MATH 155 Calculus I Spring 2015 Catalog Data: Objective: Goals: MATH 155 Calculus I (4-0) Credit 4. Limits; derivatives; differentiation of algebraic, trigonometric, exponential and logarithmic functions; applications of derivatives; integration; applications of integrals to area, volume and work. Prerequisites: Grade of C or better in MATH 126 and MATH 128; or ACT math score of 28 or higher. This course is designed to give students in mathematics, engineering and the sciences the basic concepts of limits, continuity, differentiation and integration. Upon successful completion of the course the student should be able to: 1. Find the limit of a function at a given number and limits at infinity 2. Find infinite limits 3. Discuss the continuity and differentiability of a given function 4. Find the first and second derivative of a function and use this information to analyze the function and sketch its graphs. 5. Apply derivative analysis to optimization problems, linearization problems and approximation problems. 6. Integrate basic functions and be able to use some techniques of integration. 7. Use integration in applications, including finding the area between curves, finding the volume of solids of revolution, and finding the work done on a system. Textbook: James Stewart, Calculus, Seventh Edition, Brooks/Cole Publishing Company, 2011. Chapter 1, sections 4,5,6,8 Chapter 2, sections 1,2,3,4,5,6,7,8,9 Chapter 3, sections 1,2,3,4,5,7,8,9 Chapter 4, sections 1,2,3,4,5 Chapter 5, sections 1,2,3,4,5 Chapter 6, sections 1,2,3,4,5,6 Instructor: Susan Barton, Ph.D., Professor of Mathematics Email: Sbarton@mix.wvu.edu Office/Phone: Engineering Lab Building 101H / 304-442-3297 Office Hours: MWF 9 10 and 2 3 (Wed 9am office hours are in the Math Lab) TR 8 10 (Thurs 9am office hours are in the Math Lab) Class: MTWRF 12:00 12:50 in Engr 514 Method: This is a lecture based course meeting 5 times a week. Supporting documents may be community.wvu.edu/~smb031 Tutoring: You may stop by my office any time, office hours are just the times I promise to be there. You may also make an appointment. Additional help: The Math Lab (Elab 107) is open from 8am to 4:30pm for quiet study. A schedule will be posted before the second week of class detailing the hours that tutoring is available. Free tutoring is also available through the Student Success Center (located on the third floor of Vining Library) and Student Support Services (located in Old Main 308/309). Calculators: Graphing calculators will be forbidden on most exams and quizzes. No phone may be used as a calculator.
Course Grade: Semester grades are made up of the following components. 4 Best Quizzes 25 points each 100 points total 4 Exams 100 points each 400 points total 1 Participation Grade 50 points 50 points total 1 Homework Grade (scaled) 100 points 100 points total 1 (Cumulative) Final Exam 200 points 200 points total Total 850 points A:90-100%, B:80-90%, C:70-80%, D:60-70%, F:0-60% Borderline grades may be improved based on performance and grade distribution of the whole class. Explanation of Grading and Assessment: Quizzes/Homework: There will be at least 6 quizzes for 25 points apiece. I will keep the best 4. This thus counts for 100 points (about 12% of your course grade). Homework will be assigned in two parts. Exercises you need to do to learn the material (listed at the end of the syllabus) and homework that I will grade (assigned in class). Graded homework will be worth about 12% of your final grade. Attendance/Participation: One point will be assigned for every day that you are in the room when attendance is taken AND you do not use your cell phone or other distracting device in class. This is a participation point and may be taken away at the instructor s discretion. The result will be scaled to 50 points (about 6% of your grade). Exams: Four in class hourly tests, each worth 100 points (about 12%) of your course grade. Final Exam: A comprehensive final exam worth 200 points (about 24%) of the course grade will be given. NOTE: Only excused absences will enable a student to make up exams. This means that you must have an excuse for the day of the missed exam and every subsequent day until you have made it up. In general quizzes may not be made-up Academic Integrity: The integrity of the classes offered by any academic institution solidifies the foundation of its mission and cannot be sacrificed to expediency, ignorance, or blatant fraud. Therefore, I will enforce rigorous standards of academic integrity in all aspects and assignments of this course. For the detailed policy of West Virginia University regarding the definitions of acts considered to fall under academic dishonesty and possible ensuing sanctions, please see the Student Conduct Code http://studentlife.wvu.edu/office_of_student_conduct/student_conduct_code. Should you have any questions about possibly improper research citations or references, or any other activity that may be interpreted as an attempt at academic dishonesty, please see me before the assignment is due to discuss the matter. Inclusivity: The West Virginia University community is committed to creating and fostering a positive learning and working environment based on open communication, mutual respect, and inclusion. If you are a person with a disability and anticipate needing any type of accommodation in order to participate in this class, please advise me and make appropriate arrangements with the Office of Disability Services (293-6700). For more information on West Virginia University's Diversity, Equity, and Inclusion initiatives, please see http://diversity.wvu.edu."
