MATH 120 – Linear Algebra with Differential Equations
Spring 2014-2015
Instructor
Adnan Khan, Sultan Sial
Room No.
249 SSE
Office Hours
TBA
Email
adnan.khan@lums.edu.pk
Telephone
8015
Secretary/TA
Shazia Tabassum (8160)
TA Office Hours
TBA
Course URL (if any)
http://suraj.lums.edu.pk/~adnan.khan/classes/classes/LinearAlgebra/
Course Basics
Credit Hours
3
Lecture(s)
2
75 min
Recitation/Lab (per week)
Tutorial (per week)
N/A
N/A
Course Distribution
Core
Elective
Open for Student Category
Close for Student Category
COURSE PREREQUISITE(S)
Math in A Levels, FSc or Equivalent
COURSE OBJECTIVES
To provide students with a solid grounding in concepts and methods of linear algebra
Help them develop the ability to formulate and solve problems using these techniques
To improve their ability to reason abstractly and understand proofs
Develop careful (mathematical) as opposed to intuitive thinking
Learning Outcomes
After completing this course, students should be able to:
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Grading Breakup and Policy
Solve systems of linear equations and to use linear systems to model and analyze.
Perform matrix operations, including matrix inversion.
Translate linear systems into matrix equations, and use matrix inverses to solve, where appropriate.
Perform vector operations in Rn and interpret them geometrically.
Verify and/or refute the validity of vector space axioms in specific examples.
Apply the vocabulary of vector spaces (linear combination, span, subspace, linear independence and linear
dependence, basis, dimension, and orthogonal) to specific examples in Rn.
Exemplify linear transformations in Rn and distinguish linear transformation from non-linear mappings.
Solve first and Second Order Differential Equations
Compute eigenvalues and eigenvectors interpret them geometrically, and use them to help analyze some applied
situation.
Solve Systems of Linear Differential Equations
Write simple two or three-step proofs, and construct illustrative counterexamples.
Assignments:
Homework:
Midterm Examination:
Final Examination:
COURSE OVERVIEW
Lectures
Lectures 1-5
Lectures 6-8
Lectures 9-11
Lectures 12-14
Lectures 16-18
Lectures 19-21
9%
16%
35%
40%
Topics
Introduction to Systems of Linear Equations
Gaussian Elimination
Matrices and Matrix Operations
Inverses; Rules of Matrix Arithmetic
Elementary Matrices and a Method for finding A-1
Further Results on Systems of Equations and Inevitability
Diagonal, Triangular, and Symmetric Matrices
Determinants by Cofactor Expansion
Evaluating Determinants by Row Reduction
Properties of the Determinant Function
A combinatorial Approach to Determinants
Euclidean n-Space
Linear Transformations from Rn to Rm
Properties of Linear Transformations from Rn to Rm
Linear Transformations and Polynomials
Real Vector Spaces
Subspaces
Basis and Dimension
Row Space, Columns Space, and Null space
Rank and Nullity
Inner Products
Orthogonality in Inner Product Spaces
Orthonormal Bases; Gram-Schmidt Process; QR Decomposition
Best Approximation; Least Squares
Change of Basis
Orthogonal Matrices
Eigenvalues and Eigenvectors
Diagonalization
Orthogonal Diagonalization
General Linear Transformations
Kernel and Range
Inverse Linear Transformations
Lectures 26-28
Matrices of General Linear Transformations
Similarity
Isomorphism
Textbook(s)/Supplementary Readings
Lectures 22-25
1. Elementary Linear Algebra by Howard Anton(2005),9th edition, John Wiley & Sons,Inc. USA
2. Differential Equations with Boundary Vaue Problems by Dennis Zill and Michael Cullin (5th edition)
3. A First Course in Linear Algebra (2010) by R.A Beezer (Available online)
4. Linear Algebra and it’s Applications by Gilbert Strang, 4th edition, Thomson
Online Resources and software
Course webpage: http://suraj.lums.edu.pk/~adnan.khan/classes/classes/LinearAlgebra
Mirror Site for Lectures and other online resources: http://math.lums.edu.pk/moodle
Online Computational Engine: www.wolframalpha.com
Numerics: MATLAB will be used for numerical calculations (the syntax and commands will be discussed in class)