Math 150 Calculus with Analytic Geometry I Spring 2014 CRN: 59774

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1 Math 150 Calculus with Analytic Geometry I Spring 2014 CRN: Instructor : Anne Gloag agloag@sdccd.edu Phone: (619) Classroom: M108 Time: TTH 11:30 2:00 PM Office Hours: Mondays and Wednesdays 12:30-2:00 Math Lab 2:00-2:20 M206 Tuesdays and Thursdays 9:00-9:30 M206 11:00-11:30 M206 2:00-3:00 M108 or M211D Text and Materials: Calculus Early Transcendentals (E-Book/Jb), Stewart, Edition 7, Cengage Learning; ISBN REQUIRED: WebAssign: In this course you are required to sign up for Webassign in order to access homework sets, lecture material and practice problems. You can access the site at: and purchase access when you sign up. An electronic version of the textbook is available to you in the courseroom. Some textbooks will come with an access code if it is bundled with the webassign access kit, so if you choose to purchase a textbook that comes with the access code you do not need to purchase another access code. To sign up you need the Class Key: miramar Strongly Recommended: Graphing Calculator (TI-84 or similar). Phones should not be used as calculators because you cannot use them during tests or the final exam. Course Description: This course is a primary introduction to university-level calculus. The topics of study include analytic geometry, limits, differentiation and integration of algebraic and transcendental functions. Emphasis is placed on calculus applications. Analytical reading and problem solving are required for success in this course. This course is intended for the transfer student planning to major in mathematics, computer science, physics, chemistry, engineering, or economics. Transfer Information: Associate Degree Credit & transfer to CSU and/or private colleges and universities CSU General Education IGETC UC Transfer Course List MATH 121 and 150 combined: maximum credit, one course. Prerequisite: MATH 141 with a grade of "C" or better, or equivalent

2 Objectives: Upon successful completion of the course the student will be able to: 1. Evaluate various types of limits graphically, numerically, and algebraically, and analyze properties of functions applying limits including one-sided, two-sided, finite and infinite limits. 2. Develop a rigorous limit proof for simple polynomials. 3. Recognize and evaluate limits using the common limit theorems and properties. 4. Analyze the behavior of algebraic and transcendental functions by applying common continuity theorems, and investigate the continuity of such functions at a point, on an open or closed interval. 5. Calculate the derivative of a function using the limit definition. 6. Calculate the slope and the equation of the tangent line of a function at a given point. 7. Calculate derivatives using common differentiation theorems. 8. Calculate the derivative of a function implicitly. 9. Solve applications using related rates of change. 10. Apply differentials to make linear approximations and analyze propagated errors. 12. Apply differentials to make linear approximations and analyze propagated errors. 11. Apply derivatives to graph functions by calculating the critical points, the points of nondifferentiability, the points of inflections, the vertical tangents, cusps or corners, and the extrema of a function. 12. Calculate where a function is increasing, or decreasing, concave up or concave down by applying its first and second derivatives respectively, and apply the First and Second Derivative Tests to calculate and identify the function's relative extrema. 13. Solve optimization problems using differentiation techniques. 14. Recognize and apply Rolle's Theorem and the Mean-Value Theorem where appropriate. 15. Apply Newton's method to find roots of functions. 16. Analyze motion of a particle along a straight line. 17. Calculate the anti-derivative of a wide class of functions, using substitution techniques when appropriate. 18. Apply appropriate approximation techniques to find areas under a curve using summation notation. 19. Calculate the definite integral using the limit of a Riemann sum and the Fundamental Theorem of Calculus and apply the Fundamental Theorem of Calculus to investigate a broad class of funcgtions. 20. Apply integration in a variety of application problems, including areas between curves, arclengths of a single variable function, volumes 21. Estimate the value of a definite integral using standard numerical integration techniques which may include the Left-Endpoint Rule, the Right-Endpoint Rule, the Midpoint Rule, the Trapezoidal Rule, or Simpson s Rule. 22. Calculate derivatives of inverse trigonometric functions, hyperbolic functions and inverse hyperbolic functions. 23. Calculate integrals of hyperbolic functions, and of functions whose anti-derivatives give inverse trigonometric and inverse hyperbolic functions. Student Learning Outcomes: 1. Analyze polynomial, rational, trigonometric, radical, exponential, logarithmic and inverse functions to graph them, indicating symmetry, asymptotes, discontinuities, limits and extrema. 2. Develop a rigorous limit proof of the derivative for simple polynomials, and use the limit definition to determine the derivative of a function. 3. Determine the derivative of polynomial, rational, trigonometric, hyperbolic, radical, exponential, logarithmic and inverse functions, and describe how the derivative relates to the function.

