MATH101 Calculus I

This course covers topics from Differential Calculus with an introduction to Integral Calculus. The course studies Limit and Continuity of functions, the Intermediate Value Theorem, Derivatives, Differentiation rules, Rolle's Theorem and the Mean Value Theorem, Applications of Differentiation, Anti-derivatives, Definite Integrals, and the Fundamental Theorem of Calculus. Applications of derivatives (to physical problems, related rates, maximum-minimum word problems and curve sketching), and of definite integrals (to some physical and geometric problems) are considered.

After completing this course, students should have developed a clear understanding of the fundamental concepts of single variable calculus and a range of skills allowing them to work effectively with the concepts.
The basic concepts are:
1. Derivatives as rates of change, computed as a limit of ratios
2. Integrals as a "sum," computed as a limit of Riemann sums
After completing this course, students should demonstrate competency in the following skills:
1. Understand the concept of a limit and continuity and determine limits of functions, both algebraic and transcendental
2. Compute and apply derivatives to real world problems
3. To utilize calculus techniques in order to analyze the properties and sketch graphs of functions
4. Understand both definite and indefinite integration, the Fundamental Theorem of Calculus and be able to apply some of the techniques for integrating functions to real world problems

Course Policies
The following are the policies for this course:
1. Attendance: It is mandatory to attend every lecture equipped with a writing instrument and either a notebook or paper.
2. Mobile Phone Usage: Mobile phones, including text messaging or checking messages, are strictly prohibited during lectures. Please ensure your mobile phone is turned off or set to silent mode.
3. Use of Electronic Devices: Laptops and other electronic devices are not permitted in the classroom unless you have obtained permission from the instructor to use them solely for note-taking purposes.
4. Language: English is the designated language for all classroom interactions and discussions.
5. Electronic Communication: All course-related electronic communication will be conducted through the university email or Teams platform. I will make every effort to respond to your emails within 24-48 hours. If you do not receive a reply within this timeframe, please feel free to resend your message.
6. Deadlines: It is crucial to adhere to all assignment and quiz deadlines. Late submissions will not be accepted unless accompanied by a serious and compelling reason, subject to instructor approval. Make-up assignments or quizzes will not be provided.
By following these policies, we can ensure a productive and engaging learning environment for everyone in the course.

Attendance Policy
1. It is mandatory for students to attend a minimum of 70 percent of lectures and 80 percent of other course components, such as tutorials, workshops, lab hours, and application classes, regardless of the reason for absence (medical or otherwise). This requirement is outlined in Article 16, item 1.
2. Failure to meet the attendance requirements may result in students being prohibited from taking the midterm and final examinations. This policy is stated in Article 16, item 2.
3. Exchange students are also expected to maintain a minimum attendance of 50 percent in all course activities, regardless of the reason for their absence (medical or otherwise). This is specified in Article 16, item 3.
4. If a student is unable to take an examination due to excessive absenteeism, they will receive a mark of "N/A" for that particular course. This is outlined in Article 16, item 4.
5. It is important to note that if a student is absent for one third or more of a class session, they will be considered absent. Additionally, three instances of tardiness will be counted as one absence. Leaving the class early will also be considered as being tardy.
6. In the event that a student misses a class, it is their responsibility to make up the material that was missed.
By adhering to these attendance policies, students can ensure their academic success and maintain a positive learning environment.

Textbook

University Calculus: Early Transcendentals, Global Edition, by Joel Hass, Christopher Heil, Maurice D. Weir, George Thomas. Publisher: Pearson Education Limited, 2019.

Additional Literature

1. UNIVERSITY CALCULUS EARLY TRANSCENDENTALS, Joel Hass, Christopher Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas, Jr.
2. Calculus, Ron Larson, Bruce Edwards
3. Thomas Calculus

Learning Outcomes

After successful completion of the course, the student will be able to:

Recognize and graph basic polynomial, rational and trigonometric functions.
Compute basic limits and have an understanding of the formal definition.
Use all the rules for computing derivatives and be familiar with the definition of derivatives and tangent line.
Apply derivatives for finding maxima/minima of a function.
Apply derivatives to determine monotinicity and concavity and graph functions
Find basic anti derivatives and definite integrals

Teaching Methods

Class lectures with lots of examples. Active tutorial sessions for engaged learning and continuous feedback on progress. Homework with more challenging or theoretical assignments.

Teaching Method Delivery

Face-to-face

Teaching Method Delivery Notes

WEEK

TOPIC

REFERENCE

Week 1

Review of some important Functions