MATH 210 CALCULUS WITH ANALYTIC GEOMETRY I TEXTBOOK: Calculus, 8th Edition by James Stewart Assignment Sheet APPENDIX A: 7 12, 13, 15, 19, 23, 25, 27, 29, 33, 34, 43, 45, 46, 49, 51, 53, 61, 62, 65 APPENDIX B: 3, 9, 12, 14, 15, 21, 25, 27, 29, 31, 32, 33, 35, 41, 45, 48, 51, 53, 54, 55, 57 APPENDIX C: 1, 4, 5, 7, 9, 11, 27, 29, 33, 34, 35, 37, 39 APPENDIX D: 1, 3, 7, 9, 11, 23 29 all, 31, 33, 35, 37, 43, 47, 51, 53, 55, 65, 67, 69, 73 Chapter 1: Functions and Limits 1.1 3, 4, 7 10 all, 15, 21, 25, 27 33 all, 35, 40, 43, 53, 59, 63, 69, 71, 73 78 all 1.2 1, 3, 7, 10, 15, 17, 19, 21; Optional: 24, 27 1.3 1, 3, 5, 9, 14, 15, 17, 19, 21, 23, 31, 33, 34, 36, 37, 39, 43, 47, 53, 57, 61 2 Supplemental Problem: Sketch the graph of the function y x 4x 5 using Test 1 the instructions for problems 9 24. 1.4 Optional: 1, 3, 6, 7 1.5 1 9 all, 11, 15, 17, 19, 26, 29, 31, 33 1.6 1 9 all, 11 31 odd, 35, 39 45 odd, 46, 47, 49, 52-57 all 1.7 1, 3, 5, 11, 13, 16, 19, 21, 25, 29, 31, 41 1.8 1, 3, 4, 14, 16, 17 22 all, 25, 27, 29, 43, 45, 49ab, 53, 55, 57a, 59a Chapter 2: Derivatives 2.1 1 13 odd, 17, 18, 20, 21, 23, 31, 33, 35, 37, 46, 57 2.2 1, 3, 5, 7, 9, 13, 21, 25, 27, 39, 41, 49, 55, 62 Test 2 2.3 1 45 odd, 51, 55 63 odd, 69, 73, 77, 79, 81, 97, 103, 104 2.4 1 23 odd, 29, 31, 33, 35, 39 49 all 2.5 1 47 odd, 51, 59, 61, 65, 66, 69, 84 2.6 1 4 all, 5 23 odd, 27, 29, 35, 37, 47, 57 2.7 (Optional) 1, 5, 7, 9, 15, 17, 23, 33 2.8 1, 5, 7, 13, 15, 17, 19, 20, 25, 27, 29, 43, 45, 46
Chapter 2: Derivatives 2.9 1, 11, 12, 15 27 odd, 31, 33 Test 3 Chapter 3 Applications of Differentiation 3.1 1 5 all, 7 10 all, 15, 18, 21, 24, 27, 29 41 odd, 47 51 odd, 52, 55 3.2 5, 6, 8, 9, 11 14 all, 17, 18, 21, 25 3.3 1 5 all, 8, 9, 11, 13, 14, 15, 17, 18, 21, 23, 25, 29, 33, 35, 39, 41 3.4 1, 2, 3, 7 31 odd, 35, 37, 49, 51, 57 3.5 1 39 odd, 49, 53 3.6 Optional: 1, 4, 8, 9, 11 3.7 3, 5, 7, 11, 12, 13, 21, 23, 25, 34, 37, 41, 51 3.8 4, 7, 11, 13, 15, 19 3.9 1 17 odd, 21 39 odd, 45, 53, 55 Chapter 4: Integrals 4.1 1, 3, 13, 17, 21, 24 4.2 1, 4, 7, 9, 11, 17, 19, 21 25 all, 29, 33, 34, 35, 37, 40 43 all, 47 50 all, 55, 57, 59, 61, 63 4.3 2, 3, 5, 7 15 all, 17 33 all, 35, 37, 38, 39 53 odd, 54, 55, 60, 61, 62 4.4 1, 3, 5, 6, 7 16 all, 19 33 all, 35, 37, 39, 40, 41, 47, 49, 55 58 all 4.5 1, 3, 5, 7 10 all, 11, 13 21 all, 23, 25 29 all, 31 51 odd, 57, 59 Test 5 Chapter 5: Applications of Integration 5.1 1, 3, 5, 6, 7, 9, 11, 13 18 all, 22, 24, 26, 27, 33, 35 5.2 1 11 odd, 15, 16, 19 31 all, 47, 48, 49, 51, 54 5.3 1, 2, 3, 5, 7, 8, 9 19 odd, 21a, 22a, 25a, 37, 39, 41 5.4 1, 3, 5, 7, 8, 9, 13, 15, 16, 17, 19, 20, 21, 23, 24 5.5 1 9 odd, 13, 14, 15 8.1 1, 3, 7, 9, 11, 12 Supplemental Problem: Find the arc length of 3/ 2 y x 1 from x = 1 to x = 5