3 4. Determine the definite and indefinite integral of polynomial, rational, trigonometric, hyperbolic, radical, exponential, logarithmic and inverse functions, using formulas or numerical integration techniques, and describe how the integral relates to the function. 5. Analyze and solve physical, geometric, related rates and optimization problems using the appropriate functions, derivatives or integrals. Participation: It is recommended that all students come to every class session. Come prepared for class by reading ahead in the textbook on the topics that will be covered during the lesson. Participate by asking questions about homework problems and the concepts covered in the lesson. Regular attendance and participation are key factors to your success in this class. There is no grade deduction for absences but there will be graded classroom assignments that you will need to complete in each session and missing class will hurt your grade. Students are expected to spend and additional minimum of 8 hours outside class reading each section assigned in the text, watching the videos of each chapter s material online and completing the homework sets assigned in Webassign. Grading Criteria: You will be evaluated based on the following criteria: 1. Tests: Homework: Activities: Final Exam: 300 Total possible points: 1000 Final Grade: A B C D < F Tests: There will be five tests in this course. The tests are short answer and you have one attempt for each test. Each test is 90 minutes long. Test 1: Chapters 1-2 February 18 Test 2: Chapter 3 March 13 Test 3: Chapter 4 April 10 Test 4: Chapter 5 April 29 Test 5: Chapter 6 May 13 Homework: There are assigned Homework Sets for each chapter of the textbook covered in this course. Homework is due as indicated. Homework sets are accessed in Webassign. You should complete the homework by the posted due dates but you can still access and work on the assignments after the due date. To do this you must request an automatic extension. You have 14 days from the due date to request the extension and 7 days after you accept the conditions to complete the work. However, you will incur a late penalty of 20% on the parts of the assignment that were not completed by the deadline.

4 In class assignments: There will be in-class assignments almost each class period. These assignments are focused on the applications of Calculus to real life situations and on strengthening specific skills. These assignments are due at the end of the class period unless otherwise indicated. Final Exam: The final exam is comprehensive. The final exam will be given on May 22 in the same room and at the same time as the regular class. The final consists of short answer questions. The exam is 90 minutes long. You are allowed the use of a calculator (scientific or TI-83/84). Contacting your Instructor: Please me if you have any personal questions and concerns. You should use agloag@sdccd.edu for fastest response. Please do not send me questions about particular homework problems through . These questions are best addressed in class where all students can hear the question and answers. You can also reach me at Please leave a message if I don t answer the phone and I will get back to you as soon as I can. Academic Accommodation: Any student who may need an academic accommodation should discuss the situation with me during the first two weeks. Cheating policy: I have a zero tolerance policy on cheating. Cheating of any type will not be tolerated. This includes, but is not limited to: copying other people s work, use of notes on exams or quizzes, using calculators to store formulas, communicating with others during tests and quizzes in any way ( this includes using electronic devices), or similar activities. This does not include discussing homework with others prior to handing it in. I will penalize all cheaters to the fullest extent possible, with the minimum punishment being zero on that assignment that cannot be dropped. The most likely punishment will include an F in the class. Classroom Etiquette: As a diverse community of learners, students must strive to work together in a setting of civility, tolerance, and respect for each other and for the instructor. Conflicting opinions among members of a class are to be respected and responded to in a professional manner. There are to be no offensive comments, language, or gestures. How to get help: If you need help in this class there are several resources available: 1. Your instructor is always happy to help. You can see me before or after class and during office hours, or we can set up an appointment. The best way to contact me is via (agloag@sdccd.edu) and let me know that you are having troubles. Let me know specific problems and concepts with which you are struggling. 2. Your fellow students are a great resource. It is a proven fact that students who are part of a study group are more successful that students who are not. So get to know your fellow students early in the semester and plan some study sessions. 3. The Math Lab at Miramar is open five day a week (MTW: 9 6:30, Th: 9 8, F: 9-12). Free tutoring is available there from great tutors and faculty. Computers are also available for you to complete your work. 4. The PLACe on the Miramar campus also offers free tutoring. It is located in the Library building: L101 and is open M-Th: 8:30 6:30. Disclaimer: I reserve the right to change the policies in the syllabus do to unforeseen circumstances.

