MA2158 Linear Algebra and Calculus

Part I

Course Duration: One semester
Credit Units: 3
Level: B2
Medium of Instruction: English
Prerequisites: MA1200 or MA1300 and MA1201 or MA1301, ; or MA2176 or equivalent
Precursors: Nil
Equivalent Courses: MA3158 

Exclusive Courses: MA2149, MA2170

Part II      

Course Aims
This course aims to develop mathematical concepts and techniques in advanced linear algebra, multi-variable calculus and Fourier series  as well as their applications in science and engineering. It provides students skills and 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 at high levels concepts from advanced linear algebra and multi-variable calculus.

1

2.

compute eigenvalues and eigenvectors of matrices, and solve first and second order ordinary differential equations.

3

3.

Compute partial derivatives and multiple integrals of multivariate functions.

3

4.

implement basic operations in vector calculus and evaluate line and surface integrals of vector fields.

3

5.

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

2

6.

the combination of CILOs 1-5

3

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--6

39 hours in total

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

 

2

4 hours

3

4 hours

1, 5

3 hours

4

2 hours

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

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.

2--4

         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

 2, 5

15-30%

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

Hand-in assignments

1--5

0-15%

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

Examination

6

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 advanced linear algebra, ordinary differential equations and multi-variable calculus.

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 calculus  learned in this course.

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

Part III

Keyword Syllabus
Eigenvalues and eigenvectors. Applications in elasticity. First-and second-order ordinary differential equations and applications. Vector calculus. Partial differentiation. Multiple integration. Gradient, divergence and curl. Theorems of Gauss, Stokes and Green. Applications in energy methods, stress and strain transformations, etc. Fourier series.

Related Links
Department of Mathematics