Math 402 Calculus III Folsom Lake College Spring 2019 Monday&Wednesday section number 20571 Course Meetings: Mon./Wed. 8:00am 10:20am Aspen Hall 208 (FL1) Folsom Main Campus Instructor: Kevin Pipkin Office: Aspen Hall 143 (FL1) E-mail: pipkink@flc.losrios.edu Phone: (916) 608-6674 Canvas: https://canvas.losrios.edu Website: www.flc.losrios.edu/~pipkin Text: Calculus Early Transcendental Functions 4 th ed, by Larson, Hostetler, Edwards. (Publisher: Brooks/Cole) Bring the text to each class meeting. (See my website s main page for a picture and ISBN information.) Office Hours: Appointments outside of these hours can sometimes be made. Please ask. Monday Tuesday Wednesday Thursday 10:30am 11:45am 10:30am 11:45am 10:30am 11:45am 10:30am 11:45am You should bring in your notes and problems you have been working on when you come to office hours. There is no substitute for practicing. This is an expectation. Office hours should be used to ask for assistance on specific homework problems, questions from the text, or specific information from the lecture. Learning math is a hands on task. Office hours are not for repeating a lecture. Course Description: This course extends the first year Calculus concepts of limits, derivatives, and integrals to vector-valued functions and functions of more than one variable. Topics covered will include three-dimensional analytic geometry and vectors, partial derivatives, multiple integrals, line integrals, surface integrals, and the theorems of Green, Gauss (Divergence), and Stokes. Many applications of the calculus will be included. Prerequisite: Minimum C or better in Math 401 (2 nd semester Calculus) or show proof of passing the Advanced Placement Calculus BC exam with a score of 3 or better. Page 1
Course Objective/Requirements: This is a five-unit course that meets for 5 hours of lecture each week. Credit for this course is degree applicable and transferable. Calculus is a required sequence for Math, Science, Computer, and Engineering majors. It may also a requirement for some other majors. Calculus takes the previously learned concepts (arithmetic, algebra, functions, trigonometry, exponents, logarithms, conics, sequences, etc.) and allows us to utilize them in a changing environment. In addition to this, you are beginning to study mathematics in a more abstract way. Proving and deriving concepts will be a regular part of our math diet. Students need to be adept at nearly every concept from the prerequisite chain of courses up through Math 401. Very little, if any, time will be spent going over concepts from previous courses. You should expect to spend a minimum of 10 hours per week on practice and study outside of class in order to be successful in learning the material. Students are expected to read the text and should regularly be comparing the text to class notes. Do not expect to be able to ask homework questions during class time so take advantage of my office hours, studying with your peers, and the tutoring center. For many concepts, there is not one unique method for developing/deriving the material. You will be accountable for the methods covered in class unless otherwise indicated. Class Policy: You should act like you are in a institution of higher learning. Know the syllabus. You are expected to behave in a courteous manner both toward your classmates and me at all times. Profanity is unacceptable. I do not allow any electronic devices such as phones, smart devices, headsets, etc. in the classroom. Tablet devices may be used for note taking but may not be used for personal communications, games, or other activities that may distract you or others from the lecture itself. If you are behaving in a manner that inhibits me from teaching or anyone around you from learning, you will be asked to leave and disciplinary action will be pursued. I encourage participation in class and may call on individuals to help solve problems or answer questions. Please show respect for those volunteering to help in class and allow others to have the same opportunity. Please do not distract other students or the instructor from the task at hand. Attendance: FLC policy states that you may be dropped after missing 6% of the class meeting time. For this course, if you have missed more than 2 days of class, you may be dropped from the course at my discretion. It is the student s responsibility to find out about any missed announcements and lecture material. You must get notes from other students in class and inquire with them about what was missed. Arriving more than 5 minutes late or leaving the class early can be constituted as an absence. First Lecture: Wednesday, January 23: Fri. & Mon. 2/15 & 2/18: College is closed. (President s Weekend Holiday) April 15-21: College is closed. (Spring Break Holiday) Sunday, April 21 is the last day to withdraw from the course and receive only a W. Last Lecture Day: Wednesday, May. 15. (Last regular lecture day for the semester. Finals begin after this.) Exam 2 (Final): Wednesday, May 22 (7:00am 8:50am) Calculators: Calculators will not be allowed on exams and quizzes as this will fundamentally alter the curriculum. Scientific calculators may be required for some assignment problems but only to give approximate solutions. Students should not have to purchase a calculator for these few assigned problems because there are numerous online and free applications available. Graphing technology may be used in class from time to time to introduce or demonstrate concepts but you are not required to have a graphing calculator. Free graphing software and links to helpful online sources will be available on Canvas that can be used if you wish to spend additional time outside of class on these introductory concepts. Page 2
Homework: (All graded work is to be done in pencil.) A list of assigned problems is provided to all students on Canvas. Hard copies will be made available on request. Assignments based on the required homework problems will be posted in class. These will be collected periodically and are due at the beginning of class unless otherwise noted. Assignments and may include problems not found in the textbook. All assignments and due dates will be announced in class. The required problems have been chosen to highlight key concepts of the course. It is up to you, the student, to put in enough practice and preparation for the exams. These required problems will not be sufficient for this. The type of feedback for each assignment may vary. In addition to the required homework, there will be additional recommended practice problems assigned for each section to help guide you as you practice and study. These will not be collected but are a critical component of your study and preparation for exams and should also be attempted before coming to office hours. I will not accept late work. Homework will be considered late after the first 5 minutes of class. I will drop the lowest homework assignment at the end of the semester to allow for illness, car or work issues, family emergencies, etc. You should work on assignments between each class meeting and well before they are due. It will be extremely difficult to keep up with the class if you do not. I may not be able to answer homework questions during class time so take advantage of my office hours and the tutoring center hours. Homework guidelines are listed later in this syllabus. Exams and Quizzes: (All graded work is to be done in pencil.) There are quizzes and exams scheduled (not counting the Final Exam) that cover chapters 11 15. The approximate dates are listed below. These dates are not likely to change but will be announced if they do. These are designed to meet the learning outcomes for the course. Calculators and student created notes will not be allowed on exams as this would fundamentally alter the design of the curriculum. Additional quizzes may not be announced. Come to class prepared. You must not only know the material, but also be able to work with it efficiently. Quizzes may not be made up. The Final Exam score will be used to replace a single missing quiz/exam with an equivalent percentage. This policy is to respond to situations such as being sick on a Quiz day, family or work emergency, or transportation issues. If you miss Exam 1, you must schedule a time to take a make-up before spring break. The timing of this is based on my availability. Quiz Ch. 11: 2/13 30 points (1 st 55 minutes of class) Exam 1 (Ch. 13-14.3): 4/03 100 points Quiz Ch. 12: 2/27 40 points (1 st hour of class) Exam 2 (14.4 Ch. 15): 5/22 100 points **On Quiz/Exam days, if you arrive early and wish to study more, you need to do so outside of the classroom. Once you come in to the classroom, you should get out your pencils/eraser; turn off and put away your phone. Exam 2: This exam is mandatory and cannot be made up. It is scheduled for Wednesday, May 22 from 7:00am 8:50am. Please mark your calendar now and be prepared for this date. The Exam 2 percentage may be used to replace a single missing Quiz. This policy is to respond to situations such as being sick, family or work emergencies, or transportation issues on a regular exam day. The course grade is based on your overall performance. Passing Exam 2 does not guarantee passing the course. Exam 2 will not be used to replace a low scoring exam or quiz. I will not return Exam 2 to students but will keep them through most of the next semester in case you wish to make an appointment to see it. Page 3
