations and polar coordinates; techniques of integration; sequences and series; improper integrals.    

Course Prerequisite(s): MATH 2413 Calculus I

Required or Recommended Course Materials:

Thinkwell Access (Canvas) - Thinkwell provides lecture videos as well as practice exercises and homework assignments.  See “Getting Started with Thinkwell” on Homepage for more information.

 

Internet access is required.

 

Scientific Calculator. (Use of calculators may be restricted on tests.  See Canvas Homepage for more info on calculators.)

 

Note: (Optional)  You may want to purchase a Calculus textbook.  There is no book to go along specifically with the Thinkwell videos, but any Calculus textbook will give more examples and practice. There are some free textbooks online or you can find older editions of books typically for a big discount!  We will be doing some assignments from OpenStax Calculus Volume 2. 

             

 

INSTRUCTOR INFORMATION

Name of Instructor:

Ben Owens

Campus/Office Location:

Flower Mound 107

Office Hours:

Online conferences can be made by appointment.  I am generally free in the evenings after 8:00.  Please email to make an appointment.

Flower Mound

Monday: 8-9:30 ; 12:30-2

Tuesday: 8-8:30 ; 12:30-2

Wednesday: 12:30-3:30

Thursday: 8-8:30; 12:30-2

Fridays: by appointment only

Telephone Number:

940-498-6295

E-mail Address:

bowens@nctc.edu

 


 

STUDENT LEARNING OUTCOMES (From Academic Course Guide Manual/Workforce Education Course Manual/NCTC Catalog

At the successful completion of this course the student will be able to:

1

Use the concepts of definite integrals to solve problems involving area, volume, work, and other physical applications.

2

Use substitution, integration by parts, trigonometric substitution, partial fractions, and tables of anti-derivatives to evaluate definite and indefinite integrals.

3

Define an improper integral.

4

Apply the concepts of limits, convergence, and divergence to evaluate some classes of improper integrals.

5

Determine convergence or divergence of sequences and series.

6

Use Taylor and MacLaurin series to represent functions.

7

Use Taylor or MacLaurin series to integrate functions not integrable by conventional methods.

8

Use the concept of polar coordinates to find areas, lengths of curves, and representations of conic sections.

 

GRADING CRITERIA

# of Graded Course Elements

Graded Course Elements

Percentage or Point Values

40

Thinkwell Homework (Online)

10%

20

OpenStax Assignments (Online)

5%

15

Discussion Assignments (Online)

5%

3

Tests (In person)

60%

1

Final Exam (In person)

20%

Grade Scale:   90 – 100% = A;   80 – 89% = B; 70 – 79% = C;  60 – 69% = D;  Below 60% = F

 

***Tests must be taken on an NCTC campus with a Math division proctor, at an NCTC Testing Center, or at an approved test proctoring location.  NCTC offers testing at any campus (Gainesville, Corinth, Flower Mound, Bowie, Graham).  If it is more convenient for you to take the test at a different location (another college/university for instance) please email me to make arrangements for your testing.***

 

All assignments are due on Sunday nights.  If for some reason the due dates need to be adjusted I will email the class.  See “Assignment Descriptions” on the Course Homepage for more details about assignments.

 

COURSE SUBJECT OUTLINE (Major Assignments, Due Dates, and Grading Criteria)

 

Tests must be completed in the time frames listed below.

 

 

Test Completion Window

Sections Covered on Test

Test 1

February 19 – 23

Ch. 14, Ch. 15, Ch. 16

Test 2

March 19 – 23

Ch. 17, Ch. 18

Test 3

April 23 – 27

Ch. 19

Final Exam

May 8 – 14

All Chapters (14 – 20)

 

Week

Thinkwell Sections

Open Stax: Calculus Volume 2 https://openstax.org/details/books/calculus-volume-2

Week 1

Introduction / Review

An Introduction to Calculus II

I.1.1 - Welcome to Calculus II

I.1.2 - Review: Calculus I in 20 Minutes

14.1 - The Area Between Curves

14.1 - The Area between Two Curves

14.2 - Limits of Integration and Area

14.3 - Common Mistakes to Avoid When Finding Areas

14.4 - Regions Bound by Several Curves

Integration Review/Tables

16.1.1 – Integration Using Tables

16.1.2 – Making u-Substitutions

 

 

 

 

2.1 Area between Curves

 

 

 

 

