Spring 2020 Calculus 2

MATH 2202: Calculus II

Spring Semester 2020

Instructor – Dr Sarah Holliday


MATH 2202/60 - Calculus II CRN 14011 Meets TR at 2:00 pm - 3:40 pm in D237 

MATH 2202/61 - Calculus II CRN 14012 Meets TR at 4:00 pm - 5:40 pm in D237 

Course Description:

This course is the second in the calculus curriculum and consists of two parts. The first part is concerned with the techniques of integration and applications of the integral. The second part is concerned with infinite sequences and series.

Prerequisite: A grade of “C” or better in MATH 1190.


Expected Learning Outcomes: Upon completing this course, students will be able to:

1. evaluate a wide variety of standard integrals.
2. apply integrals to a variety of problems involving area, volume, curve length, work done by a force and other similar quantities.
3. understand the concept of convergence of improper integrals and be able to evaluate some basic improper integrals;
4. understand the concept of convergence of infinite series and be able to derive and use a variety of tests for convergence of a series;
5. understand the concept of a power series, be familiar with the important properties of power series, and understand the concept of the Taylor series of common functions.

Instructor Name: Dr Sarah Holliday
Instructor office location and number: D216
Instructor contact method: shollid4@kennesaw.edu
Office hours: TR 11:00 am - 1:45 pm
Attendance policy: On-time attendance is expected. Students are responsible for making up any material they miss if they fail to attend class. Students who wish to be excused from a class (and any associated quiz/assignment that day) must notify the instructor in advance. 
Missed exams: In order to be excused from an exam, you must (1) notify the instructor before the start of the exam (or as soon after as the circumstances allow), and (2) provide official documentation (a doctor's note, a parent note, etc.) excusing your absence in a timely manner. 

Dates

First day of classes Monday January 6
Drop add ends Friday January 10
MLK Day Holiday Monday January 20
First Test Thursday January 30
Second Test Thursday February 20
Last day to withdraw Wednesday February 26
Third Test Thursday March 12
Spring Break March 30-April 3
Fourth Test Thursday April 16
Last day of classes Monday April 27

Section 60 April 28, 1-3pm, in this room.
Section 61 April 30, 3:30-5:30pm, in this room.

Grades due May 8


Grading policy 

Homework & Quizzes: 20%
Exams: 60%
Final Exam: 20%

Required materials

Textbook: Thomas’ Calculus, Early Transcendentals, 14th edition, by Joel Hass, Christopher Heil, and Murice D. Weir
Technology: No calculator is required, and no calculator will be allowed on quizzes and exams.  The use of cell phones, pagers, text or other messaging devices is not allowed during class.

Online Resource: MyLab Math by Pearson. CourseID: linked in the D2L shell
This is the textbook publisher’s online homework, assessment, and tutorial resource. It includes access to the complete eText version of the textbook, prerequisite review materials, numerous interactive figures, tutorial videos, the student’s solutions manual, and much more. Separate instructions will be provided on how to access and enroll in the appropriate MyLab Math course. 
Homework list at bottom of page

Day One Access:

MATH 2202 is part of a new textbook program called Day One Access. After enrolling in the course, you should receive an e-mail from KSU University Stores with instructions on how to access the course content. The purpose of Day One Access is to make sure that you have access to the digital course materials on or before the first day of class at a highly competitive rate. Everyone enrolled will automatically have access to the digital course materials through January 11, 2020. Those who have not opted-out or dropped the class by January 11, will receive a charge from the bookstore on their student account. You have the ability to Opt-Out through Saturday, January 11th via the link in the email sent to you by University Stores.


You must also login and register your materials by Sunday, January 12th. If you do not do this by this date, you may lose access and an access code may be required despite not having opted out. If this happens, please email dayone@kennesaw.edu


If you would like to know more about Day One Access, please visit https://ksustore.kennesaw.edu/textbooks/day_one_access.php.

 
If you would like to know if a loose-leaf copy of the textbook is available or have any other questions or concerns, please email dayone@kennesaw.edu.

