MAT 191 Calculus I, # 35578, Session I, Summer 2002

Class meets MTWTh 18:00-20:30 in SBS F 121.

Instructor:  Serban Raianu

Office: NSM A-123; Office phone number: (310) 243- 3139

Office hours: MTWTh: 17:00-17:50,  or by appointment.

Course Description: MAT 193, Calculus II,  covers Chapters 2-6 from the textbook: Differential and integral calculus of one variable: limits, continuity, derivatives and application of derivatives,  integrals, Fundamental Theorem of Calculus,  basic techniques of integration and application of integrals.

Text: James Stewart, Calculus, 5th edition, Brooks/Cole, 2003.

Objectives: After completing MAT 193 the student should be able to:

• Understand the four basic concepts of one-variable calculus; the limit, the concept of continuity, the derivative and the integral of a function of one variable
• Use the rules of differentiation to compute derivatives of algebraic and trigonometric functions
• Use derivatives to solve problems involving rates of change, tangent lines, velocity (speed), acceleration, optimization, and related rates.
• Investigate the graph of a function with the aid of its first and second derivatives: asymptotes,  continuity, tangency,  monotonicity,  concavity,  extrema,  inflection points, etc.
• Understand the meanings of indefinite integral and the definite integral of a function of one variable, and their relationship to the derivative of a function via the Fundamental Theorem of Calculus
• Use rules of integration including the Substitution Rule to evaluate indefinite and definite integrals

Prerequisites: MAT 153 or equivalent with a grade of "C" or better.

Grades: Grades will be based on three in‑class 75-minutes examinations (60% total), a comprehensive final examination (25%), and quizzes, homework, attendance and other assignments (15%) for the remainder.

Each of the three 75-minutes exams will be graded  on a 100 scale, then the sum of the scores is divided by 5 and denoted by E.

Homework will be collected three times, on the days of the three exams, and each homework is worth 5 points. No late homework will be accepted. The average of all homework scores is denoted by H.

5 to 10 minutes quizzes will be given in principle every class meeting, with the exception of the review and exam days, and will be graded on a scale from 1 to 5. The average of the quizzes scores is denoted by Q.

There are also 5 points awarded for attendance and class participation. This portion of the grade is denoted by A.

The final exam will be graded out of a maximum possible 200, then the score is divided by 8 and denoted by F.

To determine your final grade,  compute E+H+Q+A+F. The maximum is 100, and the grade will be given by the rule:

A: 93‑100;      A‑: 90‑92;      B+: 87‑89;      B: 83‑86;   B‑: 80‑82

C+: 77‑79;      C: 73‑76;        C‑: 70‑72;      D: 60‑69;   F: Less than 60.

Makeups: No makeup examinations or quizzes will be given. If you must miss an examination for a legitimate reason, discuss this, in advance, with me, and I may then substitute the relevant score from your final examination for the missing grade.

Students with Disabilities: Students who need special consideration because of any sort of disability are urged to see me as soon as possible.

Academic Integrity: The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

Technology: Symbolic calculators, such as TI-89 or TI-92 are not acceptable for this course.

Tentative schedule and homework assignments

1. M 6/2:         2.1 The Tangent and Velocity Problems: 1, 6, 8

2.2 The Limit of a Function: 4, 13, 14, 19, 24

2. T 6/3:          2.3 Calculating Limits Using the Limit Laws:1e,f,10a,11,17, 23, 27, 36, 43,60

2.5 Continuity: 3, 5, 15, 23, 35, 41b

3. W 6/4:         2.6 Tangents, Velocities, and Other Rates of Change: 1,3,7,15,18,25

3.1 Derivatives: 7, 13, 15, 17, 21, 25, 29

4. Th 6/5:        3.2 The Derivative as a Function: 5, 27, 36

3.3 Differentiation Formulas: (odd only) 1-41,51,53

5. M 6/9:         3.4 Rates of change in the Natural and Social Sciences: 1,3,15,21

3.5 Derivatives of Trigonometric Functions: (odd) 1-15

6. T 6/10:        3.6 The Chain Rule: (odd) 1-41

7. W 6/11:       3.7 Implicit Differentiation: (odd) 1-19

3.8 Higher Derivatives: (odd) 5-19,23,25

8. Th 6/12:      Review and Exam I

9. M 6/16:       3.9 Related Rates: (odd) 1-9

3.10 Linear Approximations and Differentials:5,7,21,23,25

10. T 6/17:      4.1 Maximum and Minimum Values: (odd) 7-25

4.2 The Mean Value Theorem: 19, 23, 27

11. W 6/18:     4.3 How Derivatives Affect the Shape of a Graph: 1, 11, 14, 23, 37, 49, 51

4.4 Limits at Infinity; Horizontal Asymptotes: 11, 13, 15, 21, 37, 51

12. Th 6/19:    4.5 Summary of Curve Sketching: 5, 13, 45, 55

4.6 Graphing with Calculus and Calculators: 7, 13, 23

13. M 6/23:     4.7 Optimization Problems: 1,3,5,9,11,15

4.8 Applications to Business and Economics:5,7,11,13,15

14. T 6/24:      4.9 Newton's Method: 5,7,11,13,15

4.10 Antiderivatives: (odd) 1-35

15. W 6/25:     5.1 Areas and distances: 1,2,5

5.2 The Definite Integral:37,47,49,53

16. Th 6/26:    Review and Exam II

17. M 6/30:     5.3 The Fundamental Theorem of Calculus: (odd) 7-35

5.4 Indefinite Integrals and the total Change Theorem: (odd) 1-39

18. T 7/1:        5.5 The Substitution Rule: (odd) 7-31

6.1 Areas between Curves: (odd) 5-25

19. W 7/2:       6.2 Volumes: 4-11,13,19,25,28,31,33,61

20. Th 7/3:      6.3 Volumes by Cylindrical Shells: (odd only) 3-5,9-13,15-19,21-25,35-39

21. M 7/7:       6.4 Work: 5,7,9,11,13,15,16,17

6.5 Average Value of a Function: (odd only) 1-7,15

22. T 7/8:        Review and Exam III

23. W 7/9:       Review

24. Th 7/10:    Final examination