JOHN CABOT UNIVERSITY COURSE CODE: "MA 198-1" COURSE NAME: "Calculus I" SEMESTER & YEAR: Spring 2015

SYLLABUS INSTRUCTOR: Stefano Guarino EMAIL: [email protected] HOURS: TTH 4:30 PM 5:45 PM TOTAL NO. OF CONTACT HOURS: 45 CREDITS: 3 PREREQUISITES: Prerequisite: Placement or completion of MA 197 with a grade of C- or above OFFICE HOURS:

COURSE DESCRIPTION: The aim of this course is to introduce the students to all fundamental concepts of calculus: limiting behaviours, difference quotients and the derivative, definite integrals, antiderivative and indefinite integrals and the fundamental theorem of calculus. Using an intuitive yet rigorous approach, the students will both understand the rationale behind these concepts, and learn how to apply them to solve practical problems.

SUMMARY OF COURSE CONTENT: This course will explore the fundamental topics of traditional calculus such as limits, continuity, derivatives, and integrals of algebraic and transcendental functions of one variable. Particular emphasis will be given to applications and to the ability to analyse a real-word problem in mathematical terms. The students will understand that the concept of function is extremely flexible and can be used to describe a multitude of phenomena. They will learn how to use the instruments of calculus to gain an insight into the properties of such phenomena. Registration into the course is by placement or by completion of MA197 with a grade of C- or higher.

LEARNING OUTCOMES: Upon successful completion of this course, students should have familiarity with limiting, differentiation and integration techniques, applied to algebraic and transcendental functions. More specifically, they should be able to: - Define a limit. - Use algebraic techniques to evaluate limits. - Define continuity and determine whether or not a function is continuous at a point and on an interval. - Define a derivative and use the definition to differentiate selected functions. - Use the product, quotient, and chain rules to differentiate selected functions. - Implicitly differentiate selected two-variable equations. - Evaluate indefinite and definite integrals of elementary functions, including selected trigonometric functions. - State the basic properties of the definite integral. - Apply the Fundamental Theorem of Calculus.

TEXTBOOK: Book Title Author Publisher ISBN number Library Call Number Comments Format Local Bookstore Online Purchase Calculus, 10th INTERNATIONAL edition Ron Larson and Bruce Edwards Cengage Learning 978-1-285-09108-2

REQUIRED RESERVED READING: NONE RECOMMENDED RESERVED READING: NONE

GRADING POLICY -ASSESSMENT METHODS: Assignment Guidelines Weight Homework Homework assignments will be graded: the average grade weighs 10 percent of the final grade. 10% Attendance Full credit for attendance will be given to students with three or fewer unexcused absences. Four or more absences will result in a proportional reduction of the grade. 10% Quizzes Along the course, students will be asked to solve and hand in simple, ten-to-fifteen-minute quizzes. The average quiz score weighs fifteen percent of the final grade (the lowest quiz score can be dropped). 15% Mid-term exam At the middle of the course, students will take a test concerning all topics introduced till then. The mid-term exam score weighs twenty percent of the final grade. 20% Final exam The final exam score weighs forty-five percent of the final grade. Nevertheless, a grade of C- or higher in the final exam is necessary to successfully complete the course. 45% -ASSESSMENT CRITERIA: AWork of this quality directly addresses the question or problem raised and provides a coherent argument displaying an extensive knowledge of relevant information or content. This type of work demonstrates the ability to critically evaluate concepts and theory and has an element of novelty and originality. There is clear evidence of a significant amount of reading beyond that required for the course. BThis is highly competent level of performance and directly addresses the question or problem raised.There is a demonstration of some ability to critically evaluatetheory and concepts and relate them to practice. Discussions reflect the student’s own arguments and are not simply a repetition of standard lecture andreference material. The work does not suffer from any major errors or omissions and provides evidence of reading beyond the required assignments. CThis is an acceptable level of performance and provides answers that are clear but limited, reflecting the information offered in the lectures and reference readings. DThis level of performances demonstrates that the student lacks a coherent grasp of the material.Important information is omitted and irrelevant points included.In effect, the student has barely done enough to persuade the instructor that s/he should not fail. FThis work fails to show any knowledge or understanding of the issues raised in the question. Most of the material in the answer is irrelevant. -ATTENDANCE REQUIREMENTS: Full credit for attendance will be given to students with three or fewer unexcused absences. Four or more absences will result in a proportional reduction of the grade. Coming late to class or leaving early will be possible only with permission of the instructor.

ACADEMIC HONESTY As stated in the university catalog, any student who commits an act of academic dishonesty will receive a failing grade on the work in which the dishonesty occurred. In addition, acts of academic dishonesty, irrespective of the weight of the assignment, may result in the student receiving a failing grade in the course. Instances of academic dishonesty will be reported to the Dean of Academic Affairs. A student who is reported twice for academic dishonesty is subject to summary dismissal from the University. In such a case, the Academic Council will then make a recommendation to the President, who will make the final decision.

STUDENTS WITH LEARNING OR OTHER DISABILITIES John Cabot University does not discriminate on the basis of disability or handicap. Students with approved accommodations must inform their professors at the beginning of the term. Please see the website for the complete policy.

SCHEDULE

Session Session Focus Reading Assignment Other Assignment Meeting Place/Exam Dates 1st week, 2nd week, and 3rd week LIMITS AND THEIR PROPERTIES (Chap 1): Finding limits graphically and numerically. Evaluating limits analytically. Continuity and one-sided limits. Infinite limits. Limits at infinity. Chapter 1; Chapter 3 sect. 3.5 TBD   3rd week, 4th week, and 5th week DIFFERENTIATION (Chap 2): The Derivative and the tangent line problem. Basic differentiation rules and rates of change. The product and quotient rules and higher-order derivatives. The chain rule. Implicit differentiation. Related rates. Chapter 2 TBD   6th week LOGARITHMIC, EXPONENTIAL, AND OTHER TRANSCENDENTAL FUNCTIONS (Chap 5): The natural logarithmic function: differentiation. Exponential functions: Differentiation. Bases other than e and applications. Chapter 5 TBD   7th week, 8th week, 9th week, and 10th week APPLICATIONS OF DIFFERENTIATION (Chap 3): Extrema on an interval. Rolle’s theorem and the mean value theorem. Increasing and decreasing functions and the first derivative test. Concavity and the second derivative test. A summary of curve sketching. Chapter 3 TBD Week 7: Mid-term exam 10th week, 11th week, and 12th week INTEGRATION (Chap 4): Antiderivatives and indefinite integration. Area. Riemann sums and definite integrals. The fundamental theorem of Calculus. Chapter 4 TBD   13th week and 14th week INTEGRATION TECHNIQUES, L’HOPITAL’S RULE, AND IMPROPER INTEGRALS (Chap 8): Basic integration rules. Integration by parts. Integration by substitution. Partial fractions. Indeterminate forms and l’Hopital’s rule. Chapter 8 TBD Final exam (comprehensive). See University schedule for date and time.