MATH 111: Calculus I Spring 2021 Coordinated Course ..., Exercises of Calculus

Download MATH 111: Calculus I Spring 2021 Coordinated Course ... and more Exercises Calculus in PDF only on Docsity! MATH 111: Calculus I Spring 2021 Coordinated Course Syllabus NJIT Academic Integrity Code: All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams. Under the University Code on Academic Integrity, students are obligated to report any such activities to the Instructor. DMS Online Exam Policy Spring 2021: Exams will be proctored using both Respondus LockDown Browser+Monitor and Webex. Students will be required to join a Webex meeting from their phone with their cameras on, and to access the exam through LockDown Browser on a Mac or Windows PC with webcam. Students must follow all instructions related to environment checks and camera positioning. Please be sure you read and fully understand our DMS Online Exam Policy. COURSE INFORMATION Course Description: Topics include limits, differentiation, applications of differentiation, and integration. Number of Credits: 4 Prerequisites: MATH 110 or placement by performance on standardized entrance examinations. Course-Section and Instructors Course-Section Instructor Math 111-002 Professor S. Erfani Math 111-004 Professor C. Castillo Math 111-006 Professor R. Dandan Math 111-008 Professor E. Dupay Math 111-010 Professor S. Mahmood Math 111-012 Professor S. Mahmood Math 111-018 Professor I. Peltekov Math 111-020 Professor S. Erfani Math 111-024 Professor E. Dupay Math 111-104 Professor D. Aytas Office Hours for All Math Instructors: Spring 2021 Office Hours and Emails Required Textbook: Title Thomas' Calculus: Early Transcendentals Author Hass, Heil, and Weir Edition 14th Publisher Pearson ISBN # 978-0134768496 University-wide Withdrawal Date:The last day to withdraw with a W is Monday, April 5, 2021. It will be strictly enforced. STUDENT RESPONSIBILITIES Read and understand the syllabus Adhere to all policies and procedures Report conflicts and/or special circumstances in a timely manner Report any instances of violations of Academic Integrity to your Instructor Communicate directly with your Instructor on ALL course-related matters, including material, procedures, policies and exams. NOTE: Do not attempt to contact other instructors or the course coordinator – you will not get a response. All course information will be communicated to you directly by your instructor. Effectively manage time and devote sufficient time to succeeding in this course Keep track of your grades Make use of all resources available to help you learn Be respectful of peers and your instructor Accept responsibility for your grades – requests for extra credit opportunities will be denied COURSE GOALS Course Objectives Students should (a) learn about limits and their central role in calculus, (b) learn about derivatives and their relationship to instantaneous rates of change, (c) understand many practical applications of derivatives, (d) gain experience in the use of approximation in studying mathematical and scientific problems, (e) learn about integrals: their origin in the area problem and their relationship to derivatives. Students should gain an appreciation for the importance of calculus in scientific, engineering, computer, and other applications. Students should gain experience in the use of technology to facilitate visualization and problem solving. Course Outcomes Students have improved logical thinking and problem-solving skills. Students have a greater understanding of the importance of calculus in science and technology. Students are prepared for further study in mathematics as well as science, engineering, computing, and other areas. Course Assessment: The assessment