B.sc (Mathematical Methods by SM Yusuf)

• The Laplace transform
• Properties of the Laplace transform
• Exercise 11.1

   

Inverse laplace transformation

Convolution Theorem

Exercise solution

Complex numbers

properties of complex numbers

solution

Roots of the complex numbers 

logarithmic functions

• Logarithmic functions
• Inverse hyperbolic functions
• Inverse trigonometric functions
• Complex power

sum of series

Introduction

Definition

Properties of group

Theorem

• Subgroups
• Definition (subgroup)
• Cyclic Groups
• Definition (cyclic group)

• Permutations
• Cycles
• Transpositions
• Order of a Permutation

• Rings and Fields
• Properties of Rings
• Theorems

• Introduction
• Algebra of matrices
• Partitioning of matrices

• Inverse of a matrix
• Elementary row operations
• Elementary column operations

• Gaussian elimination method
• Gauss-Jordan elimination method
• Consistency criterion

• Determinant of a square matrix
• Definition of a determinant
• Determinant as sum of products of elements

• An algorithm to evaluate Det A
• Determinants and inverses of matrices

Definitions 

Examples

solutions

• Eigenvalues and Eigenvectors

  • Eigenvalues and Eigenvectors

solutions

• Sequences
• Infinite series

• Differential equation
• Initial and boundary conditions

solutions

Solve the Homogeneous Differential Equations

Theory: Exact Differential Equations

solutions of Integrating factor

Linear Differential Equations Solutions

 Orthogonal Trajectories

Solutions

 Solutions with Singular Solutions