MA1301

MA1301 Enhanced Calculus and Linear Algebra II

Part I

Course Duration: One semester
Credit Units: 3
Level: B1
Medium of Instruction: English
Prerequisites:
(i) MA1300 or
(ii) Grade B or above in MA1200 (approval from MA must be obtained)
Precursors: Nil
Equivalent Courses: Nil
Exclusive Courses:
MA1101 ,
MA1201 ,
MA1001 ,
MA1002 ,
MA1003 ,
MA1004

Part II

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

develop fluency in concepts and techniques from integral calculus, linear algebra and complex numbers,
introduce elementary theory of differential and integral calculus, and
foster skills in implementing methods of calculus and linear algebra to mathematical and physical applications.

Course Intended Learning Outcomes (CILOs)
Upon successful completion of this course, students should be able to

No.
CILOs Weighting(if applicable)
1. explain elementary theory of differential and integral calculus. 2
2. perform techniques of integration to evaluate integrals of functions. 2
3. explain at high level concepts from vector and matrix algebra. 1
4. manipulate expressions and solve geometric problems with vector arithmetic. 2
5. implement techniques of matrix arithmetic and of solving linear systems. 2
6. perform operations and solve equations involving complex numbers. 2
7. develop mathematical models through calculus and linear algebra, and appropriately apply to problems in science and engineering. 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 (A or B) according to mathematical background and/or results in HKDSE mathematics. Please refer to Section 3 of MA1300 Form 2B for details

TLAs
ILO No. Hours/week
Learning through teaching is primarily based on lectures. 1 – 7 39 hours in total (A);
46 hours in total (B)
Learning through tutorials is primarily based on interactive problem solving allowing instant feedback. 1 3 hours in total (A);
4 hours in total (B)
2 2 hours in total (A);
3 hours in total (B)
3, 4 2 hours in total (A);
3 hours in total (B)
3, 5 2 hours in total (A);
3 hours in total (B)
6 2 hours in total (A);
3 hours in total (B)
7 2 hours in total (A);
3 hours in total (B)
Learning through take-home assignments helps students implement theory of calculus, methods of integral calculus, linear algebra and complex numbers, as well as apply knowledge of which to mathematical and physical problems. 1 – 7 after class
Learning through online examples for applications helps students apply methods of calculus, linear algebra and complex numbers to problems in science and engineering. 7 after class
Learning activities in Math Help Centre provides students extra assistance in study. 1 – 7 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 – 7	15 – 30%	Questions are designed to see how well students have learned theory of calculus, techniques of integral calculus, as well as concepts and methods of linear algebra and complex numbers. These assessment tasks monitor students’ progress and reveal gaps in knowledge.
Hand-in assignment(s)	1 – 7	0 – 15%	These are skills based assessment to see whether students are familiar with elementary theory of calculus as well as essential methods and applications of integral calculus, linear algebra and complex numbers.
Examination	1 – 7	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 practical applications.

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 (CILOs 1 – 6),

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.(CILOs 1 – 7),

B−, B, B+

To achieve a grade of B, a student should

have good or very good mastery of all of the core components (CILOs 1 – 6),

and have demonstrated good to very good levels of fluency in mathematical writing and synthesis of core components in applications (CILOs 1 – 7).

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 (CILOs 1 – 6);

or, alternatively, of most of the core components of the course together with some demonstrated ability to synthesise them in applications (CILOs 1 – 7).

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

of most of the core components of the course (CILOs 1 – 6);

or, alternatively, of some of the core components of the course together with some demonstrated ability to synthesise them in at least an application (CILOs 1 – 7).

Part III

Keyword Syllabus
A) Basic theorems of differentiation

B) Applications of differentiation: rate of change, local extrema, optimization problems, power and
Taylor series, l’Hôpital rule

C)      Definite and indefinite integrals; Techniques of integration, integration by substitution,
          integration by parts; Improper integrals
D)     Physical and geometric applications of integration
E)      Vectors in R² and R³; Scalar products, cross products, triple scalar products; Linear
        (in)dependence; Applications to equations of lines and planes

F)      Matrices; Determinants, cofactor expansion; Systems of linear equations, Gaussian elimination,
         Cramer’s rule; Matrix inverses, Gauss-Jordan elimination method
G)     Arithmetic of complex numbers; Polar and Euler forms; De Moivre’s theorem and its
         applications