MA2149 Mathematical Analysis

Part I

Course Duration: One semester
Credit Units: 3
Level: B2
Medium of Instruction: English
Prerequisites: A-Level Pure Mathematics/Applied Mathematics;
MA1200/MA1300 and MA1201/MA1301; or
MA2176 ; or
MA2183 or equivalent
Precursors: Nil
Equivalent Courses: Nil
Exclusive Courses: MA2158, MA2170

Part II      

Course Aims
This course aims to introduce important ideas in Linear Algebra, Advanced Calculus and Ordinary Differential Equations necessary for an understanding of their application to Science and Engineering. It will help students develop the ability to think quantitatively and analyse problems critically.

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

No.

CILOs

Weighting (if applicable)

1.

explain clearly mathematical concepts from linear algebra, advanced calculus and complex numbers.

2

2.

implement basic operations in complex numbers and matrices, and compute eigenvalues and eigenvectors of matrices.

3

3.

solve first and second order ordinary differential equations.

3

4.

evaluate Taylor series expansions, partial derivatives and multiple integrals of functions.

3

5.

apply mathematical and computational methods to a range of application problems involving linear algebra, ordinary differential equations and multi-variable calculus.

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)

TLAs

ILO No.

Hours/week

Learning through teaching is primarily based on lectures.

1--5

39 hours in total

Learning through tutorials is primarily based on interactive problem solving allowing instant feedback.

 

2

2 hours

3

2 hours

4

2 hours

1, 5

1 hour

Learning through take-home assignments helps students understand basic concepts and techniques of linear algebra, ordinary differential equations and multi-variable calculus, and their applications.

1--5

         after-class

Learning through online examples for applications helps students apply mathematical and computational methods to some problems in applications.

5

         after-class

Learning activities in Math Help Centre provides students extra help.

1--5

         after-class

 

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

Test

1--3

15-30%

Questions are designed for the first part of the course to see how well the students have learned concepts and techniques of linear algebra and ordinary differential equations.

Hand-in assignments

1--5

0-15%

These are skills based assessment to help students demonstrate advanced concepts and techniques of linear algebra, ordinary differential equations, multi-variable differential calculus and Fourier series and some applications in science and engineering.

Examination

1--5

70%

Examination questions are designed to see how far students have achieved their intended learning outcomes. Questions will primarily be skills and understanding based to assess the student’s versatility in linear algebra, ordinary differential equations, multi-variable differential calculus and Fourier series.

Formative take-home assignments

1--5

0%

The assignments provide students chances to demonstrate their achievements on linear algebra, ordinary differential equations and multi-variable differential calculus  learned in this course.

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 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.

D       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. 

Part III

Keyword Syllabus
Complex numbers, vectors, matrices, eigenvalues and eigenvectors, ordinary differential equations, Taylor series, differential calculus of multivariate functions, Fourier series.

Related Links
Department of Mathematics