DHA Suffa University Karachi
Department of Basic Sciences
Linear Algebra and Ordinary Differential Equations
BS-2303
TEACHER’S CONTACT DETAILS (To be filled in by instructor)
Instructor Muhammad Ashhad Shahid
Room No FF-130 (Main campus,DSU)
Office Hours Friday (Whole day)
Email 9mashhad@gmail.com, ashhad.shahid@dsu.edu.pk
Telephone Ext# 169
COURSE BASICS
Credit Hours 3
Course Code BS-2303
Lecture(s) No. of Lec(s) per Week 3 Duration 50 minutes
Lab (per
No. of Lec(s) per Week N/A Duration -
week)
Tutorial (per
No. of Lec(s) per Week 0 Duration -
week)
COURSE DISTRIBUTION
Core Yes
Elective No
Class CE-sem2, ME-2A/2B
Semester 2nd
COURSE DISCRIPTION
This course is based primarily on Linear Algebra and Differential Equations. This is an exciting course which
focuses on real world problems solving. Later this course will also discuss the applications of Ordinary
Differential Equations (ODEs) and Linear Algebra with problems in engineering
COURSE OBJECTIVES
This is an introductory course of the Linear Algebra and Differential equations (DE) which includes
an in-depth coverage of methods of solving system of linear equations and vectors spaces and
1.
linear combination of vectors, differential equations and mathematical modelling with
differential equations for real word problems
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COURSE LEARNING OUTCOMES
Taxonomy
S. No. CLO Statement Domain PLO
Level
Illustrate how to solve a system of linear equations that
1. Cognitive 2 1
appears in different engineering applications
Solve first and second order differential equations and
2. partial differential equations using the concepts developed Cognitive 3 1
in the course
Apply the concepts of ordinary derivatives and partial
3. Cognitive 3 1
derivatives for modelling of physical systems
GRADING BREAKUP AND POLICY
Quizzes 10%
Mid-Semester Exam 30%
Project/ Assignments and 10%
Class participation
Final Examination 50%
EXAMINATION DETAILS
Yes/No: Yes
Mid-Semester Exam Duration: 120 minutes
Exam specifications: Closed book, closed notes, calculators allowed
Yes/No: Yes
Final Exam Duration: 180 minutes
Exam specifications: Closed book, closed notes, calculators allowed
COURSE PREREQUISITE(S)
BS-1301 Calculus & Analytical Geometry
WEEKLY COURSE OUTLINE
Session Session Topic
Week 1 Matrices, special types, elementary row operations, echelon, reduced echelon form, rank
(1-3) of matrix, simultaneous linear equations, and homogeneous system of linear equations
A combinatorial approach to determinants, properties, minors and cofactors, evaluating
Week 2-3
determinants by row reduction method. Inverse using cofactors, Cramer’s rule, vector in 2-
(4-9)
space and 3-space , norm, arithmetic, dot product, projection, cross product
Week 4
Gaussian elimination & Gauss Jordan methods.
(10-12)
Week 5 Lines and planes in 3-Space. Euclidean vector space, inner product, norm, distance, angle,
(13-15) linear transformations Rn, to Rm, properties of linear transformation
Week 6-7 General vector spaces, inner product, norm, distance, angle, linear combinations,
(16-21) basis and dimension, row space, column space and null Space
Week 8-9 Inner product space, angle and orthogonally in inner product space. orthogonal bases,
(22-27) Gram-Schmidt process, QR-decomposition
Week 9 MID-SEMESTER EXAMINATION
Week 10 Classification, formation, family of Curves, first order differential equations (DE) including
(28-30) variable-separable form, homogeneous / non-homogeneous DE
Week 11-12
Exact / non-exact form
(31-36)
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Week 13
Linear and Bernoulli’s DE, Orthogonal trajectories.
(37-39)
Week14
Linear homogeneous / non-homogeneous Higher ODEs with Constant Coefficient
(40-42)
Week 15
Method of undetermined coefficients, Variation of parameter
(43-45)
Week 16 Solution of partial differential equations through direct method and method of separation
(46-48) of variable
FINAL EXAMINATION
TEXTBOOK(S)/SUPPLEMENTARY READINGS
Reference Books:
S. No. Book Title Author Name Edition Publisher
1. Advanced Engineering Mathematics Erwin Kryszig 9th Edition John Wiley
2. Elementary Linear Algebra Howard
10th edition John Wiley
Anton
Differential Equations with Boundary Dennis G Zill
3. Value Problems and M.R 9th edition Brooks/Cole
Cullen
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