Specific Course Topics

  1. Techniques of integration 
    1. u-substitution 
    2. Integration by parts 
    3. Trigonometric integrals 
    4. Trigonometric substitution 
    5. Partial fraction decomposition 
  2. Applications of Integration 
    1. Area between curves 
    2. Volumes by cross-section
    3. Solids of revolution: Disk, Washer, and Shell methods 
    4. Arc length 
    5. Work – Hooke’s Law and Pumping/Lifting
  3. Improper Integrals 
    1. L’Hopital’s Rule: review of 0/0 and infinity/infinity indeterminate forms 
    2. 0*infinity, infinity - infinity, and exponent indeterminate forms 
    3. Evaluating improper integrals 
    4. Integral comparison test: Direct and Limit
  4. Sequences 
    1. Definition and convergence 
  5. Series tests 
    1. Definition 
    2. Geometric series convergence 
    3. Integral test 
    4. Comparison tests – direct and limit 
    5. Absolute convergence 
    6. Alternating series test 
    7. Ratio and Root tests 
  6. Power series 
    1. Definition and convergence 
    2. Taylor series and Maclaurin series 
    3. Approximations with Taylor/Maclaurin series 


How to be successful in this course:

Whether or not you succeed in this course depends primarily on your choices. If you do a few things consistently, namely:

attend class and actively participate in class activities,
complete assignments on time,
study for exams, and
seek help when you need it, both from your instructor and from the SMART Center,

then you will give yourself every chance to be successful.

Science and Math Academic Resource and Tutoring (SMART) Center at KSU: In the SMART Center you will find people and resources to help with most general education Mathematics, Chemistry, and Physics courses along with select Engineering classes offered at KSU. No appointments are necessary to use the SMART Center’s services, stop by any time they are open for help in your classes. For more information about hours and tutor schedule see: https://uc.kennesaw.edu/academicinitiatives/smart/index.php

 
Diversity statement: Kennesaw State University prides itself on offering a premiere, personalized educational experience for leadership and engagement within a diverse nation and world. This educational experience is achieved through recognition and appreciation of the differing backgrounds and experiences reflected within the University community. It is my intent that students from all diverse backgrounds and perspectives be well served by this course, that students’ learning needs be addressed both in and out of class, and that the diversity that students bring to this class be viewed as a resource, strength and benefit.


Accommodations Statement: Any student with a documented disability or medical condition needing academic accommodations of class-related activities or schedules must contact the instructor immediately. Written verification from the KSU Student Disability Services is required. No requirements exist that accommodations be made prior to completion of this approved University documentation. All discussions will remain confidential. More information, including location and contact information, can be found at http://sds.kennesaw.edu/index.php.

Approximate schedule of lectures 

5.5: Indefinite Integrals and the Substitution Method (also homework exercises from Section 7.1 involving logs and exponentials)
5.6: Definite Integral Substitutions and the Area Between Curves
6.1: Volumes Using Cross-Sections
6.2: Volumes Using Cylindrical Shells
6.3: Arc Length
6.5: Work and Fluid Forces
8.1: Using Basic Integration Formulas
8.2: Integration by Parts
8.3: Trigonometric Integrals
8.4: Trigonometric Substitutions
8.5: Integration of Rational Functions by Partial Fractions
4.5: Indeterminate Forms and L’Hôpital’s Rule
8.8: Improper Integrals
10.1: Sequences
10.2: Infinite Series
10.3: The Integral Test
10.4: Comparison Tests
10.5: Absolute Convergence; The Ratio and Root Tests
10.6: Alternating Series and Conditional Convergence
10.7: Power Series
10.8: Taylor and Maclaurin Series
10.9: Convergence of Taylor Series
10.10: Applications of Taylor Series

WITHDRAWAL FROM THE UNIVERSITY OR FROM INDIVIDUAL COURSES AND ACADEMIC INTEGRITY

Spring Term, 2020

Withdrawal

Students who officially withdraw from this course before February 26, 2020 at 11:45pm will receive a grade of "W" and receive no credit. Students who withdraw after the February 26, 2020 deadline and before the last week of classes, or who have exceeded the maximum number of withdrawals, will receive a grade of "WF," which will be counted as an "F" in the calculation of their grade point average.

