MA 1021 CALCULUS I Syllabus
Contact Information
Instructor: Weijie Pang
Email: wpang@worcester.edu
Office: Stratton Hall 002
Office hours:
Monday & Wednesday & Friday, 11:30 a.m. - 12:30 p.m., 3:30 p.m. – 4:30 p.m.
TA: xxxxxxxx
Email: xxxxxxx
Office: Stratton Hall 204
Office hours: Tuesday, 11:30 a.m. - 13:30 p.m
Prerequisites: Algebra, trigonometry and analytic geometry.
Lecture: Mon – Thursday, 1:00 p.m. – 1:50 p.m.
Textbook: Thomas, G. B., Weir, M. D., Hass, J., & Giordano, F. R. (2010). Thomas' Calculus Early Transcendentals. Pearson.
Description:
Calculus I is the fundamental of many scientific, technological and engineering courses. It’s the prerequisite for Calculus II, III, IV, Advanced Calculus and all other mathematical courses. The main topics for this course are limits, derivatives and their application in real world. We will first introduce the rigorous definition of limit and then practice the computation of limits. Students must remember the definition and compute the limit by hands and by software (Maple). Then we define the continuity of functions by the limit. Students will be able to differentiate continuous functions with discontinuous functions. We also introduce the rigorous definitions, computations and applications of derivatives. Students must remember the definition, compute it by hands and software (Maple) and explain the meaning of the derivative in practical problems. We also introduce the optimization problem, implicit differentiation, linear approximation and Newton’s method. Students need to solve these problems by hands and software. After we learn Mean-Value theorem, we will learn the extreme value, concavity and curve sketch. Students need to solve the related questions by hands.
During this course, students need to finish one poster presentation project (three members) to introduce the three applications of Calculus in one field of Science, Technology, Engineer and Art. Students need to finish weekly homework, bi-weekly quizzes and a final exam. Besides the assignments, students need to answer the questions in classes to gain in-class performance score. If students have any questions and problems about this course, welcome to my office hours and personal appointments.
Course Outline
Week 1: Functions, Operations on Functions, Transcendental Functions (1.1-1.6), Limit Concepts (2.1, 2.2) ,
Week 2:Rigorous Definitions, One-Sided Limits (2.3, 2.4), Continuity (2.5), Limits involving infinity (2.6)
Week 3: Introduction to the Derivative (3.1-3.4), Derivatives of Trig Functions (3.5), Chain Rule (3.6)
Week 4: Implicit Differentiation (3.7), Derivatives of Inverse Functions: Logs and Inverse Trig Functions (3.8, 3.9),
Week 5: Related Rates (3.10), Differentials and Linear Approximation (3.11), Extreme Values (4.1), Mean Value Theorem (4.2)
Week 6: First and Second Derivative Tests, Concavity, Curve Sketching (4.3-4.4),
Week 7: Applied Optimization (4.6), Newton's Method (4.7), Review
Objective
By the successful completion of this course, students will be able to
1. compute the limits and derivatives by hands and Maple.
2. solve related practical problems by the knowledge of limits and derivatives.
3. communicate the mathematical knowledge and terminologies with their peers.
4. have the teamwork and collaboration skill and poster presentation ability.
Homework:
There will be seven homework, one per each week. The homework will be posted (https://canvas.wpi.edu) on every Thursday. Please hand in your homework on next Thursday in class. The solution will be posted within 24 hours after the deadline. The graded homework will be returned in class.
Late homework will not be accepted or graded. But only the top six of seven homework will be counted into the final score.
Quiz:
There will be quizzes on Wednesday at the second, fourth and sixth week. Each quiz will cover the recent two weeks materials. All quizzes are open book and open notes. Students need to finish two questions in 20 minutes. The total point of each quiz is 20 points, with 10 points per question.
If students can not show up at the quiz day, please inform the instructor 24 hours ahead to schedule a make-up test.
Poster Presentation Project:
This is a team assignment of three-students-team. Team members need to review the practical application of Calculus in one field of science, technology, engineer, and art, select three examples in one field. Then design a poster board to introduce these three applications. Poster presentation day is the last class day. The presentation will be graded by the instructor and all peers. Please read the project assignment for more details.
Final Exam:
A final exam will cover all materials from the first class to the last one. It will be a one-hour exam with the closed book and closed notes. But you could have one page of a cheating sheet, which is one-sided 8 1⁄2 x 11 in (A4) size paper. The time is in class at the last day.
Class Participation:
The in-class participation will be 10% of final score. The score only depends on the times of the participation but not depend on the correct of the answers. Asking questions and answering questions are strongly recommended.
Discussion:
Discussion about any mathematical questions are allowed and strongly recommended. You could learn how to communicate with your peers in mathematical methods during these discussions. And discussions is also a good and effect method to solve problems and find the mistakes. But the copy of other people’s solution is not accepted. Please read the Academic Dishonesty Policy in this syllabus.
Grading Scheme:
Course Philosophy:
In this course, students are strongly recommended to discuss and communicate with their classmate, friends and all others. During the discussion, students could find their distinct and effective way to study mathematical knowledge. Also the instructor will provide diverse teaching styles for students. In the first week, all students need to make a one to one face meeting with the instructors. In this meeting, we could discuss the your confusions, worries and goals for this course. By this meeting, instructor will provide more specific teaching methods for different students. If you have any problems or confusions for this course during the study, you are welcome to email me and make a personal appointment to discuss these issues. As we all know, mathematics, especially calculus, has a lot of applications in many fields. Because students come from different majors, if you have some special requirements or interesting topics, please let me know. I'm very glad to update our materials for more useful and applied topics.
Students with disabilities:
If you need any adaptations because of disabilities and medical issues, please contact me and make an appointment as soon as possible.
Academic Dishonesty Policy:
Please read WPI’s Academic Honesty Policy (https://www.wpi.edu/offices/policies/honesty/policy.html). Any dishonesty actions are not accepted. Each student is responsible for his or her assignments and works. Please ask the instructor if you have any questions about it.