AMERICAN UNIVERSITY OF SHARJAHCollege of Arts and Sciences Department of Mathematics and Statistics Course Outline - Spring 2010 MTH 103 Course Title: Prerequisites: Calculus I MTH 001, or MTH 004, or Engineering Math Placement Test, or SAT II Math 1C test with score 600 and above _______________________________________________________________________________ ____ Textbook: ³Calculus,´ by R. Smith and R. Minton, Third Edition, McGraw Hill. Course Instructors: Section 8 2, 5 3, 4 1 7, 9 Instructor Taher Abualrub Suheil Khoury* Ismail Kucuk Timothy Marshall Gergely Orosi Office NAB 261 NAB 246 NAB 255 NAB 260 NAB 254 Extension 2920 2918 2921 2978 2332 E-mail [email protected][email protected][email protected][email protected][email protected] * Course Coordinator Office Hours: Instructor T. Abualrub S. Khoury I. Kucuk T. Marshall G. Orosi Sun. Mon. Tue. 10:00-11:00 11:00-11:50* 11:00-11:50 2:00-2:50 Wed. Thu. 10:00-11:00 10:00-11:00 10:00-11:00 11:00-11:50* 11:00-11:50 2:00-3:50 1:00-4:00 11:00-11:50 1:00-4:00 * By appointment y Other office hours are available by appointment Math Learning Center: The Math Learning Center (MLC) located in NAB239A provides free tutoring services to all students who experience difficulties with their mathematics courses.6:15 2 hours 45% Second Midterm Final Exam 35% Wednesday. No need to make an appointment: just drop in! For the spring semester 2010.6:15 5:00 . 2010 TBA . Grading: Grading Quizzes and\or Homework Lab First Midterm % 15% 5% Dates TBA TBA Wednesday.php and provided to the instructors to be posted on iLearn. on the MLC Webpage http://www. please send an e-mail to [email protected]/cas/maths/student_services. the MLC will open on Sunday. The weekly hours are: y y Sunday through Wednesday: 11:00 am to 4:00 pm Thursday 10:00 am to 2:00 pm To see who's working. when and in what courses they can help you with.edu Note: No tutoring is available during final exam week or the two first weeks of the term. April 21. For any other questions or concerns. January 31st at 11 a. do your homework and study (in group if you wish).aus. In the MLC you can get help from qualified tutors. 2010 Time TBA TBA 5:00 . check this semester's detailed schedule which will be posted in the MLC (NAB239A). February 24. 12. 2. 8. 3. Compute the definite integral of any polynomial or root function. . Find the first and higher-order derivatives of a function by applying basic differentiation rules.Course Objectives: This course is designed to help the students: 1. and points of inflection. Find the derivative of a function by using the limiting process. the Intermediate Value. Apply the basic integration rules to find the anti-derivative of a function. 18. Define the definite integral as a limit of Riemann sum approximations. in the computer-based laboratory. derivatives. 17. 5. and integrals and utilize the Computer Algebra System Maple. Apply the ideas and techniques of differentiation and integration to a variety of applications such as extreme values. Determine if a limit exists and evaluate limits analytically. 4. Use the derivative to find the equation of the tangent line at a point. graphing). and derivatives. rates of change. 13. State the definition of derivative and give its geometrical interpretation. 15. Perform curve sketching (derivatives and curve shape. 16. Develop the mathematical concepts of limits. Utilize the Fundamental Theorem of Calculus to find the area under a curve. geometric. optimization. Evaluate limits graphically and numerically. and numeric terms. Describe the basic ideas of differential calculus in algebraic. 14. 9. and the Mean Value theorems. 7. 6. lower and middle sums for a region. Employ numerical methods to evaluate limits. Find areas and volumes of revolution. extreme values. and integrate using the substitution technique. Apply differentiation and integration formulas. efficiently as a tool. and utilize graphs to estimate relative rates. intervals for which the function is increasing or decreasing. concavity. areas. Solve related rates and optimization problems. derivatives and integrals. Apply the extreme value theorem to determine extrema on a closed interval. Course Outcomes: This course requires the student to demonstrate the following: 1. 3. 