NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York

Transcription

1 NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York DEPARTMENT: Mathematics COURSE: MAT 1475/MA 475 TITLE: Calculus I DESCRIPTION: Topics include functions, limits, differentiation, tangent lines, L Hôpital s Rule, Fundamental Theorem of Calculus and Applications. TEXT: Single Variable Calculus: Early Transcendentals Or Calculus: Early Transcendentals 6 th edition James Stewart Brooks/ Cole CREDITS: 4 PREREQUISITES: MAT 1375/MA 375 or MAT 1376/MA Prepared by: Prof. N. Benakli Prof. H. Carley Prof. Y. Celikler Prof. Laura Ghezzi Prof. Neil Katz Prof. A. P. Taraporevala Spring 2009 A. Testing Guidelines: The following exams should be scheduled: 1. A one-hour exam at the end of the First Quarter. 2. A one session exam at the end of the Second Quarter. 3. A one-hour exam at the end of the Third Quarter. 4. A one session Final Examination. B. A graphing calculator is required. We recommend the TI-83 / TI-84 Plus.

2 Learning Outcomes for MAT 1475/ MA 475 Calculus I 1. Students will be able to solve problems related to limits and continuity. 2. Students will be able to find the derivative of functions using the definition, sum rule, product rule, quotient rule, and the chain rule. 3. Students will be able to: Use the derivative of a function to find an equation for the tangent line at a point. Use L Hôpital s Rule to evaluate limits. Sketch the graph of functions. Solve optimization problems. Solve related rates problems. 4. Students will be able to evaluate definite and indefinite integrals of polynomials, trigonometric and exponential functions.

3 Mathematics Department Policy on Lateness/Absence A student may be absent during the semester without penalty for 10% of the class instructional sessions. Therefore, If the class meets: The allowable absence is: 1 time per week 2 absences per semester 2 times per week 3 absences per semester Students who have been excessively absent and failed the course at the end of the semester will receive either the WU grade if they have attended the course at least once. This includes students who stop attending without officially withdrawing from the course. the WN grade if they have never attended the course. In credit bearing courses, the WU and WN grades count as an F in the computation of the GPA. While WU and WN grades in non-credit developmental courses do not count in the GPA, the WU grade does count toward the limit of 2 attempts for a developmental course. The official Mathematics Department policy is that two latenesses (this includes arriving late or leaving early) is equivalent to one absence. Every withdrawal (official or unofficial) can affect a student s financial aid status, because withdrawal from a course will change the number of credits or equated credits that are counted toward financial aid. New York City College of Technology Policy on Academic Integrity Students and all others who work with information, ideas, texts, images, music, inventions, and other intellectual property owe their audience and sources accuracy and honesty in using, crediting, and citing sources. As a community of intellectual and professional workers, the College recognizes its responsibility for providing instruction in information literacy and academic integrity, offering models of good practice, and responding vigilantly and appropriately to infractions of academic integrity. Accordingly, academic dishonesty is prohibited in The City University of New York and at New York City College of Technology and is punishable by penalties, including failing grades, suspension, and expulsion. The complete text of the College policy on Academic Integrity may be found in the catalog.

4 MA 1475 Calculus I Text: Calculus Early Transcendentals, 6 th ed by Stewart Session Calculus I Homework Four Ways to Represent a function (pages 11-20) 1.3 New Functions from old functions (pages 37 43) P. 21: 2, 5-9 odd, 27, 29, 36, 39, 40, 44, all, 61, odd P. 44: 29, 31, 33, 34, all The Limit of a Function (pages 88 96) P. 97: 5-9 odd, 12, odd, all, 30, Calculating Limits using the Limit Laws (pages ) 2.5 Continuity (pages ) Derivatives and Rates of Change (pages ) 2.8 The Derivative as a Function (pages ) Derivatives of Polynomial and Exponential Functions (pages ) Derivatives of Polynomial and Exponential Functions (pages ) (cont.) P. 106: 1, odd, odd, 48 P. 128: 3, 4, odd, odd P. 150: 1-9 odd, 14, 17, odd, 40, 41 P. 162: 1, 3, 13, odd, all, 42, 49 P. 180: 1-31 odd P. 181: 33, 35, 39, odd, 7 First Examination The Product and Quotient Rules (pages ) P. 187: 3 21 odd, odd, 43, Derivatives of Trigonometric Functions (pages ) P. 195: 1-35 odd, 18, 39, 40, Chain Rule (pages ) P. 203: 1-23 odd, odd, 50, 51, Implicit Differentiation (pages ) P. 213: 5-19 odd, all, 29, 33, 35, all, Derivatives of Logarithmic Functions (pages ) P. 220: 3-15 odd, odd Derivatives of Logarithmic Functions (pages ) (cont.) P. 174: odd, Related Rates (pages ) P. 245: 1-7 all, 9, 11, 12, 19, odd

