# Virtual University of Pakistan

## Featured Courses

Home > Courses > Mathematics > MTH303

## 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

 Topic Lecture Resource Page Introduction 1 Handouts 3-4 Fundamentals of Differential Equation 2 Handouts 5-8 Separable Equations 3 Handouts 9-17 Homogeneous Differential Equations 4 Handouts 18-25 Exact Differential Equations 5 Handouts 26-33 Integrating Factor Technique 6 Handouts 34-43 Quiz 1 First Order Linear Equations 7 Handouts 44-50 Bernoulli Equations and Practice Examples Handouts 51-77 Applications of First Order Differential Equations 10 Handouts 78-88 Radioactive Decay 11 Handouts 89-94 Application of Non Linear Equations 12 Handouts 95-102 Higher Order Linear Differential Equations and their Solutions Handouts 103-126 Construction of a Second Solution 15 Handouts 127-133 Assignment No. 1 Homogeneous Linear Equations with Constant Coefficients 16 Handouts 134-144 Method of Undetermined Coefficients Superposition Approach 17 Handouts 145-158 Undetermined Coefficient Annihilator Operator Approach Handouts 159-179 Variation of Parameters 20 Handouts 180-189 Introduction and Overview of Linear Algebra 21 Elementary Linear Algebra and its Application 1-5 Introduction to Matrices. 22 (3rd edition) 6-17 Mid term Examination System Of Linear Equations. 23 By David C. Lay 18-29 Row reduction and Echelon Form of a Matrix. 24 30-43 Vector Equations. 25 44-55 Matrix Equations. 26 56-65 Solution Set of Linear Equations. 27 66-73 Linearly Dependent and Linearly Independent Sets. 28 81-88 Quiz No. 2 Linear Transformations. 29 89-225 The Matrix of Linear Transformations. 30 98-107 Matrix Algebra. 31 121-133 Assignment # 2 Inverse of a Matrix. 32 134-143 Characterization of Invertible Matrices. 33 144-149 Partitioning of a Matrix. 34 150-157 Matrix Factorization. 35 158-167 Iterative Solution of Linear Systems. 36 168-201 Introduction to Determinants. 37 202-207 Properties of Determinants. 38 208-216 Quiz No. 3 Cramer"s rule, Volume and Linear Transformations. 39 217-222 Vector Spaces. 40 232-241 Null Spaces, Column Spaces and Linear Transformations. 41 242-252 Bases for a vector Space. 42 253-261 Coordinate systems 43 262-271 Dimension of a Vector Space 44 272-278 The Rank Theorem and Invertible Matrix Theorem 45 279-286 Final Term Exams