5. Use implicit differentiation to find the rate of change. and volumes. 4. Approximate zeros of a function using Newton's Method. Compute the value of the limit using L¶Hôpital¶s rule. Compute linear approximations and differentials. and implement the limit and derivative concepts and techniques to analyze functions. Apply Rolle¶s. 10. 11. Find upper. limits. 2. and interpret them graphically and physically in the context of real-world problems. Utilize the first and second derivative tests to find relative extrema. Attendance: It is the university policy that if a student is absent 15% of the class sessions (which. it does not matter. . but you are also expected to be there on time. if detected. amount to 7 hours). Late attendance: Not only are you expected to be in class. you are guilty as well). Getting Help: Students are encouraged to consult their instructor during his office hours or by appointment or through the Math Learning Center. Missing quizzes or exams: Quizzes cannot be made up. he/she will be withdrawn from the course with a grade of WF. will result in a WF grade in the course for all who are involved (i. if somebody copied your homework. Copying. in our case. Three (3) late attendances will count as one absence. 5.e. Academic integrity: You are expected to submit your own work. cheating or plagiarism. 4. 3. Lateness is defined as: showing up to class after the instructor has finished calling the class roster.. and within the first 10 minutes of the lecture. 2. Showing up more than 10 minutes late to the lecture counts as an absence. project etc.Remarks and Rules 1. 2 4.Course Syllabus and Weekly Schedule Section 1.8 4.6 5.5 4.6 2.3 2.3 1.3 4.5 3. Disks.4 2.4 4.3 Material The Concept of Limit Computation of Limits Continuity and its Consequences Limits Involving Infinity Tangent Lines and Velocity The Derivative Computation of Derivatives: The Power Rule The Product and Quotient Rules The Chain Rule Derivatives of Trigonometric Functions Derivatives of Exponential and Logarithmic Functions Implicit Differentiation and Inverse Trigonometric Functions The Mean Value Theorem Linear Approximations and Newton¶s Method Indeterminate Forms and L¶Hôpital¶s Rule Maximum and Minimum Values Increasing and Decreasing Functions Concavity and the Second Derivative Test Overview of Curve Sketching Optimization Related Rates Antiderivatives Sums and Sigma Notation Area The Definite Integral The Fundamental Theorem of Calculus Integration by Substitution Area Between Curves Volume: Slicing.1 5.6 3.2 5.7 2.9 3.1 2.8 2.2 1.4 1.7 3.2 2.1 3.5 2.4 3. and Washers Volumes by Cylindrical Shells Review .2 3.5 2.1 4.3 3. 27.3 4. 11. 5. 77. 3.1 5. 10. 19. 48 2. 33. 64 1. 36. 3. 29. 21. 33. 4. 32. 28-30. 15. 68. 7. 7. 11. 7. 11. 6. 4. 23. 20. 49. 35 1. 17. 7. 42 2-14. 19. 19. 25. 27. 43. 15. 5. 22. 25. 6.3 2.5 2. 23. 57 1. Minton Section 1. 21.8 4. 31. 15. 5. 11. 7. 29. 3. 25. 17. 7. 5. 35. 19.Math 103 Suggested Problems TEXTBOOK: Calculus. 31. 11. 23. 43 1. 6. 17. 27. 20. 19.2 4. 21. 31. 6. 17. 71 1-5. 33. 29. 27. 49 3. 18. 39. 10. 55. 11. 31. 9. 21. 24. 31 1.2 3. 23. 2. 13. 50 1. 15. 31. 24. 15. 7.7 3. 19-22. 27. 17. 15. 9. 25. 40 2. 44. 28. 21. 21. 12. 39. 43. 11.4 2. 15. 10. 16. 37 10. 16. 9. 9. 41. 36 5. 3. 5. 11. 15. 3.6 2. 16-18. 45. 27-29. 10. 49 3. 25. 16. 21. 3. 29. 36. 3.6 3. 27.8 2. 7. 31. 17-20. 35. 35. 33. 9. 17. 9. 41 1. 63 1. 47. 53 5. 7. 13. 23-28. 16. 14. 27.5 2. 35. 21. 35. 39.3 3. 23. 7. 21-24. 35 2. 15. 8.5 4. 41. 7. 7. 49 5. 27. 73 1. 33. 5. 9. 21. 26. 24. 9.1 2. 17-22. 25.6 5. 63-66.1 3. 3.4 1. 31. 40. 14. 17. 34. 55. 19. 5-13. 11. 25. 22. 24. 24. 37. 7. 57 3. 16. 19. 14. 7. 25-28. 8. Smith and R. 35. 13. 15. 3rd edition by R. 7.7 2. 80 5. 34. 37. 23. 32. 7. 33. 15. 48.2 2. 59. 33. 33. 5. 39. 17. 32.5 3. 18. 29.1 4. 23. 17. 32. 44. 5. 29. 5. 11. 25. 9. 17. 38 1. 13. 9. 20. 21. 29. 8. 27. 15. 19. 13. 11. 4. 13. 22. 25. 3. 11.2 5. 8.2 1. 23. 3. 43 5. 32.9 3. 12. 33. 8. 13. 39. 17-21. 13. 37 1. 69. 5. 33. 9. 14. 40. 3. 12. 23. 29. 23-25 . 44 1. 7. 27. 19. 25. 27. 53. 23. 20.4 4. 47. 37 1. 5. 9.3 Page 85 95 106 118 155 166 177 186 194 203 213 224 233 251 263 274 284 293 306 316 324 351 360 367 380 390 400 438 453 462 Exercises 1-6.3 1. 13. 9. 20. 41 1. 15. 41. 38. 11. 39. 31.4 3. 4. 7. 47. 15. 35. 42 4. 4. 3.