Spring 2019 MATH 131: Mathematical Concepts-Calculus

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1 Class time and location TR 11:10am-12:25pm in HELD 105 Learning Outcomes: Upon successful completion of this course, students will: Logically formulate mathematical variables and equations to quantitatively create mathematical models representing problems in everyday life. Recognize and construct graphs of basic functions, including polynomials, exponentials, logarithms, and trigonometric functions and use them to model real-life situations. Identify patterns in numeric data to calculate limits and derivatives of functions numerically. Compute limits of functions numerically, graphically, and algebraically. Justify whether a function is continuous or not using the mathematical definition of continuity. Compute derivatives using the limit definition of the derivative. Understand the derivative as a rate of change in order to quantitatively apply it to everyday life. For example, recognize that derivatives can be used to find the velocity and acceleration of an object given its position function. Compute derivatives of polynomials, rational, trigonometric, exponential, and logarithmic functions. Apply the product rule, quotient rule, and chain rule to take derivatives of compositions of functions. Compute the linear approximation of a function and use it in applications of approximation and error estimation. Investigate the relationship between a function and its first and second derivatives, and use the information obtained from its derivatives to identify pertinent information about the function. Find the local and absolute extrema of functions, including optimization applications such as minimizing the cost of fencing in a particular area of land. Compute antiderivatives and understand the concept of integration as it relates to area. Apply the definite integral to quantitatively determine solutions to problems in everyday life including areas between curves, average value of a function, and total distance traveled. Recognize and appreciate the derivative (rate of change) and the definite integral (accumulation of change) and utilize the Fundamental Theorem of Calculus as the bridge between the two. Apply the substitution method to compute integrals. Core Objectives: Critical Thinking Students will analyze a function and justify whether or not is continuous using the definition of continuity. Students will use inquiry to determine the best method for taking derivatives of complicated functions. Students will identify and categorize information about a function in order to construct a graph of its derivative. Students will apply calculus to find innovative ways to graph complicated functions without the aid of technology. Students will analyze and synthesize data and think creatively to develop mathematical models for optimization purposes. Students will examine how the Fundamental Theorem of Calculus connects differential and integral calculus. Communication Skills Students will symbolically relay mathematical information and concepts by creating variables and writing equations. Students will recognize, construct, and interpret graphs of basic functions. Students will write mathematical information symbolically to describe the behavior of functions Students will justify results that use mathematical definitions such as the definition of continuity. Students will explain verbally in class the connection between derivatives, rates of change, and slopes of tangent lines. Students will explain (both in writing and verbally) mathematical solutions to problems. Empirical and Quantitative Skills Students will evaluate limits numerically and use the information to draw conclusions about the behavior of a function. Students will calculate a derivative numerically and explain the result in the context of the problem. Students will manipulate empirical data to develop a mathematical model to use in an optimization problem and then apply calculus to find and interpret the optimal solution. Students will apply the Fundamental Theorem of Calculus to quantitatively compute the accumulated change of a quantity. 1