3.5 Other Techniques for Integration

1.5 Substitution

Week 2

L’Hopital’s Rule

15.1 Indeterminate Quotients

15.1.1 - Indeterminate Forms

15.1.2 - An Introduction to L'Hôpital's Rule

15.1.3 - Basic Uses of L'Hôpital's Rule

15.1.4 - More Exotic Examples of Indeterminate Forms

15.2 - Other Indeterminate Forms

15.2.1 - L'Hôpital's Rule and Indeterminate Products

15.2.2 - L'Hôpital's Rule and Indeterminate Differences

15.2.3 - L'Hôpital's Rule and One to the Infinite Power

15.2.4 - Another Example of One to the Infinite Power

Integration Techniques

16.2 - Integrals Involving Powers of Sine and Cosine

16.2.1 - An Introduction to Integrals with Powers of Sine and Cosine

16.2.2 - Integrals with Powers of Sine and Cosine

16.2.3 - Integrals with Even and Odd Powers of Sine and Cosine

https://openstax.org/details/books/calculus-volume-1

(Open Stax:  Calculus Volume 1)

4.8 L’Hopital’s Rule

 

 

 

 

 

 

3.2 Trigonometric Integrals

Week 3

16.3 - Integrals Involving Powers of Other Trigonometric Functions

16.3.1 - Integrals of Other Trigonometric Functions

16.3.2 - Integrals with Odd Powers of Tangent and Any Power of Secant

16.3.3 - Integrals with Even Powers of Secant and Any Power of Tangent

16.4 - An Introduction to Integration by Partial Fractions

16.4.1 - Finding Partial Fraction Decompositions

16.4.2 - Partial Fractions

16.4.3 - Long Division

16.5 - Integration by Partial Fractions with Repeated Factors

16.5.1 - Repeated Linear Factors: Part One

16.5.2 - Repeated Linear Factors: Part Two

16.5.3 - Distinct and Repeated Quadratic Factors

16.5.4 - Partial Fractions of Transcendental Functions

 

 

 

 

 

 

 

 

 

 

 

 

3.4 Partial Fractions

 

 

Week 4

16.6 - Integration by Parts

16.6.1 - An Introduction to Integration by Parts

16.6.2 - Applying Integration by Parts to the Natural Log Function

16.6.3 - Inspirational Examples of Integration by Parts

16.6.4 - Repeated Application of Integration by Parts

16.6.5 - Algebraic Manipulation and Integration by Parts

16.7 - An Introduction to Trigonometric Substitution

16.7.1 - Converting Radicals into Trigonometric Expressions

16.7.2 - Using Trigonometric Substitution to Integrate Radicals

16.7.3 - Trigonometric Substitutions on Rational Powers

16.8 - Trigonometric Substitution Strategy

16.8.1 - An Overview of Trigonometric Substitution Strategy

16.8.2 - Trigonometric Substitution Involving a Definite Integral: Part One

16.8.3 - Trigonometric Substitution Involving a Definite Integral: Part Two

3.1 Integration by Parts

 

 

 

 

 

 

3.3 Trigonometric Substitution

Week 5

Improper Integrals

17.1 - Improper Integrals

17.1.1 - The First Type of Improper Integral

17.1.2 - The Second Type of Improper Integral

17.1.3 - Infinite Limits of Integration, Convergence, and Divergence

Applications of Integral Calculus

18.1 - The Average Value of a Function

18.1.1 - Finding the Average Value of a Function

18.2 - Finding Volumes Using Cross-Sections

18.2.1 - Finding Volumes Using Cross-Sectional Slices

18.2.2 - An Example of Finding Cross-Sectional Volumes

 

3.7 Improper Integrals

 

 

 

 

 

 

 

 

2.2 Determining Volume by Slicing

Week 6

18.3 - Disks and Washers

18.3.1 - Solids of Revolution

18.3.2 - The Disk Method along the y-Axis

18.3.3 - A Transcendental Example of the Disk Method

18.3.4 - The Washer Method across the x-Axis

18.3.5 - The Washer Method across the y-Axis

18.4 - Shells

18.4.1 - Introducing the Shell Method

18.4.2 - Why Shells Can Be Better Than Washers

18.4.3 - The Shell Method: Integrating with Respect to y

2.2 Determining Volume by Slicing

 

 

 

 

2.3 Volumes of Revolution: Cylindrical Shells

Week 7

18.5 - Arc Lengths and Functions

18.5.1 - An Introduction to Arc Length

18.5.2 - Finding Arc Lengths of Curves Given by Functions

18.6 - Work

18.6.1 - An Introduction to Work

18.6.2 - Calculating Work

18.6.3 - Hooke's Law

18.7 - Moments and Centers of Mass

18.7.1 - Center of Mass

18.7.2 - The Center of Mass of a Thin Plate

2.4 Arc Length of a Curve and Surface Area

 

2.5 Physical Applications

 

 

 

2.6 Moments and Centers of Mass

Week 8

Sequences and Series

19.1 - Sequences

19.1.1 - The Limit of a Sequence

19.1.2 - Determining the Limit of a Sequence

19.1.3 - The Squeeze and Absolute Value Theorems

19.2 - Monotonic and Bounded Sequences

19.2.1 - Monotonic and Bounded Sequences

19.3 - Infinite Series

19.3.1 - An Introduction to Infinite Series

19.3.2 - The Summation of Infinite Series

19.3.3 - Geometric Series

19.3.4 - Telescoping Series

 

