Lake-Sumter State College Course Syllabus

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1 Lake-Sumter State College Course Syllabus Course / Prefix Number MAC 2312 Course Title: Calculus with Analytic Geometry II CRN: Credit: 4 Term: Spring 2014 Course Catalog Description: This is the second 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. Instructor: Daniel Triolo Office Location: Leesburg: Building SM Room 129 South Lake: Building 2 Room 339 Contact Information: Office Hours: triolod@lssc.edu Phone: (352) Leesburg (352) Clermont-Use this number if leaving a voic . Web: LEESBURG: MW: am F: 730-8am, pm SOUTH LAKE TR: 9-930am pm,330-4pm All students are required to use Lakehawk Mail for official college communications. See the college webpage for instructions on activating Lakehawk Mail. Prerequisites: C or higher in MAC 2311 Textbook and Other Course Materials: Calculus: Early Transcendentals, James Stewart, 7 th edition, Brooks/Cole, 2010

2 Technology and Online Computer Access Requirements: Calculator: TI-83 Plus or TI-84 Plus (including Silver Editions). Any calculator with a CAS is not allowed i.e. TI-89, TI-92, TI-nspire, etc. If you are using another brand of calculator, your instructor will determine whether it is acceptable for the course. Course Objectives: (what the course will do) To prepare the student with rigorous mathematical applications in the applied sciences requiring an understanding and application of the calculus.

3 Student Learning Outcomes (SLOs) Assessed in this Course: (what the students take with them beyond this course) of a variety of techniques of integration. a. Understand and apply integration by parts. b. Develop and use a variety of strategies for integrals involving trigonometric functions. c. Use trigonometric substitution to solve a variety of integrals. d. Integrate rational functions using partial fractions. e. Integrate using tables and computer algebra systems. f. Approximate integrals using the midpoint Riemann sum, the Trapezoidal Rule, and Simpson s Rule, and determine error bounds for each technique. g. Integrate improper integrals, including infinite intervals and discontinuous integrands. h. Understand and apply a comparison test for improper integrals. demonstrate knowledge of a variety of applications of integration. a. Define and compute arc lengths of a curve. b. Determine the arc length function of a curve. c. Find the area of a surface of revolution. d. Set up and solve a variety of physics and engineering problems including hydrostatic force and pressure, moments and centers of mass, and centroids. of first order differential equations. a. Use differential equations to model population growth, both exponential and logistic, predator-prey systems, mixing problems, and the motion of a spring. b. Draw and interpret direction fields. c. Use Euler s method to find numerical approximations to solutions of differential equations. d. Set up and solve separable differential equations. e. Determine an orthogonal trajectory of a family of curves. f. Set up and solve linear differential equations using an integrating factor. of parametric equations and polar coordinates. a. Define, graph, and interpret parametric equations. b. Find the tangent, area, arc length, and surface area of parametric curves. c. Define, graph, and interpret polar equations. d. Find the tangent, area, and arc length of polar curves. e. Define, graph, and interpret the four conic sections. f. Define, graph, and interpret the conic sections in polar coordinates.

4 of infinite sequences and series. a. Define sequences and investigate their properties (finite, infinite, increasing, decreasing, monotonic, convergent, divergent, and bounded), the limit of a sequence, and apply limit laws to convergent sequences. b. Understand and apply the Monotonic Sequence Theorem. c. Define infinite series and investigate their properties, including convergence (conditional and absolute) and divergence, and various types of series, including binomial, geometric, and harmonic. d. Understand and apply the Test for Divergence Theorem, the Integral Test (including the remainder estimate), the Comparison Test, the Limit Comparison Test, the Alternating Series Test (including estimating sums), and the Ratio Test. e. Define a power series and determine its radius and interval of convergence. f. Determine representations of functions as power series and multiply, divide, differentiate, and integrate them. g. Define and apply Taylor and Maclaurin series. h. Define and apply Taylor polynomials. i. Understand and apply Taylor s Inequality.

5 Academic Integrity: 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.) Important Information for Students with Disabilities: 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 and specific information about the OSD and potential services can be found at then go to Quick Links and click on Disability Services. Privacy Policy (FERPA): 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 will be taken daily in some form. Those who miss a substantial amount of classes will receive an F. 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. If you miss a test for any reason, you will receive a zero on it. If you miss a test I will replace the zero with your final exam score (see methods of evaluation for more details). If you miss a second test accommodations will be made only in extreme cases. The deadline for withdrawing from any course this semester is Friday, March 21, Withdrawal Deadline: The deadline for withdrawing from any course this semester is Friday, March 21, There will be 5 tests including your final exam. There will also be a group assignment. I will assign the groups and discuss the

6 Methods of Evaluation: details in class. Homework will be assigned from the text. It will not be graded, it is your responsibility to keep up. I will assign homework problems in class. Group Assignment: 10% Tests: 70% Final Exam: 20% Grading Scale: 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 We will cover most or all of the following chapters in the order listed: Course Calendar: Chapter 7: Techniques of Integration Chapter 8: Further Applications of Integration Chapter 10: Parametric Equations and Polar Coordinates Chapter 11: Sequences and Series Chapter 9: Differential Equations Test 1 will cover topics from Ch 7 and 8. Test 2 will cover Ch 10 Test 3 will cover part of Ch 11 Test 4 will cover the rest of Ch 11 and parts of Ch 9. Classroom Rules and Policies: Classroom Policies 1. If you are disruptive, then I will ask you to leave and you will be counted as absent and receive a zero if it is during a test. 2. Silent all cell phones and other electronic devices before class. Testing Policies 1. On test days, the test starts when I walk in the door. Please do not have textbooks and notes out. Study outside the classroom and come in when you are prepared to start. 2. All items must be off the table/desk except for a writing utensil (Calculator if permitted). There will be tests or portions of tests in which calculators will not be permitted. 3. You may not use your own scrap paper. I will provide you with paper if it is needed. 4. All answers must be in simplified form. 5. Turn in everything including any scrap paper. 6. Only your actual test paper will be graded therefore all of your final solutions and answers must be on the test paper. I will not grade anything on scrap paper. 7. If you are using a calculator not approved by the instructor or when calculators are not permitted you will receive an automatic zero. 8. If you arrive late then you have the remainder of the test time to complete the test, as do students who were on time. 9. If you are caught cheating or letting someone else cheat you will receive a zero or fail the course, at the discretion of the instructor.

7 Violence Statement: Lake-Sumter State College has a policy of zero tolerance for violence as stated in College Board Rule Appropriate disciplinary action will be taken in accordance with Board Rule Syllabus Disclaimer: 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.

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