MA1300

MA1300 Enhanced Calculus and Linear Algebra I

Part I

Course Duration: One semester
Credit Units: 3
Level: B1
Medium of Instruction: English
Prerequisites:
(i) HKDSE Mathematics Compulsory Part and Extended Part Mdule o1 (Level 5), or
(ii) HKDSE Mathematics Compulsory Part and Extended Part Module 2 (Levels 3 – 5); or equivalent
Precursors: Nil
Equivalent Courses: Nil
Exclusive Courses:
MA1100 ,
MA1200 ,
MA1001 ,
MA1002 ,
MA1003 ,
MA1004

Part II

Course Aims
This is the first of two required courses designed for students pursuing studies in mathematics, or engineering/physics students requiring solid background in mathematics. It aims to

strengthen skills and methods essential for study for further matematics,
develop fluency in concepts of limits and techniques of differential calculus, and
nurture skills in logical thinking and translation of ideas with formal mathematical language.
Course Intended Learning Outcomes (CILOs)
Upon successful completion of this course, students should be able to

No.
CILOs Weighting(if applicable)
1. implement mathematical methods of algebra, trigonometry and coordinate geometry proficiently. 2
2. explain properties of functions and manipulate expressions involving standard functions and their inverses. 2
3. apply concepts and theory of sequences to evaluate their limits. 3
4. describe concepts on infinite series and test their convergence/divergence. 2
5. explain at high level concepts of limit, continuity and differentiability of functions. 2
6. perform techniques of differentiation to obtain derivatives of functions. 2

Teaching and Learning Activities (TLAs)
Indicative of likely activities and tasks students will undertake to learn in this course. Final details will be provided to students in their first week of attendance in this course.
Students are assigned to lecture sessions according to mathematical background and/or results in HKDSE mathematics.
Students in Section B benefit from extra tuition hours.

HKDSE Mathematics			Section
Compulsory Part	Module 1 (Level 5)	Module 2	Section
ü		ü (Levels 4 – 5)	A
ü		ü (Levels 1 – 3)	B
ü	ü		B
New Foundation Year of CSE			A

Note: ü = passed

TLAs	ILO No.	Hours/week
Learning through teaching is primarily based on lectures.	1 – 6	39 hours in total (A); 46 hours in total (B)
Learning through tutorials is primarily based on interactive problem solving allowing instant feedback.	1	2 hours in total (A); 3 hours in total (B)
	2	2 hours in total (A); 3 hours in total (B)
	3	3 hours in total (A); 4 hours in total (B)
	4	2 hours in total (A); 3 hours in total (B)
	5	2 hours in total (A); 3 hours in total (B)
	6	2 hours in total (A); 3 hours in total (B)
Learning through take-home assignments helps students implement concepts of functions and limits, evaluate limits of sequences, series and functions, test for convergence/divergence of series as well as apply techniques of differential calculus.	1 – 6	after class
Learning activities in Math Help Centre provides students extra assistance in study.	1 – 6	after-class,depending on need

Assessment Tasks/Activities
(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)

30% Coursework
70% Examination (Duration: 2 hours, at the end of the semester)

For a student to pass the course, at least 30% of the maximum mark for the examination must be obtained.

Assessment Tasks/Activities	ILO No.	Weighting(if applicable)	Remarks
Quizzes/Test(s)	1 – 6	15 – 30%	Questions are designed to see how well students have learned basic mathematical methods, concepts of functions, limits, continuity and differentiability, as well as techniques of differential calculus. These assessment tasks monitor students’ progress and reveal gaps in knowledge.
Hand-in assignment(s)	1 – 6	0 – 15%	These are skills based assessment to see whether students are familiar with essential mathematical techniques, properties of functions, theory and methods of limits of sequences and series as well as techniques of differential calculus.
Examination	1 – 6	70%	Examination questions are designed to see how far students have achieved their intended learning outcomes. Questions will primarily be skills based to assess the extent to which students have mastered methods of the course and synthesized mathematical knowledge in more sophisticated problems.

Grading of Student Achievement: Refer to Grading of Courses in the Academic Regulations

A−, A, A+

To achieve a grade of A, a student should

have complete, or close to complete, mastery of all of the core components,

and have demonstrated high levels of fluency in mathematical writing and synthesis of core components, as evidenced by the successful use of mathematical techniques in applications.

B−, B, B+

To achieve a grade of B, a student should

have good or very good mastery of all of the core components,

and have demonstrated good to very good levels of fluency in mathematical writing and synthesis of core components in applications.

C−, C, C+

To achieve a grade of C, a student should have good working knowledge

of all of the core components of the course;

or, alternatively, of most of the core components of the course together with some demonstrated ability to synthesise them in applications,.

To achieve a grade of D, a student should have some working knowledge

of most of the core components of the course;

or, alternatively, of some of the core components of the course together with some demonstrated ability to synthesise them in at least an application.

Part III

Keyword Syllabus
A)          Polynomials; Mathematical induction
B)          Coordinate geometry and conic sections; Basic trigonometry
C)          Functions and inverses
D)          Limits of sequences and infinite series
E)          Limits, continuity and differentiability of functions
F)          Techniques of differentiation, implicit, logarithmic and parametric differentiation; Successive
              differentiation