COURSE OUTLINE: MH1101

Intended Learning Outcomes

Upon successfully completing this course, you should be able to:

1. Describe definite integrals in terms of Riemann sums and area, and the Fundamental Theorem of Calculus
2. Classify and evaluate improper integrals
3. Apply integration to real-world problems such as finding the area between curves, and the volume of a solid of revolution
4. Evaluate integrals using the Substitution rule, integration-by-parts, Trigonometric substitution, and partial fractions
5. Estimate definite integrals using numerical methods
6. Evaluate the limit of a sequence using formal definition.
7. Give examples of convergent and divergent sequences and series
8. Determine the convergence of a sequence and perform appropriate convergence tests for series
9. Describe how a function can be expressed as a power series, determine radius and interval of convergence of a power series
10. Represent certain functions by manipulating geometric series or by differentiating or integrating known series
11. Find Taylor series of a given function using definition or by manipulating known series, and verify convergence of series using the Error Bound

Course Content

Antiderivatives, definite integrals, Fundamental Theorem of Calculus

Substitution rule & improper integrals, Area between curves

Volumes, Integration-by-parts

Trigonometric integrals, Trigonometric substitution, partial fractions

Numerical integration, Limit of sequences

Finding limit of sequences

Monotonic sequence, Series

Integral test & the comparison test.

Absolute & conditional convergence, the Ratio & Root test,

Power series, radius and interval of convergence

Manipulate geometric series, term-by-term differentiation and integration, Taylor & Maclaurin series

Verify convergence of series using the Error Bound, Binomial series, finding limits using power series

Summary

Assessment

Formative Feedback

Homework (CA1 & CA2): formative feedback is written in the students’ homework solution, which are returned to the students.

Midterm Test (CA3): Feedback on common mistakes and students’ midterm test scripts will be provided.

Students will also receive formative feedback for all learning outcomes (including LO 9-11 tested in the final exam) during weekly tutorial classes from Week 2-Week 13.

Learning and Teaching Approach

Reading and References

James Stewart, Calculus (8th edition)

Course Policies and Student Responsibilities

Absence due to medical or other reasons

If you are sick and unable to attend a midterm test or missed the deadlines for your assignments, you must:
1. Send an email to the instructor regarding the absence.
2. Submit the original Medical Certificate* to an administrator.
*The Medical Certificate mentioned above should be issued in Singapore by a medical practitioner registered with the Singapore Medical Association.

In this case, a makeup assessment will be arranged. If a make-up test cannot be arranged due to unavailability of venue or other circumstances, the weightage of the test will be transferred to the final exam.

Collaboration Policy

Collaboration is encouraged for your homework because peer-to-peer learning helps you understand the subject better and working in a team trains you to better communicate with others in your profession. As part of academic integrity, crediting others for their contribution to your work promotes ethical practice.
You must write up your solutions by yourself and understand anything that you hand in.
If you do collaborate, you must write on your solution sheet the names of the students you worked with. If you did not collaborate with anyone, please explicitly write, “No collaborators." Failure to do so constitutes plagiarism.

Use of materials outside the course is strongly discouraged. If you use outside source, you must reference it in your solution.

Academic Integrity

Good academic work depends on honesty and ethical behaviour. The quality of your work as a student relies on adhering to the principles of academic integrity and to the NTU Honour Code, a set of values shared by the whole university community. Truth, Trust and Justice are at the core of NTU’s shared values.

As a student, it is important that you recognize your responsibilities in understanding and applying the principles of academic integrity in all the work you do at NTU. Not knowing what is involved in maintaining academic integrity does not excuse academic dishonesty. You need to actively equip yourself with strategies to avoid all forms of academic dishonesty, including plagiarism, academic fraud, collusion and cheating. If you are uncertain of the definitions of any of these terms, you should go to the Academic Integrity website for more information. Consult your instructor(s) if you need any clarification about the requirements of academic integrity in the course.

Course Instructors

Planned Weekly Schedule