Grading: Letter grades will be calculated based on the following overall percentages: A: 90% - 100% B: 80% - 89% C: 70% - 79% D: 60% - 69% F: below 60% Scores will be weighted as follows: Exams & Quizzes 90% Exam 2: Wed. 5/22 7:00 am 8:50 am Homework 10% Your grade for the course is based on your performance in the entire course, not just the last exam. However, if your overall grade in the class rounds to a 69%, 79%, or 89%, it will be considered as a borderline case. These are the only grades that may change. I will only raise the grade higher if your score on Exam 2 is a higher letter grade than the borderline percentage. For example, if your grade in the course rounds to a 69%, then your grade in the class will be a D unless your score on Exam 2 is a C or better. Grade Calculation:.10 (HW percentage) +.90 (Exam/Quiz percentage) = overall percentage Learning Outcomes and Objectives for MATH 402 Upon completion of this course, the student will be able to: compute a number of vector based function values on plane curves and space curves. These include velocity vectors, acceleration vectors, speed, curvature, arc-length, binormal vectors, unit tangent and unit normal vectors. optimize both a multivariate function of a surface and multivariate functions involving a constraint curve. utilize multiple integrals using rectangular, polar, cylindrical, or spherical coordinates in problems involving volume, moments, and mass. set up and evaluate line and surface integrals. apply Green s Theorem, Stokes Theorem, and the Divergence Theorem to physics and engineering applications. Academic Integrity: If you are caught cheating on an exam or quiz, you will receive a zero for its score and not be allowed to replace the score or take any kind of makeup. I will complete paperwork to ensure that there is a record of your dishonesty. When you are taking a test, it is your job to cover your work so that no one else can see what you are doing. Keep your eyes on your own paper and make it abundantly clear to me that you are working alone. I may assign seating during tests or ask you to change seats during exams. During an exam, you should not speak to anyone other than me. You may only have materials approved by your instructor on your desk. All notes and electronic devices are prohibited unless specified by the instructor. A more complete set of exam directions is included later in this syllabus. Page 4
Expectations you should have: You should not expect to understand the material when a lecture is finished. Hours will need to be spent rewriting notes, practicing problems, and studying in order to first understand, and then master and become proficient with the material. The Required Homework Problems provide a small cross section of key concepts to study and master. They are not designed to be sufficient to prepare you for exams. Mastery implies not just understanding, but also to be efficient and process the information quickly. Use proper notation. You need to be able to accurately communicate in writing your method and your solution. There is an abstract nature to this course. Your job is to understand and be able to explain why? for much of what we study. Reading the textbook needs to be part of your study habits. You should know your grade throughout the semester and be able to calculate what if scenarios. Know the syllabus policies and information. Helpful Hints for Success in a College-Level Course: Don t expect to understand the material from the lecture when you leave class. Taking a 5-unit lecture class implies that you are spending a minimum of ten hours each week outside of class in study, practice, etc. Here are a few suggestions that you should take advantage of in order to succeed during the semester. Know the syllabus. Take thorough notes during class. A very good study habit is to rewrite your notes each day into a better organized and more concise and thorough set of information. Work through the book examples and as many additional book exercises as possible before beginning your assignments. You should read ahead before each lecture. Reading the text needs to be a regular part of your studying. Hard work put in early in the semester can have great benefits later in the semester. There are a few links to online resources on my CANVAS page that may be useful during the semester. Take advantage of my office hours and the free tutoring through the college. Don t wait to get assistance. Your classmates are one of your best sources for assistance. Make a point of meeting with some of them on a regular basis to help fill in missing gaps in your knowledge. Office hours can be busy. Take some time to simply learn because it is enjoyable. Go beyond what is required Disclaimer: All information on the syllabus is subject to change if the instructor finds it necessary. Any change will be announced during a class session and will be posted to the website. Absent students are still responsible for any announced changes. If you have any special circumstances that I need to be aware of, please let me know immediately. Page 5
