Lake-Sumter State College Course Syllabus Course / Prefix Number MAC 2313 Course Title: Calculus with Analytic Geometry III CRN: 20110 20110 Credit: 4 Term: Spring 2015 Course Catalog Description: Instructor: This is the third course in a three-semester sequence. The following topics will be covered in this three-semester sequence: review of functions; limits and continuity; the derivative; differentiation of algebraic and transcendental functions; the mean value theorem and intermediate value theorem; extrema and graph sketching; area and the definite integral antidifferentiation; the fundamental theorem of calculus; inverse functions; arc length; techniques of integration; parametric equations and polar coordinates; Taylor s formula, infinite sequences and series; vectors in the plane and in space; topics from plane and solid analytic geometry; directional derivatives and curvature; differential calculus of functions of several variables; multiple integration. NOTE: A graphing calculator is required. triolod@lssc.edu Daniel Triolo Contact Information: 352-536-2106 http://www.lssc.edu/faculty/dannyt Office Location: South Lake Building 2 Room 339 Office Hours: Monday/Wednesday: 930am- 11am, 1-230pm Tuesday/Thursday: 1-3pm All students are required to use LakeHawk Mail for official college e-mail communications. See the college webpage for instructions on activating LakeHawk Mail. Prerequisites: C or higher in MAC 2312 Textbook and Other Calculus: Early Transcendentals, James Stewart, 7 th edition, Brooks/Cole, 2012 Course Materials: Technology and Online Computer Access Requirements: Course Objectives: (what the course will do) Calculator: TI-83 Plus or TI-84 Plus (including Silver Editions) To prepare the student with rigorous mathematical applications in the applied sciences requiring an understanding and application of the calculus. Student Learning Outcomes (SLOs) Assessed in this Course: 1. The student will knowledge of two and three-dimensional vectors and the geometry of space. 1 a. Define and apply three-dimensional coordinate systems, including the distance formula in three-dimensions and the equation of a sphere. b. Define and apply vectors, including their graphs, their magnitude, basic vector properties, basis vectors, vector addition, and scalar multiplication, and use vectors to find a resultant force. c. Define the vector dot product and investigate basic dot product properties. Apply the dot product to analyze orthogonal vectors, direction angles and cosines, scalar and vector projections, and the work done by a vector force.
d. Define the vector cross product and investigate cross product properties (including the magnitude and length of the cross product). Apply the cross product to analyze orthogonal and parallel vectors, the volume of the parallelepiped, the scalar and vector triple product, and torque. e. Determine and apply vector, parametric, and symmetric equations of a line or line segment and the vector, scalar, and linear equation of a plane, including the distance between a point and a plane. f. Define and apply cylindrical and quadric surfaces, including their graphs and applications. 2. The student will knowledge of a variety of vector functions. 3. The student will knowledge of partial derivatives. a. Define and apply vector functions, including their limits, continuity, and graphs. b. Define and apply space curves, including their graphs, using computer software. c. Determine and apply the derivative and integral of vector functions, including basic differentiation rules for vectors, finding tangent lines, and the Fundamental Theorem of Calculus applied to vectors. d. Determine and apply the arc length and curvature of space curves, including the arc length function and the normal, binormal, and osculating planes, and the osculating circle. e. Define and apply velocity, speed, and acceleration in space, including the tangential and normal components of acceleration. a. Define and apply functions of two or more variables, including graphs and level curves or surfaces. b. Determine the limits and continuity of a function of two or more variables. c. Define and apply partial derivatives of functions of two or more variables, including notation, geometrical interpretation, higher derivatives, and Clairaut s Theorem. d. Apply the Chain Rule to functions of two or more variables and use it to implicitly differentiate. e. Define and apply directional derivatives and the gradient vector for functions of two or more variables, analyze the direction and magnitude of the maximum directional derivative, and find tangent planes to level surfaces. 2 f. Define and apply local and absolute maximum and minimum values of a function of two or more variables. Use the Second Derivatives Test to find local extreme points and saddle points. Use the Method of Lagrange Multipliers to find the maximum and minimum values of functions of two or more variables with one or two constraints. 4. The student will a. Define and apply double integrals over rectangles,
Academic Integrity: Important Information for Students with Disabilities: Privacy Policy (FERPA): knowledge of multiple integration. 5. The student will knowledge of the calculus of vector fields. 3 including the average value of a function. b. Define and apply iterated integrals, including Fubini s Theorem. c. Define and apply double integrals over general regions and investigate properties of double integrals. d. Find double integrals using polar coordinates. e. Use double integrals to solve problems involving density, charge, mass, moments, centers of mass, moments of inertia, and radii of gyration. f. Define and apply triple integrals over rectangular boxes and general solids, including Fubini s Theorem for Triple Integrals and applications to mass, moments, center of mass, centroids, moments of inertia, and electric charge. g. Use a change of variables to evaluate multiple integrals, including changing to cylindrical or spherical coordinates. a. Define and graph vector fields, including velocity fields, gravitational fields, electric fields, gradient vector fields, and conservative vector fields. b. Define and apply line integrals, including line integrals in space and line integrals of vector fields. c. Understand and