Jordan University of Science & Technology



Jordan University of Science and Technology

Faculty of Science

Department of Mathematics and Statistics

Semester 2006/2007

Course Syllabus For Math. 101 (Calculus I)

|Course Information |

|Course Title |Calculus I |

|Course Code |Math. 101 |

|Prerequisites | --- |

|Course Website | |

|Instructor |Coordinator Dr. Ibrahim Al-Ayyoub |

|Office Location |Ph2 Level 0 |

|Office Phone # |23451 |

|Office Hours |Sun. Tue. Thu. 3 - 4 and Mon. Wed. 2 - 3 |

|E-mail |iayyoub@just.edu.jo |

|Teaching Assistant(s) |See the list at the department |

|Course Description |

|Schedule Spring Semester 2007 |

|Week # |

|Week of |

|Sections |

|Material |

| |

|1 |

|Feb. 11, 2007 |

|0.3 |

|0.4 |

|Inverse Functions |

|Trigonometric and Inverse Trigonometric Functions |

| |

|2 |

|Feb. 18, 2007 |

|0.5 |

|1.2 |

|Exponential and Logarithmic Functions |

|The concept of limits |

| |

|3 |

|Feb. 25, 2007 |

|1.3 |

|1.4 |

|1.5 |

|Computation of Limits |

|Continuity and its Consequences |

|Limits Involving Infinity |

| |

|4 |

|March 4, 2007 |

|2.2 |

|2.3 |

|2.4 |

|2.5 |

|The derivative |

|Computation of Derivatives: The Power Rules |

|The Product and Quotient Rules |

|The Chain Rule |

| |

|5 |

|March 11 |

|2.6 |

|2.7 |

|Derivatives of Trigonometric Functions |

|Derivatives of Exponential and Logarithmic Functions |

| |

|6 |

|March 18 |

|2.8 |

| |

|2.9 |

|Implicit Differentiation and Inverse Trigonometric Functions |

|The Mean Value Theorem |

| |

|7 |

|March 25 |

|3.2 |

|3.3 |

|Indeterminate Forms and L’Hopital’s Rule |

|Maximum and Minimum Values |

| |

|8 |

|April 1 |

|3.4 |

|3.5 |

|3.6 |

|Increasing and Decreasing Functions |

|Concavity and the Second Derivative Test |

|Overview of Curve Sketching |

| |

|9 |

|April 8 |

|4.1 |

|4.2 |

|4.3 |

|Anti-derivatives |

|Sums and Sigma Notation |

|Area |

| |

|10 |

|April 15 |

|4.4 |

|4.5 |

|4.6 |

|The Definite Integral |

|The Fundamental Theorem of Calculus |

|Integration by substitution |

| |

|11 |

|April 22 |

|6.2 |

|6.3 |

|Integration by Parts |

|Trigonometric Techniques of Integration |

| |

|12 |

|April 29 |

|6.4 |

| |

|5.1 |

|Integration of Rational Functions Using Partial Fractions |

|Area Between Curves |

| |

|13 |

|May 6 |

|5.2 |

|5.3 |

|Volume: Slicing, Disks and Washers |

|Volumes by Cylindrical Shells |

| |

|14 |

|May 13 |

|5.4 |

|6.6 |

|Arc Length |

|Improper Integrals |

| |

|15 |

|May 20 |

|All chapters |

|Review |

| |

|16 |

|May 27 |

| |

|Final Exam (TBA) |

| |

|Textbook |

|Title | Calculus Early Transcendental Functions “Third Edition “ by Robert Smith & Roland Minton |