5.1 Sequences

 

 

 

 

 

5.2 Infinite Sequences

Week 9

19.4 - Convergence and Divergence

19.4.1 - Properties of Convergent Series

19.4.2 - The nth-Term Test for Divergence

19.5 - The Integral Test

19.5.1 - An Introduction to the Integral Test

19.5.2 - Examples of the Integral Test

19.5.3 - Using the Integral Test

19.5.4 - Defining p-Series

19.6 - The Direct Comparison Test

19.6.1 - An Introduction to the Direct Comparison Test

19.6.2 - Using the Direct Comparison Test

19.7 - The Limit Comparison Test

19.7.1 - An Introduction to the Limit Comparison Test

19.7.2 - Using the Limit Comparison Test

19.7.3 - Inverting the Series in the Limit Comparison Test

5.3 The Divergence and Integral Tests

 

 

 

 

 

 

5.4 Comparison Tests

Week 10

19.8 - The Alternating Series

19.8.1 - Alternating Series

19.8.2 - The Alternating Series Test

19.8.3 - Estimating the Sum of an Alternating Series

19.9 - Absolute and Conditional Convergences

19.9.1 - Absolute and Conditional Convergence

19.10 - The Ratio and Root Tests

19.10.1 - The Ratio Test

19.10.2 - Examples of the Ratio Test

19.10.3 - The Root Test

19.11 - Polynomial Approximations of Elementary Functions

19.11.1 - Polynomial Approximation of Elementary Functions

19.11.2 - Higher-Degree Approximations

5.5 Alternating Series

 

 

 

 

 

5.6 Ratio and Root Tests

 

 

 

 

Week 11

19.12 - Taylor and Maclaurin Polynomials

19.12.1 - Taylor Polynomials

19.12.2 - Maclaurin Polynomials

19.12.3 - The Remainder of a Taylor Polynomial

19.12.4 - Approximating the Value of a Function

19.13 - Taylor and Maclaurin Series

19.13.1 - Taylor Series

19.13.2 - Examples of the Taylor and Maclaurin Series

19.13.3 - New Taylor Series

19.13.4 - The Convergence of Taylor Series

6.3 Taylor and Maclaurin Series

Week 12

19.14 - Power Series

19.14.1 - The Definition of Power Series

19.14.2 - The Interval and Radius of Convergence

19.14.3 - Finding the Interval and Radius of Convergence: Part One

19.14.4 - Finding the Interval and Radius of Convergence: Part Two

19.14.5 - Finding the Interval and Radius of Convergence: Part Three

19.15 - Power Series Representations of Functions

19.15.1 - Differentiation and Integration of Power Series

19.15.2 - Finding Power Series Representations by Differentiation

19.15.3 - Finding Power Series Representations by Integration

19.15.4 - Integrating Functions Using Power Series

6.1 Power Series and Functions

 

 

 

 

 

 

 

 

6.2 Properties of Power Series

Week 13

Parametric Equations and Polar Coordinates

21.1 - Understanding Parametric Equations

21.1.1 - An Introduction to Parametric Equations

21.1.2 - The Cycloid

21.1.3 - Eliminating Parameters

21.2 - Calculus and Parametric Equations

21.2.1 - Derivatives of Parametric Equations

21.2.2 - Graphing the Elliptic Curve

21.2.3 - The Arc Length of a Parameterized Curve

21.2.4 -Finding Arc Lengths of Curves Given by Parametric Equations

 

 

 

7.1 Parametric Equations

 

 

 

7.2 Calculus of Parametric Curves

Week 14

21.3 - Understanding Polar Coordinates

21.3.1 - The Polar Coordinate System

21.3.2 - Converting between Polar and Cartesian Forms

21.3.3 - Spirals and Circles

21.3.4 - Graphing Some Special Polar Functions

21.4 - Polar Functions and Slope

21.4.1 - Calculus and the Rose Curve

21.4.2 - Finding the Slopes of Tangent Lines in Polar Form

21.5 - Polar Functions and Area

21.5.1 - Heading toward the Area of a Polar Region

21.5.2 - Finding the Area of a Polar Region: Part One

21.5.3 - Finding the Area of a Polar Region: Part Two

21.5.4 - The Area of a Region Bounded by Two Polar Curves: Part One

21.5.5 - The Area of a Region Bounded by Two Polar Curves: Part Two

7.3 Polar Coordinates

 

 

 

 

7.4 Area and Arc Length in Polar Coordinates

Week 15

Review for Final Exam

 

Week 16

Final Exam

Final Exam

 

 

