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Mathematics 1502 Calculus II Spring Semester 2021 Class location: Online INSTRUCTOR: Dr

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Mathematics 1502 Calculus II Spring Semester 2021 Class location: Online INSTRUCTOR: Dr. S. Karmakar OFFICE: Instructional Complex 231 OFFICE HOURS: 10:00-12:00 MTWR All office hours are online. Please contact by email OFFICE PHONE: 678-359-5833 All students are required to wear face masks in classrooms and buildings on campus. COURSE FORMAT: ONLINE For more information related to COVID-19, visit https://www.gordonstate.edu/corona-virus/index.html E-Mail: s_karmakar@gordonstate.edu PREREQUISITE: CREDIT: MATH 1501 4 semester credit hours CALCULATOR: Graphing calculator required. TI-83/84 recommended. TEXT: Calculus, 8th Edition, by James Stewart, 2019. (There is no need to buy the hard copy of the book). You are required to buy Cengage WebAssign With the E-Book (ISBN: 9781337771429) To enroll in the class, use the Course Key: gdn 9971 2599 NOTE: This syllabus MAY be changed at the discretion of the instructor with the knowledge of the class. COURSE DESCRIPTION This course includes the study of additional topics in differential and integral calculus. These topics include, but are not limited to, differentiation and integration involving the exponential, logarithmic, and inverse trigonometric functions, indeterminate forms, techniques of integration, L’Hospital’s Rule, improper integrals, infinite sequences, infinite series, power series, numerical methods, and polar coordinates. This course will emphasize student preparation, critical thinking, and problem solving. To do well in the course, you must take good notes and study them, read the assignments in the text, do problems 2 from the text, and prepare for tests by reviewing your notes and those problems worked outside of class. Over the course of the semester, you should devote about two hours of outside class work for each hour in class. This course, as many other courses, will emphasize the written communication of ideas. In this course, you will be communicating mathematical ideas. You will learn how to read, write, and speak the language of mathematics. You should carefully study how mathematics is written in class as well as how it is written in the textbook. COURSE OBJECTIVES This course, by means of lectures, individual problem solving, application of principles, and calculation addresses the following general education expected outcome of the college: Communication Skills: Students should be able to read and listen with understanding, and to communicate clearly and effectively in writing and speaking. Mathematical Skills: Students will demonstrate a basic knowledge of the fundamentals of college-level mathematics. Upon completion of Calculus II, students should have an understanding of: 1. The definitions of logarithmic and exponential functions, and differentiation and integration involving logarithmic and exponential functions. 2. The definitions of inverse trigonometric functions, and differentiation and integration involving the inverse trigonometric functions. 3. Indeterminate forms and L’Hospital’s Rule. 4. The techniques of integration including integration by parts, trigonometric substitution, and partial fractions. 5. Approximate integration. 6. Improper integrals. 7. Arc length and area of a surface of revolution. 8. Infinite series of constants, tests for convergence and divergence of series, and approximating the sum of a series. 9. Power series, interval of convergence of power series, differentiation and integration of power series, power series representation of elementary functions, and Taylor polynomials. 10. Polar coordinates and calculus. 3 Title IX Gordon State College is committed to providing an environment free of all forms of discrimination and sexual harassment, including sexual assault, domestic violence, dating violence and stalking. If you (or someone you know) has experienced or experiences any of these incidents, know that you are not alone. All faculty members at Gordon State College are mandated reporters. Any student reporting any type of sexual harassment, sexual assault, dating violence, domestic violence or stalking must be made aware that any report made to a faculty member under the provisions of Title IX will be reported to the title IX Coordinator or a Title IX Deputy Coordinator. If you wish to speak with someone confidentially, you must contact the Counseling and Accessibility Services office, Room 212, Student Life Center. The licensed counselors in the Counseling Office are able to provide confidential support. Gordon State College does not discriminate against any student on the basis of pregnancy, parental or related conditions. Students seeking accommodations on the basis of pregnancy, parenting or related conditions should contact Counseling and Accessibility Services regarding the