2 Instructor Information Name David Manuel Address Office Blocker 243D Office Hours M 2-4pm; TW 3-4pm OBA Course Page Phone Math Department: (There is no phone in my oce, so is a better way to reach me) Required Materials TEXTBOOK : Single Variable Calculus: Concepts & Contexts, by Stewart, 4th edition. The textbook is available in different formats, and there are a variety of purchasing options available (course specific access or Cengage Unlimited). Purchase can be made through the local bookstores or through the online system WebAssign. Starting on the first day of classes, you will be granted access for a trial period while you determine the appropriate purchasing option for you. WEBASSIGN ACCESS: WebAssign will be used for homework in this class. In order to use WebAssign, you must purchase access. For access purchasing information and options, please visit CALCULATOR: A TI-83 (any version), TI-84 (any version) or the TI-Nspire (non-cas version) calculator is REQUIRED, and you must bring your calculator to each class. If you need to use a calculator other than those listed, it MUST not perform symbolic mathematics and you must have my permission to do so. I will be demonstrating calculator techniques using the TI-84. You must bring your calculator to every class period. You may not share calculators during exams or quizzes. TEXAS A&M STUDENT ID: Bring your student ID to each class. TENTATIVE COURSE TOPICS AND CALENDAR OF ACTIVITIES Week of Topic Sections 1/14 Functions, Models, Transformations of Functions 1.1, 1.2, 1.3 1/21 Exponential Functions, Inverses and Logarithmic Functions, 1.5, 1.6, 2.1 Approximating Slopes of Tangent Lines 1/28 Introduction to Limits, Calculating Limits, Continuity 2.2, 2.3, 2.4 2/4 Limits Involving Innity Exam 1 covering , 1.5, 1.6, , Review, Exam 1 2/11 Derivatives and Rates of Change, Limit Denition of Derivatives, 2.6, 2.7, 2.8 Slope Graphs and Antiderivatives 2/18 Derivatives of Polynomials and Exponential Functions, 3.1, 3.2, 3.3 Product and Quotient Rules, Derivatives of Trig Functions 2/25 Chain Rule, Derivatives of Log Functions, Applications in 3.4, 3.7, 3.8 Natural and Social Sciences 3/4 Linear Approximations and Dierentials, 3.9, Review, Exam 2 Exam 2 covering , , /11 SPRING BREAK 3/18 Local and Absolute Extrema, 4.2, 4.3, 4.6 Curve Sketching, Optimization 3/25 Antiderivatives, Approximating Area, 4.8, 5.1 4/1 The Denite Integral, Evaluating Denite Integrals, 5.2, 5.3, 5.4 Fundamental Theorem of Calculus 4/8 Substitution 5.5, Review 4/15 Exam 3 covering 3.9, 4.2, 4.3, 4.6, 4.8, , Area Between Curves Exam 3, 6.1 4/22 Average Value of Functions, Applications to Biology 6.5, 6.7, Review 4/29 Comprehensive Final Exam covering FINAL EXAM all previous sections as well as 6.1, 6.5, and 6.7 2

3 GRADING POLICIES The course grading will be based on the tables below. At the end of the semester, you will receive the grade you earned according to the scale given. Due to FERPA privacy issues, I cannot discuss grades over or phone. If you have a question about your grade, please come see me in person. GRADE BREAKDOWN Activity Date Percentage Homework Weekly 10% Quizzes Weekly 10% Exam I ( , 1.5, 1.6, ) Feb 7 20% Exam II ( , , ) Mar 7 20% Exam III (3.9, 4.2, 4.3, 4.6, 4.8, ) Apr 16 20% Final Exam May 2 20% TOTAL 100% GRADING SCALE Range Grade 90 Avg A 80 Avg < 90 B 70 Avg < 80 C 60 Avg < 70 D Avg < 60 F GRADE APPEAL POLICY: Any question regarding grading must be done before the class day after an assignment is returned to you, or NO change will be made (except for adding mistakes). HOMEWORK: All graded homework will be done online using WebAssign. These will be due every Monday at 11:55pm over the previous week s (completed) sections. On exam weeks, a section not completed the previous week will be due on Wednesday 11:55pm (BEFORE a Thursday s exam). In addition, suggested homework is posted on the MATH 131 course homepage. These problems are for practice and will not be handed in; however, quiz and exam questions may be similar to suggested homework problems. (NOTE: If you purchase a student solution manual, it is recommended that you do not open it until AFTER you have attempted the question on your own!) QUIZZES: Each Tuesday (except the week of and week after an exam), you will receive a take-home quiz over the concepts from the online homework assignments due the previous night. The quiz will be due at the beginning of class Thursday. You may not receive help from anyone except me, but you may use notes and calculators. In addition, there will be Prep Work assignments which will count as quiz grades. These will be due at the BEGINNING of class on the assigned deadline days to prepare for that day s lecture. These will be mainly graded on attempt. EXAMS There will be three in class exams during the semester. You must bring a picture id (student id or driver s license) to the exams. More information regarding exams will be given closer to the first exam day. The tentative exam schedule is as follows: Exam I: Feb 7 Exam II: Mar 7 Exam III: Apr 16 FINAL EXAM The final exam will be comprehensive and is required for all students. If your final exam grade is higher than your lowest test grade, the grade on your final will replace that test grade in the final grade calculation. The final exam is on Thursday, May 2 3-5pm in HELD 105 (You can refer to for the University nal exam schedule) 3

