Math 101: CALCULUS 1 Course Syllabus Course Information

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1 Course Title CALCULUS 1 Course Number Math 101 Credit Hours: Prerequisites Contact Hours Lecture days and time Class Room 3 hours None Qatar University College of Arts and Sciences Department of Mathematics and Physics Math 101: CALCULUS 1 Course Syllabus Course Information Class meetings: 4 hrs per week L54 Sun Mon & Wed L52 Sun Mon & Wed D201 Semester fall 2012 Semester Start Date Sep., 16 th, 2012 Last day of classes Dec., 27 th, 2012 Number of weeks TEXTBOOK REFERENCES 15 weeks Calculus, by James Stewart, 7 th Edition, Brooks/Cole Calculus with Analytic Geometry. By C. H. Edwards and D. E. Penny, 5 th Edition, 1998, Prentice Hall Calculus. Howaer Anton 8 th edition (2007) by Howard Anton, (John Wiley & Sons, Inc, New York). Calculus. By R.T. Smith and R.B. Minton, Second Edition, 2002, McGraw-Hill. Calculus. By R.T. Smith and R.B. Minton, Second Edition, 2002, McGraw-Hil 1

2 Faculty Information Instructor Modi Hamad A Alnasr Department Mathematics, Statistics and Physics Office Location SB209 Office phone Office Hours Sun.11-12, modialnasr@qu.edu.qa COURSE OBJECTIVES The course aims at: 1. Introduce limits and continuity, and develop skills for their determination. 2. Introduce the derivative, and develop skills for using rules of differentiation. 3. Provide skills related to applications of the derivative. 4. Introduce the definite and indefinite integrals, and develop skills for their evaluation. 5. Provide skills related to some applications of the integral. LEARNING OUTCOMES By the end of the course, the students should be able to: 1. Evaluate Limits of functions using various techniques including L Hopital s Rule 2. Discuss the continuity functions 3. Identify the properties of inverse functions and their derivatives 4. Find the derivative of algebraic, trigonometric, exponential, and logarithmic functions 5. Sketch the graph of a function using the information for the first and second derivatives 6. Solve problems involving applications of derivatives including, related rates and optimization 7. Identify the definition and properties associated with definite integrals 8. Solve problems using the Fundamental Theorem of Calculus 9. Evaluate integrals using the method of substitution 10. Solve problems involving applications of integrals including finding volume of solids of revolution and area between curves. 2

3 Delivery Methods We will use different types of teaching methods including: Presentation explaining material. Problem solving. Discussion - actively involving students in learning by asking questions that provoke thinking and verbal response. Using Math packages explaining some material including Autograph. The lecture will be posted on the e-learning tool Blackboard, so pay you attention to the class and try to understand everything. Learning Resources & Media In class we will use Digital Camera to explain mathematical formulas Data show will be used also to visualize some important graphs in the three dimension space We will use some math packages including Autograph 3.2 and Matlab. Blackboard will be used frequently: The Student companion site for the text: EVALUATION POLICY This course will be assessed by exams, project, quizzes: Assessment Type Day Date Time Weight First Exam Saturday 20/10/ :00 16:00 Second Exam Saturday 1/12/ :00 16: % 22.5 % Final Exam Saturday 29/12/ % Quizzes and assignment Class time 10 % Matlab Project 5 % Sum 100% GRADING: Note that the exam and grading will be unified Grades will be assigned based on the following scale: Percent grade below 60 Letter grade A B+ B C+ C D+ D F Earned Points INSTRUCTIONS & REGULATIONS 3