process of documented pregnancy related issues and being approved for accommodations, including pregnancy related absences as defined under Title IX. ADA and 504 If you have a documented disability as described by the Americans with Disabilities Act (ADA) and the Rehabilitation Act of 1973, Section 504, you may be eligible to receive accommodations to assist in programmatic and /or physical accessibility. The Counseling and Accessibility Services office located in the Student Center, Room 212 can assist you in formulating a reasonable accommodation plan and in providing support in developing appropriate accommodations to ensure equal access to all GSG programs and facilities. Course requirements will not be waived, but accommodations may assist you in meeting the requirements. For documentation requirements and for additional information, contact Counseling and Accessibility Services at 678-359-5585. METHOD OF EVALUATION A. There will be four (4) tests and a final examination during the semester. The Final Exam and all Tests are scheduled in WebAssign. If you miss a test, your final exam grade will count twice. If you miss a second test, you will receive a grade of “zero” for that test. A make-up test may be given for any test missed if you have a documented excuse. Students may request a make-up test by notifying the instructor via email no later than the day of the regularly scheduled test. Student athletes will only need to attach a copy of their course schedule and a copy of their game schedule. Make-up tests are given at the instructor’s convenience. There are no make-ups for the make-up tests. The tests are scheduled in WebAssign. Be sure to read announcements in D2L. B. All homework and quizzes are also scheduled in WebAssign. There are no make-up homework assignments or quizzes 4 C. The student’s final grade will be computed as follows: Homework 10% Quizzes 10% Tests 60% Final Exam 20% TOTAL 100% D. In WebAssign, you have access to resources which include PowerPoints and videos for each chapter. You should go over them before doing assignments or taking quizzes. E. The following grading scale will be used. 89.5 or above A 59.5 to 69.49 D 79.5 to 89.49 B Below 59.5 F 69.5 to 79.49 C CLASS PROCEDURES A. Attendance: This is an on-line class. Students are required to watch the videos, complete their homework, quizzes, and Tests on time. Students are responsible for every instruction, every change in the syllabus, and all material covered in the syllabus. Students who enroll in the course late are responsible for material covered before they enrolled. B. Working Problems: Most students will benefit by working many problems for practice. On the Tentative Course Outline is a list of suggested problems for each section covered. These are intended to give the student practice in specific concepts that are taught in class. These problems will not be graded. WebAssign has built –in tutorial help and also, Pre-lectures for each unit. C. Group Work: Students are encouraged to work together on the suggested problems and homework assignments. D. Technical Help: If you need technical help online with WebAssign, contact Cengage technical helpline: support.cengage.com . If you need help with D2L, go to the Gordon State home page and find links to Brightspace or Desire To Learn. You should also be able to get assistance through the Student Success Center. E. Calculator Policy: A graphing calculator is required for this course. Calculators are permitted on all assignments and tests. F. Class Etiquette: Students are expected to treat the instructor and other students with respect. 5 Tentative Course Outline MATH 1502 Spring Semester 2021 Week of Jan 25 Section 6.1: Inverse Functions 6.2*: The Natural Logarithm Function Quiz 1 6.3*: The Natural Exponential Function 6.4*: General Logarithmic and Exponential Functions 6.6: Inverse Trigonometric Functions Quiz 2 6.8: Indeterminate Forms and L’Hospital’s Rule Suggested Problems 1-41 odd 1-46 odd, 59-75 odd 1-63 odd Fri, Feb 12 Feb 15 6.8 (continued) TEST I 7.1: Integration By Parts 7.2: Trigonometric Integrals Feb 22 7.2 (continued) Quiz 3 7.3: Trigonometric Substitution Feb 1 Feb 8 Mar 1 Mar 8 Fri, Mar 12 Mar 15 Mar 22 Mar 29 Apr 5 7.4: Integration of Rational Functions by Partial Fractions 7.4 (continued) Quiz 4 7.5 Strategy for Integration 7.7: Approximate Integration 7.8: Improper Integrals 7.8 (continued) TEST II 8.1: Arc Length 8.2: Area of a Surface of Revolution 11.1 Sequences 11.1 (continued) 11.2 Series 11.3: The Integral Test 11.4: The Comparison Tests 11.5: The Alternating Series Test 11.6: Absolutely Convergent Series, the Ratio Test, and the Root Test 11.7: Strategy for Testing Series 1-59 odd, 63-67 odd, 75-83 odd 1-51 odd 1-73 odd 1-14 odd, 47-61 1-63 odd 1-29 odd 1-51 odd 1-79 odd 1-37 odd 1-39 odd, 49-59 odd 1-21 odd 1-15 odd 1-53 odd, 61-65 odd 1-51 odd 1-29 odd, 33, 35 1-35 odd 1-33 odd 1-27 odd, 31,32, 33 1-37 odd 6 Week of