Detailed list of topics covered: 1. Limits and Rates of Change a) The Tangent and Velocity Problems (1 day) b) The Limit of a Function (l day) c) Calculating Limits using the Limit Laws (l day) d) The Precise Definition of a Limit (l day) e) Continuity (2 days) f) Tangents, Velocities, and Other Rates of Change (l day) 2. Derivatives a) Derivatives (l day) b) Differentiation Formulas (2 days) c) Rates of Change in the Natural and Social Sciences (1 day) d) Derivatives of Trigonometric Functions (l day) e) The Chain Rule (1 day) f) Implicit Differentiation (1 day) g) Higher Derivatives (1 day) h) Related Rates (2 days) i) Differentials and Linear Approximations (1 day) 3. The Mean Value Theorem and Cure Sketching a) Maximum and Minimum Values (1 day) b) The Mean Value Theorem (2 days) c) Monotonic Functions and the First Derivative Test (1 day) d) Concavity and Points of Inflection (1 day) e) Limits at Infinity; Horizontal Asymptotes (1 day) f) Curve Sketching (2 days) g) Graphing with Calculus and Calculators (1 day) h) Applied Maximum and Minimum Problems (2 days) i) Newton s Method (1 day) j) Antiderivatives (1 day) 4. Integrals a) Sigma Notation (1 day) b) Area (1 day) c) The Definite Integral (2 days) d) The Fundamental Theorem of Calculus (2 days) e) The Substitution Rule (1 day) 5. Applications of Integration a) Areas between Curves (1 day) b) Volume (2 days) c) Volumes by Cylindrical Shells (1 day) d) Work (2 days) e) Average Value of a Function (1 day) 6. Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions a) Inverse Functions (1 day) b) Exponential Functions and Their Derivatives (2 day) c) Logarithmic Functions (1 day) d) Derivatives of Logarithmic Functions (2 days) e) The Logarithmic Defined as an Integral (1 day) f) Derivatives of Inverse Trigonometric Functions (2 days)
The professor reserves the right to make any necessary adjustments to this syllabus. Tentative Syllabus Monday Tuesday Wednesday Thursday Friday 12 Intro/1.5 13 1.5 14 1.6 15 1.6 16 1.8 19 20 1.8 21 Quiz 22 1.4 23 2.1 26 2.2 27 2.3 28 Quiz 29 2.3 30 2.4 Feb 2 2.4 3 Review 4 Exam 1 1.4-2.4 5 2.5 6 2.5/2.6 9 2.6 10 2.7 11 Quiz 12 2.8 13 2.8 16 2.9 17 3.1 18 Quiz 19 3.2 20 3.3 23 3.3/3.4 24 Review 25 Exam 2 2.5-3.3 Mar 2 3.5/3.7 3 3.7 4 Exam 3 pt.1 section 3.4/3.5 26 3.4/3.5 27 3.5 5 3.8 6 3.9 9 4.1 10 4.2 11 Quiz 12 4.2 13 4.3 16 4.3/4.4 17 Review 18 Exam 3 pt. 2 3.7-4.3 19 4.4 20 4.5 23 24 25 26 27 30 5.1 31 5.1/5.2 Apr 1 Quiz 2 5.2 3 6 5.3 7 5.3 8 Quiz 9 5.4 10 5.4 13 5.5 14 Review 15 Exam4 4.4-5.5 16 6.1 17 6.2 20 6.2 21 6.3 22 Quiz 23 6.3/6.4 24 6.4 27 6.5 28 6.6 29 6.6 30 Review May 1 Review
Suggested Exercises: Note: eoo means every other odd. 1.4 1, 3, 5, 7 1.5 1, 3, 7, 9, 15, 19, 21, 23, 29, 31, 33, 35, 41 1.6 1, 5, 9, 11-31 odd, 35-41 odd, 45, 47, 57 1.8 1-7 odd, 11-43 odd, 51, 53 2.1 1, 3, 7, 11, 15, 17-23 odd, 31-39 odd, 43 2.2 1-13 odd, 19, 21, 25, 29, 35, 37, 41, 43 2.3 1-45 odd, 51-67 odd, 75-81 odd, 93, 95 2.4 1-25 odd, 29, 33, 35, 37, 39-47 odd, 2.5 1-53 eoo, 59, 61, 73, 75, 79 2.6 1-31 odd, 35, 37, 49, 59 2.7 1-15 odd 2.8 1-31 odd, 37, 41, 43 2.9 1, 3, 11-27 odd, 31, 35 3.1 1-41 eoo, 45-56 eoo, 64 3.2 1-11 odd, 15-31 odd 3.3 1-41 odd, 49, 53 3.4 1-29 odd, 33-37 odd, 41, 45, 53, 55 3.5 1-39 eoo, 45, 49, 51, 3.7 1-17 odd, 21, 23, 29, 33-37 odd, 49, 3.8 1-7 odd, 15, 17, 19, 29 3.9 1-47 odd, 51-61 odd, 71 4.1 1, 3, 5, 17, 19 4.2 1-11 odd, 17-25 odd, 33-39odd, 47, 55-59odd 4.3 3, 5, 7-37odd, 39, 47, 49, 65, 67 4.4 1-1-15 odd, 19-41odd, 47, 49, 53, 55, 57 4.5 1-51 odd, 55, 63 5.1 1-31 odd, 44 5.2 1-29 odd, 39, 45, 47, 49 5.3 1-25 odd, 31, 37, 39, 43 5.4 1-23 odd 5.5 1-9 odd, 13, 15, 17 6.1 1-27 odd, 35, 37 6.2 1-17 odd, 23-57 odd, 65-71 odd, 79-93 odd 6.3 1-67 odd 6.4 1-37 odd, 41-57 odd, 61, 71-81 odd, 6.5 1-15 odd 6.6 1-19 odd, 23-39 odd, 43, 45, 49, 59-69 odd Prepared January 2015