5 Schedule and Textbook coverage: Week Dates Homework Sections Due Dates Four Ways to Represent a Function 1/28 1/ Mathematical Models 1.3 New Functions from Old Functions 2 3 2/6 2/ /20 2/25 2/27 3/6 7 3/ /13 3/18 3/20 3/ /8 4/ /15 4/ / /29 5/1 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms 2.1 The Tangent and Velocity Problems 2.2 The Limits of a Function 2.3 Calculating Limits Using Limit Laws 2.5 Continuity 2.6 Limits at Infinity 2.7 Derivatives and Rates of Change 2.8 The Derivative of a Function Test Derivatives of Polynomial and Exponential Functions 3.2 The Product and Quotient Rules 3.3 Derivatives of Trig Functions 3.4 The Chain Rule 3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic Functions 3.7 Rates of Change in the Natural and Social Sciences 3.8 Exponential Growth and Decay 3.9 Related Rates 3.10 Linear Approximations and Differentials 3.11 Hyperbolic Functions Test Maximum and Minimum Values 4.2 The Mean Value Theorem 4.3 How Derivatives Affect the Shape of a Graph 4.4 Indeterminate Forms and L Hospital s Rule 4.5 Summary of Curve Sketching 4.6 Graphing with Calculus and Calculators 4.7 Optimization Problems 4.8 Newton s Method Test Antiderivatives 5.1 Areas and Distances 5.2 The Definite Integral 5.3 The Fundamental Theorem of Calculus 5.4 Indefinite Integrals and The Net Change Theorem 5.5 The Substitution Rule Test Area Between Curves 6.2 Volumes 2/25 2/25 3/11 3/11 3/11 3/13 3/13 4/8 4/8 4/8 4/10 4/29 4/29 4/29 5/6 5/6

6 14 5/6 5/8 15 5/13 5/ /20 5/ Volumes by Cylindrical Shells 6.4 Work 6.5 Average Value of a Function Test 5 Final Exam Review Make up Tests Final Exam 5/13 5/13 5/13 Important Dates: January 27: February 7: February 14: February 17: March 3: Mar 31 Apr 5: April 11: May 24: June 2: FIRST DAY OF CLASS Add/Drop deadline; refund deadline Abraham Lincoln Day (HOLIDAY) George Washington Day (HOLIDAY) Deadline TO FILE A PETITION FOR PASS/NO PASS GRADE OPTION SPRING BREAK WITHDRAW DEADLINE, NO LATE DROPS ACCEPTED AFTER THIS DATE End of Spring Semester Spring semester grades available on e-grades Please pay careful attention to these dates, especially the Drop date and the Withdrawal date. These dates are when I clear my roster. This means that I drop students that have not been attending class regularly. I will assume that you are no longer interested in attending class if you miss more than two consecutive class sessions without informing me of your absence. However, ALWAYS file a Drop if you don t intend to continue with the class to make sure that you are no longer on the roster.

Math 181, Calculus I

Math 181, Calculus I [Semester] [Class meeting days/times] [Location] INSTRUCTOR INFORMATION: Name: Office location: Office hours: Mailbox: Phone: Email: Required Material and Access: Textbook: Stewart,