Math 2414 Ta-Keng Teng J Textbook: Finney, Weir, Giordano. Thomas Calculus, 11th Edition, Addison Wesley Longman Publishing, 2005.

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1 Math 2414 Ta-Keng Teng J Textbook: Finney, Weir, Giordano. Thomas Calculus, 11th Edition, Addison Wesley Longman Publishing, I. GENERAL OBJECTIVES Having learned the principles of differentiation and integration with polynomial and rational functions in the first course, the student learns the calculus of certain very important transcendental functions in the second course. A major portion of the course is the calculus of exponential and logarithmic functions and trigonometric functions and their inverses and applications of such. The student will have learned the basic integration technique of substituting in the first course. The methods of integration by parts, trigonometric substitution, and partial fractions will be taught in this course. However, there will not be as much emphasis on these as previously because of the availability of calculators which perform integration of functions. Knowledge of the basic principles, though, is still an important part of the course. Other important parts of the course are the ability to evaluate limits by the use of L Hopital s Rule and improper integrals. The final segment of the course is the study of sequences and series of constant terms. The student will learn the relationship between a series and a sequence of partial sums. Tests for convergence of series will be taught. This section is in preparation for the study of power series, which is the first topic for the next course. II. STUDENT LEARNING OUTCOMES Upon completion of the course, the student will be able to: 1. Use the definite integral to find the area between two given curves. 2. Use the definite integral to find the volume of a solid of revolution. 3. Find the derivative of a function that is a composition of functions containing the natural logarithm function. 4. Find the derivative of a function that is a composition of functions containing the exponential function. 5. For a given equation, use logarithmic differentiation to find dy dx. 6. Find integrals of functions containing the natural logarithm. 7. Find integrals of functions containing the exponential function. 8. Find integrals requiring a simple substitution. 9. Find integrals requiring integration by parts. 10. Find integrals requiring trigonometric substitutions. 11. Approximate definite integrals using an approved calculator. 1

2 12. Decide if a given improper integral converges or diverges. 13. Decide if a given sequence converges and justify their conclusion. 14. Decide if a given infinite series converges and justify their conclusion. 15. Classify a series of constant terms as absolutely convergent, conditionally convergent, or divergent. III. COURSE OUTLINE A. Transcendental Functions 1. The natural logarithm function 2. Logarithmic differentiation 3. Integrals yielding the natural logarithm 4. The exponential function e x 5. Other exponential and logarithmic functions 6. Exponential growth and decay 7. Derivatives of inverse trigonometric functions 8. Integrals yielding inverse trigonometric functions 9. Introduction to hyperbolic functions B. Techniques of Integration 1. Review of integration formulas and simple substitutions 2. Integration by parts 3. Integration with the trigonometric functions 4. Trigonometric substitution 5. Integration of rational functions using partial fractions C. Indeterminate forms and improper integrals 1. L'Hopital's rule and the indeterminate form Other indeterminate forms 3. Improper integrals with infinite limits of integration 4. Other improper integrals 5. Taylor's formula D. Sequences and infinite series of constant terms 1. Sequences 2. Monotonic and bounded sequences 3. Infinite series -- basic concept 4. Infinite series of positive terms 5. The integral test 6. Alternating series -- absolute and conditional convergence 7. The ratio test and the root test IV. EXEMPLARY EDUCATIONAL OBJECTIVES 1. To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical methods to modeling and solving real-world situations. 2. To represent and evaluate basic mathematical information verbally, numerically, graphically, and symbolically. 2

