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MTH303 : Mathematical Methods

Course Overview

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 Calendar

Fundamentals of Differential Equation2Handouts5-8
Separable Equations3Handouts9-17
Homogeneous Differential Equations4Handouts18-25
Exact Differential Equations5Handouts26-33
Integrating Factor Technique6Handouts34-43
Quiz 1
First Order Linear Equations7Handouts44-50
Bernoulli Equations and Practice ExamplesHandouts51-77
Applications of First Order Differential Equations10Handouts78-88
Radioactive Decay11Handouts89-94
Application of Non Linear Equations12Handouts95-102
Higher Order Linear Differential Equations and their SolutionsHandouts103-126
Construction of a Second Solution15Handouts127-133
Assignment No. 1
Homogeneous Linear Equations with Constant Coefficients16Handouts134-144
Method of Undetermined Coefficients Superposition Approach17Handouts145-158
Undetermined Coefficient Annihilator Operator ApproachHandouts159-179
Variation of Parameters20Handouts180-189
Introduction and Overview of Linear Algebra21Elementary Linear Algebra and its Application1-5
Introduction to Matrices.22(3rd edition)6-17
Mid term Examination
System Of Linear Equations.23By David C. Lay18-29
Row reduction and Echelon Form of a Matrix.2430-43
Vector Equations.2544-55
Matrix Equations.2656-65
Solution Set of Linear Equations.2766-73
Linearly Dependent and Linearly Independent Sets.2881-88
Quiz No. 2
Linear Transformations.2989-225
The Matrix of Linear Transformations.3098-107
Matrix Algebra.31121-133
Assignment # 2
Inverse of a Matrix.32134-143
Characterization of Invertible Matrices.33144-149
Partitioning of a Matrix.34150-157
Matrix Factorization.35158-167
Iterative Solution of Linear Systems.36168-201
Introduction to Determinants.37202-207
Properties of Determinants.38208-216
Quiz No. 3
Cramer"s rule, Volume and Linear Transformations.39217-222
Vector Spaces.40232-241
Null Spaces, Column Spaces and Linear Transformations.41242-252
Bases for a vector Space.42253-261
Coordinate systems43262-271
Dimension of a Vector Space44272-278
The Rank Theorem and Invertible Matrix Theorem45279-286
Final Term Exams
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