5 Linear Approximation and Differentials (pages ) P. 252: 1 4 all, odd 16 Midterm Examination Maximum and Minimum Values (pages ) P. 277: odd, 24, 26, all, 41, 43, odd, 59, How Derivatives Affect the Shape of a Graph (pages ) P. 295: 1, 9 17 odd How Derivatives Affect the Shape of a Graph (pages ) P. 295: 19, 25, 33, 35, 39, 42, Indeterminate Forms and L Hôpital s Rule (pages ) P. 304: 1, 5 11 odd, odd, 25, 27, 39, odd, (53 59 odd are optional) Limits at Infinity; Horizontal Asymptotes (pages ) P. 140: 3, 13, odd, 33, 35, 39, 41, 44 P. 296: 48, Summary of Curve Sketching (pages ) P. 314: 3, 5, 9, 13, odd, 31, 37, 38, odd, 57, Graphing with Calculus and Calculators(pages ) P. 320: 3-9 all, 11, Third Examination Optimization Problems (pages ) P. 328: 1 19 odd, 31, 33 odd Antiderivatives (pages ) P. 345: 1, 5, 7 11 odd, 14, 18, 19, 20, 23, 29, 31, 33, 36, 37, 39, 57, Areas and Distances (pages ) 5.2 The Definite Integral (pages ) 5.3 The Fundamental Theorem of Calculus (pages ) 5.4 Indefinite Integrals and the Net Change Theorem (pages ) P. 364: 1 5 odd, 11, 15 P. 378: 42, 48, 49 P. 387: 1, 3, 9 15 odd, odd, 43, 45, (63 is optional) P. 397: 1 11 odd, odd 29 REVIEW 30 Final Examination

6 MA 1475 Calculus I Text: Calculus Early Transcendentals, 6 th ed by Stewart Calculus I Homework 1.1 Four Ways to Represent a function (pages 11-20) P. 21: 2, 5-9 odd, 27, 29, 36, 39, 40, 44, all, 61, odd 1.3 New Functions from old functions (pages 37 43) P. 44: 29, 31, 33, 34, all 2.2 The Limit of a Function (pages 88 96) P. 97: 5-9 odd, 12, odd, all, 30, Calculating Limits using the Limit Laws (pages ) P. 106: 1, odd, odd, Continuity (pages ) P. 128: 3, 4, odd, odd 2.7 Derivatives and Rates of Change (pages ) P. 150: 1-9 odd, 14, 17, odd, 40, The Derivative as a Function (pages ) P. 162: 1, 3, 13, odd, all, 42, Derivatives of Polynomial and Exponential Functions (pages ) P. 180: 1-35 odd, 39, odd 3.2 The Product and Quotient Rules (pages ) P. 187: 3 21 odd, odd, 43, Derivatives of Trigonometric Functions (pages ) P. 195: 1-35 odd, 18, 39, 40, Chain Rule (pages ) P. 203: 1-23 odd, odd, 50, 51, Implicit Differentiation (pages ) P. 213: 5-19 odd, all, 29, 33, 35, all, Derivatives of Logarithmic Functions (pages ) P. 220: 3-15 odd, odd, odd, Related Rates (pages ) P. 245: 1-7 all, 9, 11, 12, 19, odd 3.10 Linear Approximation and Differentials (pages ) P. 252: 1 4 all, odd 4.1 Maximum and Minimum Values (pages ) P. 277: odd, 24, 26, all, 41, 43, odd, 59, 61

7 MA 1475 Calculus I Text: Calculus Early Transcendentals, 6 th ed by Stewart Calculus I Homework 4.3 How Derivatives Affect the Shape of a Graph (pages ) P. 295: 1, 9 19 odd, 25, 33, 35, 39, 42, Indeterminate Forms and L Hôpital s Rule (pages ) P. 304: 1, 5 11 odd, odd, 25, 27, 39, odd, (53 59 odd are optional) 2.6 Limits at Infinity; Horizontal Asymptotes (pages ) P. 140: 3, 13, odd, 33, 35, 39, 41, 44 P. 296: 48, Summary of Curve Sketching (pages ) P. 314: 3, 5, 9, 13, odd, 31, 37, 38, odd, 57, Graphing with Calculus and Calculators(pages ) P. 320: 3-9 all, 11, Optimization Problems (pages ) P. 328: 1 19 odd, 31, 33 odd 4.9 Antiderivatives (pages ) P. 345: 1, 5, 7 11 odd, 14, 18, 19, 20, 23, 29, 31, 33, 36, 37, 39, 57, Areas and Distances (pages ) 5.2 The Definite Integral (pages ) P. 364: 1 5 odd, 11, 15 P. 378: 42, 48, The Fundamental Theorem of Calculus (pages ) P. 387: 1, 3, 9 15 odd, odd, 43, 45, (63 is optional) 5.4 Indefinite Integrals and the Net Change Theorem (pages 391 P. 397: 1 11 odd, odd 393)