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| Course Category: |
Mathematics |
| Course Level: |
Undergraduate |
| Credit Hours: |
3 |
| Pre-requisites: |
N/A |
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Course Synopsis
This course contains many tools to solve different type of differential equations like, First-Order Differential Equations, Second Order Differential Equations, Applications of Linear and Nonlinear differential equations. While the aim of second segment to emphasize on system of Linear equations, vector spaces, determinants and their properties.
Course Learning Outcomes
At the end of the course, you should be able to:
- Apply the concept of Fist Order Differential Equations
- Deduce the applications of first order differential equations
- Conclude differential equations of orders with methods of their solutions and homogenous and non-homogenous equations are explained and solved
- Construct the applications of second order differential equations and different vibration models
- To master the techniques for solving systems of linear equations
- Introduce matrix algebra as a generalization of single-variable algebra of high school
- Build on the background in Euclidean space and formalize it with vector space theory
Course Contents
Separable Equations, Homogeneous Differential Equations, Exact Differential Equations, Integrating Factor Technique, First Order Linear Equation, Bernoulli Equations, Applications of First Order Differential Equations, Radioactive Decay, Applications of Non Linear Equations, Higher Order Linear Differential Equations, Homogeneous Linear Equations with Constant Coefficients, Method of Undetermined Coefficients ( Superposition Approach), Method of Undetermined Coefficients (Annihilator Operator Approach), Variation of Parameters for Higher-Order Equations,Systems of Linear Equations, Row Reduction and Echelon Forms ,Vector Equations, The Matrix Equation, Solution Sets of Linear Systems, Linear Independence, Linear Transformations, The Matrix of a Linear Transformation, Matrix Algebra, Iterative Solutions of Linear Systems, Determinants, Cramer’s Rule and Linear Transformations, Vector Spaces and Subspaces
Course Related Links
A very famous link on linear-algebra
The above link is very useful for the course of linear algebra and you can find the questions and answers related to each topic of this course
Online Interactive Linear Algebra Calculator
An intuitive description of Linear Algebra
Where you can find Video lectures of Khan Academy, VU and some other Institutes from elementary to university level. Note: Try to open this Mozilla Firefox or Google Chrome(Explorer may give error)
Here one can find the Basic Mathematics topics in detailed, Conceptual and Intuitive way
It is helpful to compute most of the matrices and other Linear Algebraic operations
Very famous lectures by Professor Gilbert Strang from MIT |
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