MA1201

MA1201 Calculus and Basic Linear Algebra II

Part I

Course Duration: One semester
Credit Units: 3
Level: B1
Medium of Instruction: English
Prerequisites:
(i) MA1200 , or
(ii) Grade B or above in MA1100 (approval from MA must be obtained), or
(iii) MA1300 (approval from MA must be obtained)
Precursors: Nil
Equivalent Courses: MA1003, MA1004
Exclusive Courses:

MA1101 ,

MA1301

Part II

Course Aims
This is the second of two required courses designed for students pursuing studies in engineering or physics. The course aims to

develop fluency in concepts and techniques from integral calculus, linear algebra and complex numbers, and
provide students with mathematical training for all further study in science/engineering and its applications.

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

No.
CILOs Weighting(if applicable)
1. perform techniques of integration to evaluate integrals of functions. 3
2. explain clearly concepts from vector and matrix algebra. 1
3. manipulate expressions and solve geometric problems with vector arithmetic. 2
4. implement techniques of matrix arithmetic and of solving systems of linear equations. 3
5. perform basic operations and solve equations involving complex numbers. 2
6. apply methods of integral calculus, linear algebra and complex numbers to model problems in science and engineering. 2

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)

Students are assigned to lecture sessions (A, B, C or D) according to mathematical background and/or results in HKDSE mathematics. Please refer to Section 3 of MA1200 Form 2B for details.

TLAs
ILO No. Hours/week
Learning through teaching is primarily based on lectures. 1 – 6
39 hours in total (A/B);
46 hours in total (C/D)
Learning through tutorials is primarily based on interactive problem solving allowing instant feedback. 1 3 hours in total (A/B);
4 hours in total (C/D)
2, 3 3 hours in total (A/B);
4 hours in total (C/D)
2, 4 3 hours in total (A/B);
4 hours in total (C/D)
5 2 hours in total (A/B);
4 hours in total (C/D)
6 2 hours in total (A/B);
3 hours in total (C/D)
Learning through take-home assignments helps students implement concepts and methods of integral calculus, linear algebra and complex numbers, as well as apply knowledge of which to problems in science and engineering. 1 – 6 after class
Learning through online examples for applications helps students apply methods of integral calculus, linear algebra and complex numbers to problems in science and engineering. 6 after class
Learning activities in Math Help Centre provides students extra assistance in study. 1 – 6 after-class,depending on need

Assessment Tasks/Activitie
(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 techniques of integral calculus, as well as concepts and arithmetic of linear algebra and complex numbers. 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 methods and applications of integral calculus, linear algebra and complex numbers.
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 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 – 5),

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 (CILO 6).

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 – 5),

and have demonstrated good to very good levels of fluency in mathematical writing and synthesis of core components in applications (CILO 6).

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 – 5);

or, alternatively, of most of the core components of the course together with some demonstrated ability to synthesise them in applications (CILO 6).

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

of most of the core components of the course (CILOs 1 – 5);

or, alternatively, of some of the core components of the course together with some demonstrated ability to synthesise them in at least an application (CILO 6).

Part III

Keyword Syllabus
A)          Definite and indefinite integrals; Techniques of integration, integration of rational functions, integration by substitution, integration by parts
B)          Physical and geometric applications of integration
C)          Vectors in R2 and R3; Scalar products, cross products, triple scalar products; Linear (in)dependence
D)          Matrices; Determinants, cofactor expansion; Systems of linear equations, Gaussian elimination, Cramer’s rule; Matrix inverses, Gauss-Jordan elimination method
E)          Arithmetic of complex numbers; Polar and Euler forms; De Moivre’s theorem and its applications