Prerequisites 1. Classify a number as natural, integer, rational, irrational or real. 2. Recall and apply properties of inequalities. 3. Solve inequalities by using the number line or by cases. 4. Recall and apply the definition of absolute value. 5. Solve equations containing one or two absolute values. 6. Solve absolute value inequalities. 7. Express sets of real numbers in interval notation. 8. Demonstrate and apply a geometric interpretation of the absolute value. 9. Recall and apply the formula for the undirected distance between 2 points. 10. Recall and apply the definition of a circle. 11. Recall and apply the formula for the equation of a circle with center (h, k) and radius r. 12. Recall and apply the formula for the equation of a circle with center at the origin and radius r. 13. Given the center and radius of a circle, write the equation of a circle. 14. Given the general form for the equation of a circle, complete the square on x and y to find the center and radius of the circle. 15. Describe the 3 possible outcomes when completing the square to obtain the center-radius form of a circle. 16. Solve problems involving circles. 17. Recall and apply the formula for finding the midpoint of a line segment. 18. Plot points in the Cartesian coordinate system. 19. Sketch a graph of an equation using a table of values. 20. Find, if possible, the x and y intercepts of a graph. 21. Recall and apply the definition of the slope of a straight line, using 2 points on the line. 22. Recall and apply the fact that parallel lines have equal slopes. ( m 1 = m ) 2 23. Recall and apply the fact that perpendicular lines have slopes that are negative reciprocals of each other: m1 1 = m2 24. Recall and apply the point-slope form for the equation of a line. 25. Recall and apply the slope-intercept form for the equation of a line. 26. Recall and apply the 2-point form for the equation of a straight line. 27. Recall and apply the intercept form for the equation of a straight line. 28. Identify equations of the type ax + by + c = 0 and find the slope and y-intercept. 29. Identify the slope and y-intercept for vertical and horizontal lines. 30. Solve problems involving the 4 formulas for lines. 31. Recall and apply the tests for symmetry with respect to the x-axis, y-axis, origin, and the line y = x. 32. Recall and apply the definition of a function. 33. Demonstrate an understanding of a function. 34. Analyze the graph of a function using such tools as the vertical line test. 35. Identify the dependent and the independent variable in a function. 36. Identify the following special functions: one-to-one, identity, constant. 37. Identify the domain and range of a function using a graph, interval notation, and set-builder notation. 38. Graph the greatest integer function and variations of the greatest integer function. 39. Graph the absolute value function. 40. Demonstrate an understanding of the "f (x)" notation and evaluate a function. 41. Perform algebraic operations on functions. 42. Demonstrate an understanding of and find composite functions. 43. Find the domain and range of algebraic and composite functions. 44. Identify a quadratic function. 45. Identify a linear function. 46. Identify a polynomial and state its degree, leading coefficient, and constant term. 47. Identify rational functions, algebraic functions, and transcendental functions. 48. Recall and apply the definitions of the 6 trigonometric functions. 49. Convert angles from degrees to radians and from radians to degrees. 50. Find the radian measure of an angle using right angle trigonometry. 51. Find the radian measure of an angle using the unit circle.