|Author(s) |Robert Smith & Roland Minton |

|Publisher |Mc Graw-Hill |

|Year |2007 |

|Edition |3rd |

|Book Website |highedstudent. |

|Other references |Any other Calculus book |

|Assessment |

|Assessment |Expected Due Date |Percentage |

|First Exam |Approx. End of week 6 |30% |

|Second Exam |Approx. End of week 12 |30% |

|Final Exam |Be announced by university |40% |

|Assignments |Homework will be assigned each week (not to be collected, or | |

| |graded by the instructor) | |

|Participation |To learn it is imperative for the student to take an active | |

| |interest in their own education. To learn mathematics the student| |

| |must read, think, and write in an analytical manner and this | |

| |takes practice. Such practice is by working exercises. When | |

| |troubles arise, and they will, the student must ask questions. | |

| |Questions may be posed to the instructor or to other students in | |

| |a variety of ways; online office hours, or in class. | |

|Attendance |Attendance is required by the university rules. If for some | |

| |reason a student reaches the 15% warning limit, he or she will be| |

| |prohibited from participating in the subsequence exams and | |

| |receives a grade of “35” in the course. | |

|Course Objectives |Percentage |

|Learn the concept of inverse functions and related techniques. |10% |

|Understand the concept of limits and its related topics such as continuity. Then understanding the concept of |25% |

|derivative as a consequence of applying the limit as a tool in solving the problem of finding the instantaneous rate| |

|of change. Then learn the techniques of differentiation of functions such as trigonometric, inverse trigonometric, | |

|exponential, and logarithmic function. | |

| Studying the behavior of the function through exploring its first and second derivatives. |15% |

|Understanding the concept of integration as a consequence of using the limits as a tool in solving the problem of |25% |

|finding the area under the curve of a function. Then learn some techniques of integration such as by parts, | |

|trigonometric substitution, and special substitution. | |

|Use the techniques of integration to study problems of finding area between curves and volumes of solids obtained |15% |

|when revolving a curve of a function around the x-axis or the y-axis. | |

|Learn the intuitive approach of the improper integrals and techniques to evaluate such integrals. |10% |

|Teaching & Learning Methods |

|General Learning Objectives |

|Understand and apply the concept of limits. |

|Differentiate and integrate various kinds of one single variable functions. |

|Describe and sketch graphs of functions using the first and second derivatives. |

|Use integration to find volumes and areas related to curves of functions. |

|Learning Outcomes: Upon successful completion of this course, students will be able to |

|Related Objective(s) |Will be able to |Reference(s) |

|Limits and Continuity |Analyze the behavior of a function as the dependent variable approaches a |Chapter 1 |

| |certain value. | |

| | | |

| |Use techniques to compute limits of various kinds of functions. | |

| | | |

| |Relate the concepts of limit and continuity and apply some consequences of | |

| |continuity such as the Intermediate Value Theorem. | |

| | | |

| |Recognize the existence of the vertical, horizontal, or slant asymptotes. | |

|Differentiation |Use the techniques of computing limits to define the derivative of a function |Chapter 2 |

| |at some point as the instantaneous rate of change. | |

| | | |

| |Derive the rules of differentiation and use them to find the derivatives of | |

| |various kinds of functions of single variable. | |

| | | |

| |Apply Rolle's and the Mean value Theorems. | |

|Application of Differentiation |Use the first and the second derivatives to |Chapter 3 |

| |Find the minimum and the maximum values of a function. | |

| |Find the intervals of increasing and decreasing. | |

| |Find the intervals of concavity. | |

| |Then using these information to drew a sketch of the curve of the given | |

| |function. | |

|Integration |Use the techniques of computing limits to define the integration of a function |Chapter 4 |

| |as the area under its curve. | |

| | | |

| |Learn the Fundamental Theorem of calculus and use it to define the definite | |

| |integral as the anti-derivate. | |

|Application of Integration |Use the integration techniques to find area between two curves, volumes of |Chapter 5 |

| |solids obtained when revolving a curve of a function around the x-axis or the | |

| |y-axis and the arc length of a segment of the curve of a given function. | |

|Integration Techniques |Integrate various kinds of functions by using some integration techniques such |Chapter 6 |

| |as substitution, parts, partial fraction, and trigonometric substitution. | |

|Useful Resources |

|Any calculus book can be used as a reference. |

|Additional Notes |

| |

|A graphing calculator is recommended but not required, Mathematics software such as Matlab, Mathematica and Maple may also be used for homework. And|

|any calculus book. |

| |

| |

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