4 ATTENDANCE AND MAKE-UP POLICIES Attendance is essential to complete this course successfully. Excused Absences: University student rules concerning excused and unexcused absences, as well as makeups, can be found at In particular, make-up exams and quizzes or late homework will NOT be allowed unless a University approved reason is given to me in writing. Notification before the absence is required when possible. Otherwise (e.g. accident, or emergency), you must notify me within 2 working days of the missed exam, quiz, or assignment to arrange a makeup. In all cases where an exam/quiz/assignment is missed due to an injury or illness, whether it be more or less than 3 days, I require a doctor s note. I will not accept the University Explanatory Statement for Absence from Class form. Further, an absence due to a non-acute medical service or appointment (such as a regular checkup) is not an excused absence. Make-up Exams: If you have a written, University approved excused absence for missing an exam, you will be expected to make-up your exam at the next available opportunity according to the departmental posted schedule. If you do not complete your make-up exam on the following scheduled make-up day, then you must have a University approved excused absence (in writing and in addition to the regular exam day you missed). Procedure/Format: When you go to take your make-up exam, you will need to bring your calculator, picture ID, and pencil. Also, in accordance with University Student Rule 7.3, you MUST notify me in writing (or ) within 2 working days of the original exam you missed if you have a University approved excused absence and want to take a make-up exam. You will be required to provide me with your written documentation for your excused absence. Late work policy: Late work will be accepted up to the start of the next class (for a Tuesday deadline) or by 5pm Friday (for a Thursday deadline). If you do not have a University approved excused absence, you will receive a 30% penalty unless you have also submitted an electronic version no later than the official deadline (day and time-note that I will not accept only electronic submissions). If you have a University approved excused absence, you must submit a copy of your documentation with your late work to avoid penalty. I will be dropping the lowest 3 quiz grades (1.5 Prep Work will NOT be dropped). ACADEMIC INTEGRITY An Aggie does not lie, cheat, or steal, or tolerate those who do. Upon accepting admission to Texas A&M University, a student immediately assumes a commitment to uphold the Honor Code, to accept responsibility for learning, and to follow the philosophy and rules of the Honor System. Students will be required to state their commitment on examinations, research papers, and other academic work. Ignorance of the rules does not exclude any member of the TAMU community from the requirements or the processes of the Honor System. Copying work done by others, either in-class or out-of-class, is an act of scholastic dishonesty and will be prosecuted to the full extent allowed by University policy. Collaboration on assignments, either in-class or out-of-class, is forbidden unless I grant permission. If you cheat on an assignment, you will receive a zero. Also, you will be reported to the University. Another form of cheating is typing formulas in the calculator or using programs that give you an advantage over classmates. If I catch anyone cheating this way, you will get a zero on the assignment and be reported to the University for cheating. For additional information please visit 4

5 AMERICANS WITH DISABILITIES ACT: The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services, in Student Services at White Creek, or call For additional information visit If you require accommodations, please see me as soon as possible so that we can make sure you have the necessary paperwork in order. I must have written documentation of the necessary accommodations at least one week before an exam in order to provide accommodations. COPYRIGHT POLICY: All printed materials disseminated in class or on the web are protected by Copy- right laws. One copy (or download from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited. ADDITIONAL HELP & PREPARING FOR EXAMS HELP SESSIONS Help sessions are an opportunity for you to ask questions and get help with your homework. These sessions are led by students, where you may come and go, as your schedule allows. Once determined, the schedule will be announced in class, posted on our course webpage, and additionally posted at WEEK IN REVIEW In addition, the help session staff will run a Week in Review problem-solving session on Monday nights which will cover the material taught in class the previous week. Old Week-in-Reviews which I conducted are posted on my webpage (problems, answers, and detailed solutions): 5

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