The only exceptions to these withdrawal regulations will be for instances involving unusual circumstances, which must be fully documented. The date the withdrawal is submitted online will be considered the official KSU withdrawal date which will be used in the calculation of any tuition refund or refund to Federal student aid and/or HOPE scholarship programs. It is advisable to print the final page of the withdrawal for your records. Failure to complete the online withdrawal process will produce no withdrawal from classes. Call the Registrar’s Office at 770-423-6200 during business hours if assistance is needed.

Academic Integrity

Every KSU student is responsible for upholding the provisions of the Statement of Student Rights and Responsibilities, as published in the Undergraduate and Graduate Catalogs. Section II of the Statement of Student Rights and Responsibilities addresses the University's policy on academic honesty, including provisions regarding plagiarism and cheating, unauthorized access to University materials, misrepresentation/falsification of University records or academic work, malicious removal, retention, or destruction of library materials, malicious/intentional misuse of computer facilities and/or services, and misuse of student identification cards. Incidents of alleged academic misconduct will be handled through the established procedures of the Department of Student Conduct and Academic Integrity (SCAI), which includes either an "informal" resolution by a faculty member, resulting in a grade adjustment, or a formal hearing procedure, which may subject a student to the Code of Conduct's minimal one semester suspension requirement.

Calculus 2 is a course in the General Education Program

Program Description: The General Education at Kennesaw State University program offers a comprehensive series of interrelated courses in the liberal arts and sciences for all Kennesaw State University students. Whereas the major program contributes depth within a chosen specialization, the General Education core provides breadth of understanding within a variety of disciplines. Together, the General Education core and the major degree program offer students the knowledge, skills, and perspectives to become informed and engaged citizens living in a diverse, global community.

Program Goals: The General Education Program at KSU has four goals. During the course of the program, students should achieve the following:

Demonstrate knowledge and understanding of general education disciplines.
Demonstrate proficiency in communication.
Demonstrate skills in inquiry, critical thinking, analysis, and problem solving through scholarly and/or creative activity across the general education disciplines.
Demonstrate an understanding of ethics, diversity, and a global perspective.

MATH 2202 satisfies one of Kennesaw State University’s general education program requirements. It addresses the Applied Math learning outcome. This learning outcome states:

Applied Math: Students will demonstrate an ability to effectively apply symbolic representations to model and solve problems.

For more information about KSU’s General Education program requirements and associated learning outcomes, please visit the topic "University-Wide Degree Requirements" in the KSU Undergraduate Catalog.

Review Material: 

Chapter 4: Applications of Derivatives
*4.5: Indeterminate Forms and L’Hôpital’s Rule: 1, 3, 9, 11, 13, 15, 19, 21, 25, 27, 29, 35, 49, 51, 55, 57, 59, 63, 65, 67, 69, 71, 75, 85, 87
*4.8: Antiderivatives: 1, 3, 9, 13, 15, 25, 29, 31, 35, 39, 41, 43, 45, 47, 49, 65, 77, 79, 85, 89, 91, 97, 99, 105, 113, 119, 125, 131

Chapter 5: Integrals
*5.1: Area and Estimating with Finite Sums: 1, 2, 5, 7, 8, 9, 13, 14, 15, 16, 17, 19
*5.2: Sigma Notation and Limits of Finite Sums: 1, 3, 7, 9, 11, 12, 13, 14, 15, 19, 21, 23, 37, 39, 41, 42, 44, 46, 50
*5.3: The Definite Integral: 1, 3, 5, 7, 11, 13, 15, 17, 19, 29, 35, 41, 43, 51, 57, 59, 64, 68, 71, 73, 75, 79, 85, 88, 89, 91
*5.4: The Fundamental Theorem of Calculus: 1, 3, 5, 7, 9, 11, 13, 15, 17, 26, 27, 39, 43, 47, 51, 55, 57, 59, 61, 63, 67, 70, 73, 75, 81, 86