ATTENDANCE POLICY

Regular and punctual attendance is expected of all students in all classes for which they have registered.  All absences are considered to be unauthorized unless the student is absent due to illness or emergencies.  It is the student’s responsibility to provide documentation as to the emergency for approval by the faculty member.  Approved college-sponsored activities are also excused absences.  The instructor is responsible for judging the validity of any reason given for an absence.  Valid reasons for absence, however, do not relieve the student of the responsibility for making up required work.  Students will not be allowed to make up an examination missed due to absence unless the absence is documented and excused by the instructor.  Student will be dropped from a class by the Registrar upon recommendation of the instructor who feels the student has been justifiably absent or tardy a sufficient number of times to preclude meeting the course’s objectives.    Persistent, unjustified absences from classes or laboratories will be considered sufficient cause for College officials to drop a student from the rolls of the College. From Board Policy FC (LOCAL)

LAST DAY TO WITHDRAW

Last day to withdraw from a 16-week course with a “W” is Thursday, April 4, 2019.

 

MATH LAB

Students who need help with any math class can visit the NCTC Mathematics Lab to receive assistance. No appointments are necessary. See the most current tutoring hours for all five campuses at http://www.nctc.edu/student-services/student-success/tutoring/mathematics-lab.html

 

TIMES SUBJECT TO CHANGE BASED ON TUTOR AVAILABILITY:

GAINESVILLE –

1403 (Library)

CORINTH –

182

FLOWER MOUND –

2nd floor in MSU

Mon & Thurs

9:00 am – 4:00 pm

Mon – Thurs

8:30 am – 6:30 pm

Mon & Wed

9:00 am – 3:00 pm

Tues & Wed

9:00 am – 5:00 pm

 

Tues & Thurs

9:00 am – 3:00 pm

Fri 9:00 am – 12:00 pm

Fri 9:00 am – 12:00 pm

Fri 9:00 am – 12:00 pm

Sun 1:00 – 5:00 pm

Sat 10:00 am – 1:00 pm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DISABILITY SERVICES (Office for Students with Disabilities)

The Office for Students with Disabilities (OSD) provides accommodations for students who have a documented disability. On the Corinth Campus, go to room 170 or call 940-498-6207. On the Gainesville Campus, go to room 110 or call 940-668-4209.  Students on the Bowie, Graham, Flower Mound, and online campuses should call 940-498-6207.

North Central Texas College is committed to both the spirit and letter of federal equal opportunity legislation, including the Americans with Disabilities Act (ADA) of 1990, ADA Amendments Act of 2009, and Section 504 of the Rehabilitation Act of 1973 (P.L. 93-112).   http://www.nctc.edu/catalog/student-services/office-students-with-disabilities.html

 

CORE CURRICULUM FOUNDATIONAL COMPONENT AREA (For classes in the Core)________       


           Communication

           Mathematics                

           Life and Physical Science

           Language, Philosophy & Culture

           Creative Arts

           American History

 

           Government/Political Science

           Social and Behavioral Sciences

           Component Area Option

 


REQUIRED CORE OBJECTIVES (For classes in the Core)


           Critical Thinking

             Communication

             Empirical and Quantitative

 

             Teamwork

             Personal Responsibility

             Social Responsibility


COURSE TYPE

            Academic General Education Course (from ACGM but not in NCTC Core)

           Academic NCTC Core Curriculum Course

           WECM Course

 

STUDENT HANDBOOK

Students are expected to follow all rules and regulations found in the student handbook. https://www.nctc.edu/_documents/academics/student-handbook.pdf

 

ACADEMIC DISHONESTY

Scholastic dishonesty shall include, but is not limited to cheating, plagiarism, academic falsification, intellectual property dishonesty, academic dishonesty facilitation and collusion.  Faculty members may document and bring charges against a student who is engaged in or is suspected to be engaged in academic dishonesty.  See Student Handbook, “Student Rights & Responsibilities: Student Conduct ([FLB(LOCAL)]”. 

Consequences for academic dishonesty may include:

  1.  Zero on the assignment
  2. Failing grade for the course

 

Name of Chair :

Dr. Elizabeth Howell

Office Location:

Corinth 236

Telephone Number:

940.498.6209

E-mail Address:

ehowell@nctc.edu

Name of Instructional Dean:

Sara Flusche

Office Location:

Gainesville 1306

Telephone Number:

940.668.3351

E-mail Address:

sflusche@nctc.edu

 

 

 

 

 

 

 

 

 

 

CAMPUS RESTRICTIONS

Tobacco-Free Campus:  NCTC restricts the use of all tobacco products, including cigarettes, e-cigarettes, cigars, pipes, and smokeless tobacco, on campus property.

 

Campus Carry: Effective August 1, 2017, a license holder may carry a concealed handgun on or about the license holder's person while the license holder is on the campus of an institution of higher education or private or independent institution of higher education in this state. For more information, see the website at http://www.nctc.edu/police/campus-carry.html.

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