52. Recall and apply the equation = s. r 53. Identify the period of a trigonometric function. 54. Recall and apply the fundamental trigonometric identities. 55. Identify and give the meaning of the following symbols and abbreviations: iff, wrt,= =, s.t.,=,, w/e MATHEMATICS DEPARTMENT POLICIES Disruptive Behavior: Behavior that is disruptive to the instructor or students is contrary to quality education. Should the instructor determine that an individual student's verbal or nonverbal behavior is hampering another student's ability to understand or concentrate on the class material, the instructor will speak with that student in an effort to rectify the problem behavior. If the behavior continues after this discussion, the instructor will have the disruptive student leave the class. Permission to return to class may be dependent upon assurances that the student has met with some responsible individual about the problem: the mathematics department chairman, a counselor, the Dean of Student Support Services, etc. Cheating and/or Plagiarism: An instructor who has evidence that a student may have cheated or plagiarized an assignment or test should confer with the student. Students may then be asked to present evidence (sources, first draft, notes, etc.) that the work is his own. If the instructor determines that cheating or plagiarism has occurred, he may assign a failing grade to the test, the assignment, or the course, as he sees fit. Access Office: The college s Access Office guides, counsels, and assists students with disabilities. If you receive services through the Access office and need special arrangements (seating closer to the front of the class, a notetaker, extended time for testing, or other approved accommodation), please make an appointment with your instructor during the first week of classes to discuss these needs. Any information you share will be held in strict confidence, unless you give the instructor permission to do otherwise. Attendance and Grading: Attendance is expected at all class meetings. Each individual instructor determines the grading system for his/her class. Grading scales, methods of grading, make-up policy, and penalties resulting from excessive absences will be discussed early in the semester. Final Exams (Departmental): In the Fall and Spring semesters, a portion of the final examinations given in MTH:020, MTH:030, MTH:140 and MTH:160 may be designed by the Mathematics Department. All MTH 210, 220, 230 Calculus final examinations will be given during the Wednesday of finals week. In the Summer semesters, any culminating experience ( i.e. Final Exam) is given on the last day of that Summer session. Course Repeater Policy: Students must file a petition seeking departmental approval before enrolling in the same Meramec mathematics course for the third time. The petition process will involve writing a formal petition and meeting with a math faculty advisor to design a course of action that will improve chances for success.
Course Objectives: 1. Upon successful completion of the course, the student will know or understand: 0. Limits 1. Continuity 2. Derivatives of algebraic and trigonometric functions 3. Applications of the derivative 4. Integrals 5. Applications of integration 6. Connections between mathematical methods 7. Relationships between mathematics and other disciplines 8. Appropriate use of technology 2. Upon successful completion of the course, the student will demonstrate the ability to: 0. Students will use the definition to compute limits. Students will use the properties of limits to evaluate finite, infinite, and one-sided limits. 1. Students will use the definition of a continuous function to recognize and graph continuous and discontinuous functions. 2. Students will find derivatives of algebraic and trigonometric functions using the basic differentiation rules, the product and quotient rules, and the chain rule. Students will find derivatives using implicit differentiation. 3. Students will use real data to develop models of real world applications and solve word problems involving related rates, optimization and differentials, making estimates, predictions, and making informed estimates. Student will apply the first and second derivative tests to curve sketching. 4. Students will find antiderivatives, compute definite integrals, and apply several integration techniques including integration by substitution. 5. Students will use the definite integral to calculate areas, volumes, arc length, and work. 6. Students will demonstrate understanding of the connections between methods in mathematics by using several techniques: verbal, numerical, graphical, and symbolic. 7. By learning the historical background of mathematical concepts, students will develop the view that mathematics is a growing discipline, interrelated with human culture and connected to other disciplines. 8. Students will use appropriate technology to enhance their mathematical thinking and understanding, to solve mathematical problems, and to judge the reasonableness of their results. 1. Describe how mathematics contributes and shapes our civilization and culture, and recognize its connections to other disciplines. 2. Represent mathematical information graphically, symbolically, numerically, and verbally with clarity, accuracy, and precision. 3. Model situations with real-world data and analyze the models (e.g. algebraic, geometric and statistical) to make estimations, predictions and informed decisions. 4. Solve nonlinear equations algebraically, graphically and numerically. 5. Formulate and use generalizations based upon pattern recognition. 6. Use technology as an aid to understanding and as a tool in the solution of problems. 7. Recognize and use the connections within mathematics (e.g., geometry can be used to analyze a problem that will be solved using algebra).