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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