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NORTH CENTRAL TEXAS COLLEGE
COURSE SYLLABUS
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Course Title:
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Calculus II (Online)
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Course Prefix & Number:
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MATH 2414
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Section Number:
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310
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Semester/Year:
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Spring 2019
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Semester Credit Hours:
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4
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Lecture Hours:
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48
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Lab Hours:
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Course Description (NCTC Catalog): Differentiation and integration of transcendental functions; parametric equations and polar coordinates; techniques of integration; sequences and series; improper integrals.
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Course Prerequisite(s): MATH 2413 Calculus I
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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.
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INSTRUCTOR INFORMATION
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Name of Instructor:
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Ben Owens
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Campus/Office Location:
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Flower Mound 107
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Office Hours:
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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
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Telephone Number:
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940-498-6295
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E-mail Address:
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bowens@nctc.edu
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STUDENT LEARNING OUTCOMES (From Academic Course Guide Manual/Workforce Education Course Manual/NCTC Catalog
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At the successful completion of this course the student will be able to:
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1
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Use the concepts of definite integrals to solve problems involving area, volume, work, and other physical applications.
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2
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Use substitution, integration by parts, trigonometric substitution, partial fractions, and tables of anti-derivatives to evaluate definite and indefinite integrals.
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3
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Define an improper integral.
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4
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Apply the concepts of limits, convergence, and divergence to evaluate some classes of improper integrals.
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5
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Determine convergence or divergence of sequences and series.
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6
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Use Taylor and MacLaurin series to represent functions.
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7
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Use Taylor or MacLaurin series to integrate functions not integrable by conventional methods.
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8
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Use the concept of polar coordinates to find areas, lengths of curves, and representations of conic sections.
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GRADING CRITERIA
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# of Graded Course Elements
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Graded Course Elements
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Percentage or Point Values
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40
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Thinkwell Homework (Online)
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10%
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20
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OpenStax Assignments (Online)
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5%
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15
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Discussion Assignments (Online)
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5%
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3
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Tests (In person)
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60%
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1
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Final Exam (In person)
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20%
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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.
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Test Completion Window
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Sections Covered on Test
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Test 1
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February 19 – 23
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Ch. 14, Ch. 15, Ch. 16
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Test 2
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March 19 – 23
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Ch. 17, Ch. 18
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Test 3
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April 23 – 27
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Ch. 19
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Final Exam
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May 8 – 14
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All Chapters (14 – 20)
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Week
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Thinkwell Sections
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Open Stax: Calculus Volume 2 https://openstax.org/details/books/calculus-volume-2
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Week 1
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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
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2.1 Area between Curves
3.5 Other Techniques for Integration
1.5 Substitution
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Week 2
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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
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https://openstax.org/details/books/calculus-volume-1
(Open Stax: Calculus Volume 1)
4.8 L’Hopital’s Rule
3.2 Trigonometric Integrals
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Week 3
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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
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3.4 Partial Fractions
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Week 4
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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
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3.1 Integration by Parts
3.3 Trigonometric Substitution
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Week 5
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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
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3.7 Improper Integrals
2.2 Determining Volume by Slicing
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Week 6
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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
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2.2 Determining Volume by Slicing
2.3 Volumes of Revolution: Cylindrical Shells
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Week 7
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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
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2.4 Arc Length of a Curve and Surface Area
2.5 Physical Applications
2.6 Moments and Centers of Mass
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Week 8
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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
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5.1 Sequences
5.2 Infinite Sequences
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Week 9
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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
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5.3 The Divergence and Integral Tests
5.4 Comparison Tests
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Week 10
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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
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5.5 Alternating Series
5.6 Ratio and Root Tests
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Week 11
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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
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6.3 Taylor and Maclaurin Series
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Week 12
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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
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6.1 Power Series and Functions
6.2 Properties of Power Series
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Week 13
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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
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7.1 Parametric Equations
7.2 Calculus of Parametric Curves
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Week 14
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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
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7.3 Polar Coordinates
7.4 Area and Arc Length in Polar Coordinates
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Week 15
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Review for Final Exam
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Week 16
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Final Exam
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Final Exam
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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 from a 16-week course with a “W” is Thursday, April 4, 2019.
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GAINESVILLE –
1403 (Library)
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CORINTH –
182
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FLOWER MOUND –
2nd floor in MSU
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Mon & Thurs
9:00 am – 4:00 pm
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Mon – Thurs
8:30 am – 6:30 pm
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Mon & Wed
9:00 am – 3:00 pm
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Tues & Wed
9:00 am – 5:00 pm
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Tues & Thurs
9:00 am – 3:00 pm
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Fri 9:00 am – 12:00 pm
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Fri 9:00 am – 12:00 pm
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Fri 9:00 am – 12:00 pm
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Sun 1:00 – 5:00 pm
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Sat 10:00 am – 1:00 pm
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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
Academic General Education Course (from ACGM but not in NCTC Core)
Academic NCTC Core Curriculum Course
WECM Course
Students are expected to follow all rules and regulations found in the student handbook. https://www.nctc.edu/_documents/academics/student-handbook.pdf
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:
- Zero on the assignment
- Failing grade for the course
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Name of Chair :
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Dr. Elizabeth Howell
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Office Location:
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Corinth 236
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Telephone Number:
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940.498.6209
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E-mail Address:
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ehowell@nctc.edu
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Name of Instructional Dean:
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Sara Flusche
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Office Location:
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Gainesville 1306
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Telephone Number:
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940.668.3351
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E-mail Address:
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sflusche@nctc.edu
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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.