Fri, Apr 9 Apr 12 Apr 19 Apr 26 Section TEST III 11.8: Power Series 11.8 (continued) 11.9: Representations of Functions as Power Series 11.9 (continued) 11.10: Taylor and Maclaurin Series 11:10 (continued) 11.11: Applications of Taylor Polynomials 11.11 (continued) TEST IV 10.3: Polar Coordinates 10.3: (continued) 10.4: Areas and Lengths in Polar Coordinates Suggested Problems 1-31 odd 1-29 odd, 37, 38, 39 1-9 odd, 13-19 odd, 25-49 odd, 55-67 odd 1-25 odd 1-25 odd, 29-45 odd, 57-67 odd 1-53 odd Review TBA FINAL EXAMINATION COVID-19 Statement Creating a Healthy Environment At Gordon State College, we are committed to the health and safety of our students, faculty and staff. Since March 2020, our campus has been addressing the impact of the Coronavirus (COVID-19) on a daily basis. The return to campus will be based on a new reality where adjustments will be made to every facet of the “oncampus” experience. This will truly be a “Power of WE!” moment, as the safety of the entire campus will depend on our institutional values. You will be expected to follow “The Healthy Highlander Way“ as you participate in classes that require class attendance. Posters describing the Healthy Highlander Way are displayed in each building on campus and can be found in the “Return to Campus Guide” linked to the GSC home page. If you have one of the symptoms of COVID-19, you should notify your professor, stay home, and contact your personal physician prior to returning to campus. Commuter students should also notify the Student Health Center at healthcenter@gordonstate.edu. In addition, residential students should contact their Community Assistant and schedule an appointment with the Student Health Center at 678-359-5456. One of the most effective ways to stop the spread of the virus is wearing a face covering. You must wear a face covering at all times when in public on any Gordon State College campus. Anyone not using a face covering when required will be asked to wear one or leave the area. Repeated refusal to comply with the requirement may result in discipline through the applicable code of conduct for students. If you are a student with one of the underlying medical conditions identified in the “Return to Campus Guide” and you would like to apply for accommodations due to being at a higher risk for severe illness with COVID- 7 19, please contact Counseling & Accessibility Office at 678-359-5585 or email the Director of Counseling and Accessibility Services Alicia Dorton at aliciad@gordonstate.edu. Making a commitment to The Healthy Highlander Way will allow our campus to remain as safe as possible during this semester. Being prepared for Class during the Pandemic Although some courses will meet in a full face-to-face format, most classes for this term will meet online or in a hybrid format. In addition, all classes will shift online after Thanksgiving for the remainder of the term. All students should be prepared at a minimum to: • Meet an online class session synchronously (at the time of the class or a set time with the professor) • Take a proctored exam using an outside proctor All students should, as a minimum, have access to: • A laptop or desktop computer (5 or fewer years old). Tablets, Chromebooks, and phones will not be sufficient. • Operating system: o Windows 10 Home or Pro (“streamlined” versions such as Windows 10S are not supported), or o macOS 10.13 or higher • Webcam with a working microphone (often this is integrated/included with laptops but USB webcams can also be utilized) • Access to a broadband Internet connection (& access to an Ethernet cable, preferably) • Microsoft Office Suite (Word, PowerPoint, Outlook, etc.). Download it here for free (via Gordon State College. Make sure to create your account using your Gordon email.) • A working Internet browser that is compatible with D2L: Microsoft® Edge, Mozilla® Firefox®, Google® Chrome™, Apple® Safari®. Students can check their devices’ compatibility via this checker. Other suggested features include: • • • Processor: minimum Intel Core i3 or equivalent RAM/Memory: 8GB or higher Storage: 128GB internal hard drive or larger (256+GB solid state drives preferred, but not required) Be aware that your individual course may have other technology requirements. Finally, it is highly recommended that you download the Brightspace by D2L Pulse App for your smartphone or tablet. ld258881@gordonstate.edu EN Home My Assignments Communication (Sign out) Grades Calendar My eBooks Math 1502, section A, Spring 2021 INSTRUCTOR Final Exam (Exam) Satyajit Karmakar Gordon State College, GA Current Score QUESTION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 POINTS –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/2 –/2 –/1 –/1 –/1 –/2 –/4 TOTAL SCORE –/26 0.0% Due Date FRI, MAY 7, 2021 5:00 PM EDT Request Extension Assignment Submission & Scoring Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. 