of objectives is achieved through homeworks, quizzes, and common examinations with common grading. Course Outline Lecture Section Topic Assignment in MyMathLab 1 2.1 Rates of Change and tangents to Curves 1, 5, 9, 13, 25 2 2.2 Limit of a Function and Limit Laws 1, 2, 13, 19, 22, 25, 31, 33, 35, 41, 47, 49, 53, 57, 63, 79, 81 3 2.4 One Sided Limits 3, 5, 9, 13, 15, 17, 27, 29, 31, 37, 41 4 2.5 Continuity 3, 5, 7, 15, 17, 21, 25, 27, 29 5 2.5/2.6 Continue Continuity; start Infinite limits Section 2.5: 35, 37, 39, 41, 43, 45, 49, 55, 61 6 2.6 Limits Involving Infinity; Asymptotes 7, 9, 11, 23, 25, 27, 31, 33, 43, 45, 49, 53, 63, 67, 89, 91, 105 7 3.1 Tangents and Derivatives at a Point 11, 13, 15, 17, 21, 35 8 3.2 The Derivative as a Function 1, 3.5, 13, 26, 33, 39, 41 9 3.3 Differentiation Rules 5, 7, 19, 25, 31, 39, 41, 43, 45 10 REVIEW FOR EXAM #1 11 3.3 Differentiation Rules 47, 53, 55, 57, 59, 62, 63, 74 12 3.4 Derivatives as a Rate of Change 1, 5, 7, 10, 13, 17, 23, 25, 31 13 3.5 Derivatives of Trig Functions 2, 12, 15, 16, 19, 26, 29, 33, 35, 51, 55, 61, 63 14 3.6 The Chain Rule 5, 17, 23, 25, 29, 33, 35, 39, 43, 47, 49, 51, 61, 63, 65, 67 15 3.6/3.7 Continue Chain Rule; start Implicit Differentiation Section 3.6: 71, 77, 81, 83, 85, 89, 97, 101 16 3.7/3.8 Continue Implicit Differentiation; start Derivatives of Inverses and Logs Section 3.7: 1, 7, 11, 15, 16, 17, 19, 23, 33, 39, 41 17 3.8 Derivatives of Inverse and Log Functions 7, 9, 13, 21, 24, 29, 31, 35, 39, 43, 57, 61, 63, 65, 69, 83, 89, 95 18 3.9 Inverse Trig Functions 5, 11, 21, 23, 31, 33, 34, 37, 41, 65 19 3.1 Related Rates 7, 11, 15, 17, 21, 23, 25 20 3.10/3.11 Continue Related Rates; Start Linearization Section 3.10: 27, 31, 33, 37, 40, 41 21 REVIEW FOR EXAM #2 22 3.11/4.1 Continue Linearization and Differentials; start Extreme Values Section 3.11: 5, 11, 13, 19, 31, 35, 41, 51, 53, 59 23 4.1 Extreme Values of Functions 7, 25, 29, 33, 35, 39, 41, 47, 49, 51, 57, 59, 78 24 4.2 The Mean Value Theorem 3, 4, 5, 6, 11, 13, 16, 21 25 4.2/4.3 Continue Mean Value Theorem; Start Monotone Functions and the First Derivative Test Section 4.2: 31, 35, 37, 41, 45, 47, 49, 51, 56 26 4.3/4.4 Continue the First Derivative Test; start Concavity and Curve Sketching Section 4.3: 11, 13, 21, 29, 37, 41, 43, 51, 63, 75, 77 27 4.4 Concavity and Curve Sketching 7, 13, 19, 25, 28, 31, 35, 39, 43, 45, 99, 117, 127 28 4.5 Indeterminate Forms & L’Hopitals Rule 7, 9, 11, 15, 19, 21, 23, 29, 33, 37, 41, 44, 46, 49 29 4.5/4.6 Finish L’Hopitals; Start Applied Optimization Section 4.5: 51, 55, 57, 58, 63, 65, 67, 71, 79 30 4.6 Applied Optimization 4, 7, 9, 11, 12, 14, 23, 29, 44, 45, 57, 62 31 4.7 Newton’s Method 1, 2, 5, 23 32 4.8 Antiderivatives 5, 11, 19, 35, 37, 39, 41, 45, 47, 54, 59, 61, 69, 97, 101, 104, 107, 113, 100 33 5.1 Area and Estimating with Finite Sums 1, 5, 8, 9, 11 34 5.2 Sigma Notation and Limits of Finite Sums 7, 9, 17, 25, 29, 37, 42, 43, 47 35 5.3 Definite Integral 1, 9, 13, 21, 22, 33, 42, 45 36 REVIEW FOR EXAM #3 37 5.3/5.4 Continue Definite Integrals; start Fundamental Theorem of Calculus Section 5.3: 57, 59, 61, 71, 79, 88 38 5.4 Fundamental Theorem of Calculus 7, 9, 13, 15, 21, 23, 27, 30, 41, 47, 53, 55, 57, 60, 61, 63, 77, 79 39 5.5 Indefinite Integrals and Substitution Method 11, 15, 18, 20, 21, 23, 25, 26, 27, 29, 33 40 5.5/5.6 Finish Indefinite Integrals and Substitution Method; start Substitution and Area Between Curves Section 5.5: 37, 43, 47, 53, 55, 59, 63, 65, 79 41 5.6 Substitution and Area Between Curves 3, 12, 17, 19, 27, 29, 33, 39, 53, 66, 71, 77, 83, 87, 93, 97, 99, 102, 115 42 REVIEW FOR FINAL FINAL EXAM Updated by Professor J. Bechtold - 2/4/2021 Department of Mathematical Sciences Course Syllabus, Spring 2021