Module Handbook-Mathematics-Universitas Brawijaya
Module Handbook
Module Name: Elementary Linear Algebra
Module Level: Bachelor
Abbreviation, if
Applicable: MAM61102
Sub-Heading, if
Applicable: -
Courses included in the
module, if applicable Elementary Linear Algebra Semester/term: 1st/ 1st year
Module Coordinator(s): Chair of the Lab. Algebra
Lectures(s)
Vira Hari Krisnawati, S.Si., M.Sc.
Dra. Ari Andari, M.Si.
Abdul Rouf Alghofari, M.Sc., Ph.D Dwi Miftah M., S.Si., M.Si.
Language Bahasa Indonesia
Classification within the
curriculum Compulsory Course
Teaching format / class hours per week during semester:
200 minutes lectures per week.
Workload:
Total workload is 6 ECTS, which consists of 3.33 hours lectures, 4 hours structured activities, 4 hours independent learning, 16 week per semester, and a total 181.33 hours per semester including mid exam and final exam.
Credit Points: 4
Requirements according to the examination regulations:
Students have attendance at least 80% on “Elementary Linear Algebra” class and registered as examinees in the academic information system
Recommended
prerequisties Students have participated in the final exam of the course.
Module
objectives/intended learning outcomes
After completing this course the student should have
CLO 1 : ability to understand the theory of matrices and determinants and apply their properties.
CLO 2 : ability to solve the system of linear equations.
CLO 3 : ability to understand the concept related to general vector spaces and subspace.
CLO 4 : ability to explain the concept related o inner vector spaces.
CLO 5 : ability to understand and prove the properties of linear transformation.
CLO 6 : ability to perform the orthogonal diagonalization of a matrix.
Module Handbook-Mathematics-Universitas Brawijaya Content:
Topics:
1. Theory of marices: various of matrices, operations on matrices, elementary transformation, inverse matrix.
2. The theory of determinant: calculate the determinant of a matrix, prove and apply the properties of determinant.
3. The system of linear equations.
4. Vectors on R2 and R3: vector algebra, inner product, cross product 5. The Euclidean vector spaces which have dimension n.
6. General vector spaces: real vector spaces, subspaces, linear independent, basis, dimension, rank, colomn spaces, row spaces, null spaces.
7. Inner product spaces: inner product, angle of two vectors and their orthogonality, orthonormal basis, Gram Schmidt’s process, transformation of basis.
8. Linear transformations from Rn to Rm, the properties of linear transformations, and similarity.
9. Eigen value problems, Orthogonal diagonalization Soft Skill Attribute Discipline, honesty, cooperation and communication
Study / exam achievements:
The final mark will be weighted as follows:
No. Assessment methods (component, activities). Weight
1. Quiz 20 %
2. Assignments 20 %
3. Middle Examination 30 %
4. Final Examination 30 %
Final grades is defined as follow:
A : 80 < Final Mark ≤ 100 B+ : 75 < Final Mark ≤ 80 B : 69 < Final Mark ≤ 75 C+ : 60 < Final Mark ≤ 69 C : 55 < Final Mark ≤ 60 D+ : 50 < Final Mark ≤ 55 D : 44 < Final Mark ≤ 50 E : 0 ≤ Final Mark ≤ 44
Forms of Media Slides and LCD projectors, laptop/ computer, whiteboards.
Learning Methods Lecture
Literature
1. Anton, H., Rorres, C, 2004, Aljabar Linier Elementer ( versi aplikasi), Jilid 1, Erlangga, Jakarta.
2. Keith Nicholson, 2001, Elementary Linear Algebra, McGraw-Hill Book Co., Singapore.
3. David C. Lay, 2012, Linear Algebra and Its Applications, 4th Edition Linear Algebra and Its Applications, Addison Wesley.
http://web.stanford.edu/class/nbio228.01/handouts/Linear%20Alge bra_David%20Lay.pdf
4. The Handbook of Elementary Linear Algebra by internal lecturer team
Notes:
Module Handbook-Mathematics-Universitas Brawijaya
