MA2183 College Calculus
Course Duration: One semester
Credit Units: 3
Medium of Instruction: English
Prerequisites: HKCEE Additional Mathematics (Grade C or above) or HKAS Mathematics and Statistics (Grade C or above) or MA2182 or equivalent
Equivalent Courses: Nil
Exclusive Courses: MA2176
Part II Course Aims
· To introduce and develop fluency in concepts and techniques from differential and integral calculus.
· To nurture and develop skills in logical thinking and translation of ideas using mathematical language and formalism.
· To provide students with essential mathematical training for all further study in mathematics and its applications.
Course Intended Learning Outcomes (CILOs)
Upon successful completion of this course, students should be able to:
|explain concepts of limit, continuity and differentiability of functions.|
|perform techniques of differentiation to obtain derivatives and Taylor series expansions of functions.|
|perform techniques of integration to evaluate integrals of functions.|
|implement integration methods in geometrical and physical problems.|
|apply mathematical methods to a range of problems in science and engineering involving differential and integral calculus.|
Teaching and Learning Activities (TLAs)
(Indicative of likely activities and tasks designed to facilitate students’ achievement of the CILOs. Final details will be provided to students in their first week of attendance in this course)
The following teaching and learning activities are spread evenly throughout the semester and are aligned with CILOs in approximately chronological order:
o A large class activity (lecture) involves students engaged in learning with one instructor/lecturer.
o A small interactive class (tutorial) involves students engaged in individual learning, interactive problem solving or small group discussion with instructors/tutors.
o Take-home assignments are extended written learning tasks which students complete
· on their own for work which is handed in, marked and returned with comments,
· and on their own or collaboratively for work which is not to be handed in.
o Online activities involve prepared materials available online using Blackboard, and focus primarily on computational methods and applications to problems in science and engineering.
o Remedial learning activities are provided by the Math Help Centre for students who require extra assistance.
Large class activities (lectures)
39 hours in total
Small interactive classes (tutorials)
|1,2,3,4,5||6 – 8 hours after class|
|Online activities using Blackboard|
6 hours after class
|Learning activities for extra help by Math Help Centre|
after class, depending on need
Assessment Tasks/ActivitiesCoursework (30%)
(Indicative of likely activities and tasks designed to assess how well the students achieve the CILOs. Final details will be provided to students in their first week of attendance in this course)
Coursework comprises “Class Quizzes” and “Assignments”.
· At least one diagnostic quiz for each of the four sections in the Keyword Syllabus (in Part III) is provided to monitor students' progress and give prompt feedback.
· These assessments are primarily formative, revealing weaknesses or gaps in knowledge or understanding.
· Feedback to the student highlights areas or particular details where the student should pay more attention to or seek remedial help.
· The major focus of these quizzes is the components CILOs 1– 5.
· Some assignment sheets are set, but not handed in, which students may complete individually or collaboratively, mark themselves against published (online) solutions, encouraging self-reflection and independent enquiry.
· Successful completion of assignments demonstrates mastery of core concepts/techniques (CILOs 1–4) and provides practice in applying mathematical methods to real-life problems (CILO 5).
· The end of semester 2-hour examination is a thorough summative assessment.
· The examination consists of four parts, each on a section in the Keyword Syllabus (in Part III).
· To be given a pass grade (i.e., D or above), a student has to obtain the minimum score of each part.
· Each part examines the extent to which students have mastered concepts and methods of the course (CILOs 1–4).
· The examination also examines students’ ability to synthesize knowledge using mathematical applications in science and engineering (CILO 5).
For a student to pass the course, at least 30% of the maximum mark for the examination must be obtained.
Grading of Student Achievement:
A−, A, A+
To achieve a grade of A, a student should
· have complete, or close to complete, mastery of mathematical concepts and techniques in this course,
· and have demonstrated very high levels of fluency in mathematical writing and synthesis of knowledge, as evidenced by the successful application of mathematical methods in science and engineering problems.
B−, B, B+
To achieve a grade of B, a student should
· have good or very good mastery of mathematical concepts and techniques in this course,
· and have demonstrated good to very good levels of fluency in mathematical writing and synthesis of mathematical knowledge in applications to science and engineering.
C−, C, C+
To achieve a grade of C, a student should have good working knowledge
· of mathematical concepts and techniques in this course,
· or, alternatively, of most of the concepts and techniques in this course, together with some demonstrated ability to synthesize them in applications to science and engineering.
To achieve a grade of D, a student should have some working knowledge
· of mathematical concepts and techniques in this course,
· or, alternatively, of some of the concepts and techniques in this course, together with some demonstrated ability to synthesize them in at least one application to science and engineering.
A) Limits, continuity and differentiability; Techniques of differentiation, product rule, quotient rule, chain rule, implicit differentiation, logarithmic differentiation, successive differentiation, Leibnitz rule
B) Applications of differentiation: rate of change, local extrema, optimization problems, l’Hôpital rule, Taylor series
C) Definite and indefinite integrals, fundamental theorems of calculus, techniques of integration, integration by substitution, integration by parts
D) Applications of integration: area of the region bounded by curves, arc length of a curve, surface area and volume by revolution of a lamina about an axis
Department of Mathematics