Math 402 Homework Guidelines: Your required homework problems should be in the following format and will be graded accordingly: Write in pencil. You may use a highlighter or other color to identify your solutions. Your name, class and the assignment number in the upper right corner. Each section should be clearly labeled with the section number and the assigned problems listed. Staple in the upper left corner with all perforations neatly trimmed off. You must do the problems in the order assigned. Write the question down! (Summarize the given information if it is a word problem.) The work and solution should be correct. When the book asks for a calculator response, the exact solution should also be given before the calculator. The work should be organized, use proper notation, and be easy to follow. (Do not mix scratch work with the actual work.) Expect to write down enough information for someone other than yourself to understand what you are doing. Use classroom examples as a model for what is expected. Use proper notation throughout each problem and make certain to completely answer the question. Get into the habit of communicating Math to others. Skip a line between problems. Do not crowd your work. Do not leave negative numerical exponents or complex fractions in your final solutions unless the directions indicate to do so. Evaluate functions for exact values whenever possible. Any graphs should be made following the methods taught in class. This could sometimes require graphing paper which is available on the website. Page 6
Exam and Quiz Directions: These basic directions will be included on each exam for the course. Directions: Use Pencil. Use Instructor provided materials only. No calculators, phones, or other electronic devices. These must be put away and silenced (including smart watches). Keep your eyes on your own paper. Make it clear that you are working on your paper only. Do not leave your papers open and exposed for others around you to see. You may not leave the room for any reason. If you need to use the restroom, you must turn in your exam. You are required to turn in your exam/quiz at the end of the provided time. Use Proper Notation. Do not blend scratch work with real work. All final solutions should be written without negative numerical exponents or complex fractions. Show your work as demonstrated in class. Vector operations must be completed unless otherwise noted. Evaluate functions for exact values whenever possible. You need to be familiar with these directions as well as the Academic Integrity section of the syllabus. Failure to adhere to these guidelines will be considered cheating and will result in a zero on the exam and loss of replacement privileges. Page 7
Approximate Calendar for the Spring 2019 Semester: If changes occur, they will be announced in class. Jan. 23 Introduction, brief review of 1 st year content, 11.1-11.2 Vectors 2-D,3-D Jan. 28 11.3/ Begin 11.4 Dot Product and Cross Product Jan. 30 11.4 Finish Cross Product Quiz 1 Feb. 4 11.5 Lines and Planes in Space Feb. 6 11.6/11.7 Surfaces in Space, Cylindrical and Spherical Coordinates intro. Feb. 11 12.1/ begin 12.2 Vector Valued Functions, Velocity and Acceleration Vectors Feb. 13 Quiz 2 (ch. 11, 1 st 55 minutes): 12.2/12.3 applications of velocity and acceleration. Feb. 15 & 18 President s Holiday Weekend (College is closed.) Feb. 20 12.4/12.5 Tangent & Normal Vectors, Arc Length, Curvature Feb. 25 Binormal Vectors, Additional applications of vector-valued functions Feb. 27 Quiz 3 (ch. 12, 1 st hour): 13.1 Functions of Several Variables {Domain, Range, Level Curves, etc.}, Mar. 4 13.2/13.3 Functions of Several Variables: Limits and Partial Derivatives Mar. 6 13.4/ 13.5 Differentials and Chain Rules w/applications Mar. 11 13.5/13.6 Directional Derivatives Mar. 13 13.7/13.8 Tangent Planes and Normal Lines, Extrema of z = f(x,y) Mar. 18 13.8 cont d / 13.10 Lagrange Multipliers Mar. 20 Highlights of Functions of Several Variables 14.1 Iterated (Double) Integrals Mar. 25 14.1/14.2 Double Integrals and Volume {includes switching the order of integration} Mar. 27 14.3 Change of Variables {Polar Coordinates} 14.4 Applications of Double Integrals {centers of mass, moments of inertia} April 1 14.5 Surface Area/ Review April 3 Exam 1 (Ch. 13 14.3) April 8 14.6 Triple Integrals 14.7 Triple Integrals in Cylindrical and Spherical Coordinates April 10 14.7 cont d 15.1 Vector Fields April 15-21 Spring Break Holiday (College is closed.) April 22 15.1 Conservative Vector Fields 15.2 Parametrization of Curves and Line Integrals April 24 15.2 Applications of Line Integrals 15.3 Path Independence Withdraw ( w ) Deadline April 29 15.3/15.4 Fundamental Thm of Line Integrals, Green s Thm. May 1 15.5/15.6 Parametric Surfaces, Surface Integrals May 6 Summary of Line and Surface Integrals May 8 15.7 Divergence Theorem May 13 15.8 Stokes Theorem May 15 Overview of Chapter 15 and multiple integrals. {Note: This is the last lecture day before final exams.} May 22 Exam 2 7:00 am 8:50 am Page 8