1. [–/1 Points] DETAILS SCALC8 6.2STAR.035. MY NOTES ASK YOUR TEACHER SCALC8 6.3STAR.053. MY NOTES ASK YOUR TEACHER SCALC8 6.4STAR.036.MI. MY NOTES ASK YOUR TEACHER SCALC8 6.2STAR.072. MY NOTES ASK YOUR TEACHER Differentiate the function. y = tan(ln(ax + b)) y' = 2. [–/1 Points] DETAILS Find an equation of the tangent line to the following curve at the given point. 3. [–/1 Points] DETAILS Differentiate the function. y = x4 cos(x) y' = 4. [–/1 Points] DETAILS Evaluate the integral. Use C for any needed constant. 5. [–/1 Points] DETAILS SCALC8 6.6.023. MY NOTES ASK YOUR TEACHER SCALC8 6.6.067. MY NOTES ASK YOUR TEACHER MY NOTES ASK YOUR TEACHER Find the derivative of the function. y = (tan−1(5x))2 y' = 6. [–/1 Points] DETAILS Evaluate the integral. (Use C for the constant of integration.) t5 1 − t12 7. [–/1 Points] dt DETAILS SCALC8 6.8.043. Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x sin(8?/x) x→∞ 8. [–/1 Points] DETAILS SCALC8 7.1.011. Evaluate the integral. (Use C for the constant of integration.) t3 ln(t) dt MY NOTES ASK YOUR TEACHER [–/1 Points] 9. DETAILS SCALC8 7.2.025. MY NOTES ASK YOUR TEACHER MY NOTES ASK YOUR TEACHER MY NOTES ASK YOUR TEACHER MY NOTES ASK YOUR TEACHER Evaluate the integral. (Use C for the constant of integration.) 16 tan4(x) sec6(x) dx 10. [–/1 Points] DETAILS SCALC8 7.2.001.MI. Evaluate the integral. (Use C for the constant of integration.) 7 sin2(x) cos3(x) dx 11. [–/1 Points] DETAILS SCALC8 7.3.503.XP. Evaluate the integral. (Use C for the constant of integration.) dx 2 x + 25 12. [–/1 Points] DETAILS SCALC8 7.4.009. Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 17x + 3 (4x + 1)(x − 1) dx 13. [–/2 Points] DETAILS SCALC8 7.8.011. MY NOTES ASK YOUR TEACHER MY NOTES ASK YOUR TEACHER MY NOTES ASK YOUR TEACHER Determine whether the integral is convergent or divergent. x2 ∞ 5 + x3 0 dx convergent divergent If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.) 14. [–/2 Points] DETAILS SCALC8 7.8.019. Determine whether the integral is convergent or divergent. 0 ze6z dz −∞ convergent divergent If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.) 15. [–/1 Points] DETAILS Find the exact length of the curve. y= x3 3 + 1 4x , 1≤x≤3 SCALC8 8.1.011. 16. [–/1 Points] DETAILS SCALC8 11.3.021. MY NOTES ASK YOUR TEACHER MY NOTES ASK YOUR TEACHER Determine whether the series is convergent or divergent. ∞ n=2 4 n ln(n) convergent divergent 17. [–/1 Points] DETAILS SCALC8 11.6.003. Determine whether the series is absolutely convergent, conditionally convergent, or divergent. ∞ n=0 (−1)n 6n + 1 absolutely convergent conditionally convergent divergent 18. [–/2 Points] DETAILS SCALC8 11.8.006. MY NOTES Find the radius of convergence, R, of the series. ∞ R= n=1 (−1)nxn n3 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) I= ASK YOUR TEACHER 19. [–/4 Points] DETAILS SCALC8 11.9.005.MI.SA. MY NOTES ASK YOUR TEACHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Find a power series representation for the function. Determine the interval of convergence. (Give your power series representation centered at x = 0.) f(x) = 20. [–/1 Points] 9 2−x DETAILS SCALC8 10.4.007. MY NOTES Find the area of the shaded region. r = 4 + 3 sin(?) Submit Assignment Home Save Assignment Progress My Assignments Request Extension ASK YOUR TEACHER Copyright © 1998 - 2021 Cengage Learning, Inc. All Rights Reserved TERMS OF USE PRIVACY 19. [0/4 Points] DETAILS PREVIOUS ANSWERS SCALC8 11.9.005.MI.SA. MY This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Find a power series representation for the function. Determine the interval of convergence. (Give your power series representation centered at x = 0.) f(x) = 24 Step 1 We wish to express f(x) = 9 2-x in the form 1-7 and then use the following equation. *E 9 X Find a power series representation for the function. Determine the interval of convergence. (Give your power series representation centered at x = 0.) 9 F(x) 2-X Step 1 We wish to express f(x) 9 in the form 2-X 1 1- and then use the following equation. = 1-r Σ 2 n=0 Step 2 Factor a 9 from the numerator and a 2 from the denominator. This will give us the following. F(x) 2 - x 1 = Find a power series representation for the function. Determine the interval of convergence. (Give your power series representation centered at x = 0.) f(x) 9 2-X Step 1 We wish to express f(x) = 9 in the form 2-X 1 1 - and then use the following equation. 1 1-r Σ 2 n = 0 Step 2 Factor a 9 from the numerator and a 2 from the denominator. This will give us the following. F(x) = 9 2-X 2 ? ON Step 3 Now, we can user= in -- ?r. n=0 Therefore, f(x) -:(-e)-3 Step 2 Factor a 9 from the numerator and a 2 from the denominator. This will give us the following. F(x) = 2 9 2-X 9 = 1- Step 3 Now, we can user= =Ž in - - §. n=0 9 Therefore, F(x) = 4-0)- EO 9x" 2(n+1) 9," 21+1 Step 4 We know that 1-r :- " has interval of convergence (-1, 1). This means the series converges for n = 0 Irl < 1. Therefore, the series f(x) = 9x 2n + 1 will converge when