Calculus 2:

5.5: Indefinite Integrals and the Substitution Method: 1, 3, 4, 5, 12, 17, 21, 23, 33, 35, 37, 41, 43, 47, 49, 55, 59, 61, 73, 77, 79
5.6: Definite Integral Substitutions and the Area Between Curves: 1, 3, 5, 9, 15, 17, 27, 29, 33, 49, 53, 55, 59, 63, 65, 67, 75, 77, 87, 89, 91, 107, 109, 111, 115, 117, Also from Chapter 7.1.3, 5, 17, 27, 38

Chapter 6: Applications of Definite Integrals
6.1: Volumes Using Cross-Sections: 1, 5, 9, 11, 17, 19, 23, 30, 31, 33, 39, 41, 43, 47, 51
6.2: Volumes Using Cylindrical Shells: 1, 3, 5, 7, 10, 11, 13, 15, 19, 21, 25, 29, 35
6.3: Arc Length: 1, 4, 5, 7, 15
6.5: Work and Fluid Forces: 3, 5, 6, 8, 11, 17, 19, 22

Chapter 8: Techniques of Integration
8.1: Using Basic Integration Formulas: 1, 2, 5, 10, 11, 14, 17, 21, 23, 26, 27, 31, 37, 38, 46, 47, Also from Chapter 7.1.7, 19, 31, 23, 29, 45
8.2: Integration by Parts: 3, 5, 7, 11, 16, 20, 21, 23, 26, 27, 47, 49
8.3: Trigonometric Integrals: 3, 6, 8, 11, 13, 19, 22, 24, 29, 33, 35, 37, 38, 41, 45, 49, 51, 55
8.4: Trigonometric Substitutions: 1, 3, 7, 11, 17, 19, 24, 25, 29, 35, 39, 42, 47, 53, 55
8.5: Integration of Rational Functions by Partial Fractions: 2, 3, 5, 9, 11, 13, 14, 16, 19, 25, 29, 35, 37, 41, 48
8.8: Improper Integrals: 1, 4, 6, 10, 13, 15, 17, 21, 24, 31, 45, 49, 59, 69

Chapter 10: Infinite Sequences and Series
10.1: Sequences: 3, 10, 15, 17, 31, 35, 37, 43, 47, 53, 57, 67, 83, 87, 91, 95, 117, 122, 125, 129, 131
10.2: Infinite Series: 7, 11, 13, 17, 35, 37, 39, 51, 53, 59, 63, 65, 67, 77, 81, 84, 96, 99
10.3: The Integral Test: 3, 4, 11, 13, 15, 17, 21, 23, 25, 31, 37
10.4: Comparison Tests: 5, 9, 17, 21, 25, 27, 28, 32, 33, 37, 41, 43, 46, 47, 51, 58, 59
10.5: Absolute Convergence; The Ratio and Root Tests: 18, 19, 21, 29, 33, 34, 37, 42, 57, 59, 61, 63
10.6: Alternating Series and Conditional Convergence: 19, 20, 21, 22, 25, 27, 31, 35, 37, 47, 53, 77
10.7: Power Series: 1, 3, 6, 9, 11, 17, 19, 25, 31, 43, 50, 54, 55
10.8: Taylor and Maclaurin Series: 1, 4, 5, 8, 11, 15, 18, 25, 29, 37, 45, 47
10.9: Convergence of Taylor Series: 1, 3, 7, 10, 15, 19, 22, 23, 27, 33, 39, 41, 47, 48, 53
10.10: Applications of Taylor Series: 2, 7, 13, 15, 19, 20, 23, 29, 35, 41, 47, 49, 57, 61, 69, 70, 71

©