4 1. Using Mobile phones during lectures or exams is prohibited. Shut off your cell phone during class, any one uses mobile will be asked to leave the lecture room. 2. Students are expected to attend all classes, if they do not show up for more than 25% of the classes, they fail the course. There are no grades for attendance. 3. Quizzes have no make-ups, so try not to miss any. 4. Students are expected to participate actively in the class. 5. Check your regularly. 6. Be responsible for all class activities, announcements, and assignments when you miss a class. 7. Do not hesitate to see me if you have any question. 8. Prior to class, look over the section that will be covered. 9. Regularly check the BLACKBOARD site at: If you are a student with special need, Please inform the professor. Then, arrangements can be done with the Special Needs Section at the university 11. Students were warned about cheating,the student who cheat on any exam will receive a score zero for that examination.. SYLLABUS ITEM Limits and Continuity: The limit. One-sided limits. Limit theorems. Vertical and horizontal asymptotes. Continuity. Continuity of trigonometric functions. The intermediate-value theorem. The extreme-value theorem. Differentiation: Tangent lines and rates of change. The derivative. Rules of differentiation. Derivatives of higher order. Differentiation of trigonometric, logarithmic and exponential functions. The chain rule. Implicit differentiation. Applications of Derivatives: Increasing and decreasing functions. Relative extreme values. The first derivative test. The second derivative test. Absolute extreme values. Concavity. Points of inflection. Vertical tangents and cusps. Curve sketching. Max-Min problems. Mean-Value theorem. Rolle's Theorem. Integration: Antiderivatives. Indefinite and definite integrals. The fundamental theorem of Calculus. Properties. Integral formulas. Average value. Integration by substitution. Inverse Functions: Review of the inverse functions, continuity and differentiability of the inverse. Integration and differentiation of logarithmic and exponential functions. L Hopital s Rule. Applications of the Integral: Area between two curves. Volumes by slicing. Volumes by cylindrical shells 4

5 Lectures schedule Syllabus Distribution over the weeks Week Date Sec. Topics 1 Sep Review of Functions The tangent and Velocity Problems The Limit of a Function 2 Oct Sep. 30 Oct Oct Oct Calculating Limits Using the Limit Laws Limits at Infinity: Horizontal Asymptotes Continuity Derivatives and Rates of Change The Derivative as a Function Differentiation Formulas Derivatives of Trigonometric Functions The Chain Rule Implicit Differentiation Rates of changes in the Natural Science Related Rates First Exam: Sa, 20/10/2012, Oct Maximum and Minimum Values The Mean Value Theorem Eid: Oct 25- Nov 3 7 Nov How Derivatives Affect the Shape of a Graph 8 Nov Summary of Curve Sketching Graphing with Calculus 9 Nov Optimization Problems Antiderivatives 10 Nov Areas and Distances The Definite Integral The Fundamental Theorem of Calculus Second Exam: Sa,1/12/2012, Dec Indefinite Integral and Net Change Theorem The Substitution Rule Areas between Curves 12 Dec Dec Dec Volumes Average Value of a Function Inverse Functions. Exponential Functions & their Derivatives. The Natural Logarithmic Function. Derivatives of Logarithmic Functions. Indeterminate Forms & L Hopital s Rule. Final Exam: Sa, 29/12/2012,

6 Recommended Problems in the Textbook, to be attempted by the students LIST OF SELECTED PROBLEMS 1.4: 3, 4, 5, 9a,c 1.5: 4, 5, 7, 8, 9, 12-16, : 1-29 odd, odd, 49, 51, odd 1.8: 3-7 odd, 9, 11, odd, odd, 61, : 5-36, 51, : 1-11 odd, 17-30, 33-36, odd, odd 2.3: 1-41 odd, 49-81, odd 2.4: 1-33 odd, : 1-57 odd, odd, 79, 88, : 1-35 odd, 39, 40, 42, odd 2.8: 1-19 odd, 12-15, 19, 25, 27, 31, 37, : 3-41 odd, odd. 3.2: 1-7 odd, 11-19, 23, : 1, 5-41 odd, : 2, 3, 4, 9-29 odd, 33, 35, odd 3.5: 1-37 odd 3.7: 3-7 odd, odd, 49, 53, : 1-17 odd, odd, odd 4.1: 3, 5, odd 4.2: 1, 3, 9, 11, odd, odd, 47, : 3, 5-35 odd, 47, 49, 55, 64, : 1-41 odd, 46, 49, 55, : 1-49 odd 5.1: 1-31 odd, : 1-35 odd, 43, odd 5.3: 1-25 odd, odd 5.5: 1-9 odd, : 1-41 odd 6.2: 1-71 odd, : 1-59 odd, odd, odd 6.4: 3-9 odd, 6.8: 5-63 odd 6

7 Important Dates Date Day Event Semester Thursday Last day to apply for re-enrollment Fall Thursday Last day to apply for an incomplete grade Summer 2012 & Spring Sunday First day of classes Fall Thursday End of Registration, add and drop Fall Thursday Last day to change of an incomplete grade Summer2012 & Spring Thursday Last day to withdraw from a course Fall Sunday Start of early Registration Spring Thursday Last day to withdraw from semester Fall Thursday Last day of classes Fall Sunday Start of Final Exams Fall Thursday End of Final Exams Fall

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