3 3. To expand mathematical reasoning skills and formal logic to develop convincing mathematical arguments. 4. To use appropriate technology to enhance mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of the results. 5. To interpret mathematical models such as formulas, graphs, tables and schematics, and draw inferences from them. 6. To recognize the limitations of mathematical and statistical models. To develop the view that mathematics is an evolving discipline, interrelated with human culture, and Students With Disabilities BC is committed to providing equal education opportunities to every student. BC offers services for individuals with special needs and capabilities including counseling, tutoring, equipment, and software to assist students with special needs. Please contact Phil Robertson, Special Populations Counselor, for further information. Academic Honesty BC assumes that students eligible to perform on the college level are familiar with the ordinary rules governing proper conduct including academic honesty. The principle of academic honesty is that all work presented by you is yours alone. Academic dishonesty including, but not limited to, cheating, plagiarism, and collusion shall be treated appropriately. Please refer to the BC Student Guide for more information, this is available online at click on the link found on the left side of the homepage. If I have evidence anyone is giving or receiving information during a test I will either a) give that person the grade of 0% on the test, b) assign the person the grade of F for the semester, or, c) recommend that person be expelled from Brazosport College with loss of all college credits from this institution. An approved calculator is the only electronic device allowed during a test. Be sure to turn off and put away any cell phone, PDA, palm pilot or any other electronic device during testing. Attendance Policy: You are allowed a total of 5 absences (excused or unexcused). If you miss more than 5 classes you will be withdrawn from this course. If you have a TSI liability, you may be withdrawn from all your classes if dropped from this class. If there are extenuating circumstances, please contact me. Three tardies (including breaks) will count as 1 absence. **If you must miss a class, it is your responsibility to find out what you ve missed and have it ready for the next class meeting. If you decide to drop the class, be sure you complete the required paperwork with the registrar. If you quit attending class and are not officially dropped by the withdrawal deadline, you will receive the grade of F. Grades 3

4 Grading Policies: Grades in this course will be assigned based on your performance on tests, quizzes, and a cumulative final. Homework is an essential part of the course and will be assigned daily. It will not directly count toward your final grade, however, many quiz and test questions will be similar to homework. It will be your responsibility to check for accuracy. (Correct answers can be found in the back of the book.) Homework problems will Grades will be assigned as follows: % A 80-89% B 70-79% C 60-69% D Below 60% F be assigned at the end of every lecture. If you are absent on a particular day then you will receive a zero for that day s quiz. Tests: There will be 3 tests given throughout the semester. Attendance & Daily quizzes will count 20% of your grade. There are no make-up quizzes. Your final exam will count 20% and can also take the place of any missed test or it will replace your lowest test grade. Final: There will be a comprehensive final. Daily Homeworks will not be graded. Daily assignments will be given in class. Although not graded, similar questions to the homework will be on the quizzes and tests. The assignments are meant to make sure that you have mastered all the concepts from a particular section. Most of the assignments will be from the text. The odd answers are given in the back of the book. An instructors copy with all the answers will be available for use in the LAC and the Library. Disruption of Class If you conduct yourself in a manner I consider disruptive to the learning atmosphere in here, I will insist you leave and count you as absent. If I tell you to leave class, leave without making inappropriate comments and meet me outside of class for a conference before returning to class. If you repeatedly disrupt the class, I will insist you leave again and will not allow you to return to class. I consider any kind of private conversation as inappropriate while class is in progress. Seating I expect to prepare a seating chart in here and I expect you to sit in the seat designated by that chart. I also reserve the right to reassign your seat at anytime during the semester. If you are not sitting in your assigned seat, I will consider you absent. If you wish to move to a different location in the class, talk with me outside of class. Help: If you need help getting started on a problem, finishing a problem, or just want reassurance, please find help. Call or come by during office hours. Sign up for free tutoring in the LAC. Office hours will be posted on the door of J-201 4

5 Find a study partner or group to meet with regularly. Use the computers, videos available in the LAC. Calculators: Calculators are not allowed on exams or quizzes. It would be wise not to use them at home while working on your homework. Other Information This list is provided to assist students locate available services. Information about the BC Library is available at or by calling Tutoring for Math, Reading, Writing, Biology, Chemistry, and other subjects is available in the LAC, To contact the math Department call The Student Services area provides the following services Counseling and Advising, ; Financial Aid, 3294; and Student Activities, Tentative Test Dates: Sep 22 Test 1 Oct 25 Test 2 Dec 1 Test 3 Dec 13 Final 5

Grading Policy/Evaluation: The grades will be counted in the following way: Quizzes 30% Tests 40% Final Exam: 30%

Grading Policy/Evaluation: The grades will be counted in the following way: Quizzes 30% Tests 40% Final Exam: 30% COURSE SYLLABUS FALL 2010 MATH 0408 INTERMEDIATE ALGEBRA Course # 0408.06 Course Schedule/Location: TT 09:35 11:40, A-228 Instructor: Dr. Calin Agut, Office: J-202, Department of Mathematics, Brazosport