apply the Fundamental Theorem for Line Integrals. d. Define and apply independence of path. e. Define a conservative vector field and determine whether given fields are conservative. f. Understand and apply Green s Theorem. g. Determine and interpret the curl and divergence of a vector field. h. Define and apply parametric surfaces, including surfaces of revolution, surface area, and tangent planes. i. Define and apply surface integrals, including oriented surfaces and surface integrals of vector fields. j. Understand and apply Stokes Theorem. k. Understand and apply the Divergence Theorem. The successful functioning of the academic community demands honesty, which is the basis of respect for both ideas and persons. In the academic community, there is an ongoing assumption of academic integrity at all levels. There is the expectation that work will be independently thoughtful and responsible as to its sources of information and inspiration. Honesty is an appropriate consideration in other ways as well, including but not limited to the responsible use of library resources, responsible conduct in examinations, and the responsible use of the Internet. (See college catalog for complete statement.) Any student with a documented disability who requires assistance or academic accommodations should contact the Office for Students with Disabilities immediately to discuss eligibility. The Office for Students with Disabilities (OSD) is located on the Leesburg Campus, but arrangements can be made to meet with a student on any campus. An appointment can be made by calling 352-365-3589 and specific information about the OSD and potential services can be found at www.lssc.edu, then go to Quick Links and click on Disability Services. The Family Educational Rights and Privacy Act (FERPA) (20 U.S.C. 1232g; 34 CFR Part99) is a Federal law that protects the privacy of a student s education records. In order for your information to be released, a form must be signed and in your records located in the
Admissions/Registrar s Office. Regular attendance is essential to your success in this course. Attendance/Withdrawal Policies: If you must miss a class, you should contact a fellow student to find out what was covered, copy notes, etc. because you are responsible for what was covered during your absence. If you wish to withdraw from this course, it is your responsibility to go to the Admissions Office and do so officially by the deadline listed in the College Catalog. Withdrawal Deadline: The deadline for withdrawing from this course this semester is March 25, 2015. 5 In Class Tests (this includes the final exam) - 20% each Methods of Evaluation: Tests They are closed book and closed notes. Any cheat sheets I will make and everyone will receive a copy with their test. All tests, including the final, must be completed without a calculator. Each test will have material from previous test topics. I will let you know at least one week ahead of time that a test is approaching. The dates below are approximate and subject to change. You will have 1 hour and 50 minutes to take each test (1 hour 55 minutes for the final). You may not leave the classroom for any reason during a test. If you do, I will collect and grade your test as is. If your final exam score is greater than the lowest of your 4 test scores then the low grade will be dropped and your final exam score will count twice. **A missed test will automatically become your lowest test score. A make-up test will only be given in extreme cases with documentation. If no documentation is provided it will be scored a 0% and you will use your final exam to replace this score. Grading Scale: Course Calendar: Classroom Rules and Policies: Violence Statement: Syllabus Disclaimer: Your course average is converted to a letter grade according to the departmental grading scale: At least 90: A At least 80 but less than 90: B At least 70 but less than 80: C At least 60 but less than 70: D Less than 60: F Chapters 12, 13 3 weeks Test 1 January 29 Chapter 14 1.5 weeks Test 2 Feb 17 Chapter 15.1-15.10 2 weeks Test 3 March 19 Chapter 16.1-16.5 1.5 weeks Test 4 April 7 Final Exam April 21 10am to 12pm 1. Come to class on time. 2. Act like an adult. 3. Do not cheat on tests. 4. If you must leave early, arrive before class begins and let me know. 5. Leave class when dismissed. 6. If you violate #2 or #3 then you will leave the class for the day, a student incident report will be submitted to the dean, and all test scores will count. 7. In addition to #6, if you are caught cheating you will receive a zero on that test. Cheating a second time will result in an F for the course. Lake-Sumter State College has a policy of zero tolerance for violence as stated in College Board Rule 2.17. Appropriate disciplinary action will be taken in accordance with Board Rule 2.17. Information contained in this syllabus is, to the best knowledge of this instructor, considered correct and complete when distributed to the student. The instructor reserves the right, acting within policies and procedures of Lake-Sumter State College, to make necessary changes in course content or instructional techniques without prior notice or obligation to the student. 4
SUGGESTED HOMEWORK EXERCISES: This list is subject to change. 12.1: 1-43odd, 2-6even 12.2: 1-33odd,41,43,24-28even, NOTE: vector v is 2d for problem #29 12.3: 1-43odd, 47,57,59,61,2-14even,62 12.4: 1-33odd, 37, 43 12.5: 1-47odd, 51-65odd, 71,73 12.6: 7-9odd, 21-28all 13.1: 1-29odd, 41, 43, 47 13.2: 1-27odd, 35-39odd, 41,42,49,51,55 13.3: 1-9odd, 13,14, 15-33odd,39, 47-51odd 13.4: 1-15odd, 17a 14.1: 1,2,5-21odd, 32-37all, 39-49odd,59-63odd,69 14.2: 1, 5-21odd, 25,29-41odd 14.3: 5-8all,10,15-43odd,47-69odd,74-78all 14.4: 1-6all 14.5: 1-33odd,45-55odd 14.6: 1-29odd, 33, 41-45odd 14.7: 1-17odd, 29-35odd, 39-45odd 14.8: 1-17odd, 29-35odd 15.2: 1-31odd 15.3: 1-31odd, 37, 43-55odd 15.4: 1-6all, 7-27odd 15.6: 1-11odd 15.7: 1-8all, 9-21odde, 27-35odd 15.8: 1-29odd 15.9: 1-27odd,39,41 15.10: 1-19odd, 23, 25 16.1: 1-9odd, 11-18all, 21-25odd, 29-32all 16.2: 1-21odd, 29a 16.3: 1,2,3-25odd,26, 31-34all 16.4: 1-13odd, 17,27 16.5: 1-11odd, 12, 13-31odd 16.6: 1,2,3,5,13-18all, 19-25odd 16.7: 5-25odd, 8, 10 16.8: 1-9odd, 11a, 13-19odd, 16.9: 1-4all, 5-13odd, 17,19,23-31odd 5