Mathematical Methods by SM Yousaf is a comprehensive textbook that provides a thorough introduction to the subject of mathematical methods. This book is designed for students studying mathematics, physics, engineering, and other related disciplines at the undergraduate level and provides a solid foundation in the concepts and techniques of mathematical methods.
The book covers a wide range of topics, including vector calculus, ordinary differential equations, partial differential equations, and complex analysis. The author, SM Yousaf, has a clear and accessible writing style, which makes the material easy to understand for students with varying levels of mathematical background.
TABLE OF CONTENTS
Chapter 1 TRIGONOMETRY
- Complex Number
- The Aegand,s Diagram
- De Moivre,s Theorem
- Basic Elementary Functions
- Logarithmic Functions
- Inverse Hyperbolic Functions
- Inverse Trigonometric Functions
- Complex Powers
- Summation of Series
CHAPTER 2 GROUPS
- Definition and Example
- Properties of Groups
- Subgroups
- Cyclic Groups
- Cosets- Lagrange’s Theorem
- Permutations
- Cycles
- Order of permutations
- Rings and Fields
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CHAPTER 3 MATRICES
- Introduction
- Algebra of Matrices
- Partitioning of Matrices
- Inverse of Matrices
- Elementary Row Operations
- Elementary Columns Operations
CHAPTER 4 SYSTEMS OF LINEAR EQUATIONS
- Preliminaries
- Equivalent Equations
- Gaussian Elimination Method
- Gaussian-Jordan Elimination Method
- Consistency Criterion
- Network Flow Problems
CHAPTER 5 DETERMINANTS
- Determinants of a square Matrix
- Axiomatic Definition of a Determinant
- Determinant is Sum of Products of Elements
- Determinant of the Transpose
- An Algorithm to Evaluate Detn A
- Determinants and Inverses of Matrices
- Miscellaneous Results
CHAPTER 6 VECTOR SPACES
- Definition and Examples
- Subspaces
- Linear Combinations and Spanning Sets
- Rows and Column Spaces
- Rank-Alternative Method
- Proofs of Theorems in Chapter 4
- Linear Transformations
- Matrix of a Linear Transformation
CHAPTER 7 INNER PRODUCT SPACES
- Definitions and Examples
- Orthogonality
- Orthogonal Matrices
- Eigenvalues and Eigenvectors
- Similar Matrices
- Symmetric Matrices
- Diagonalization of Matrices
CHAPTER 8 INFINITE SERIES
- Sequence
- Infinite series
- The Basis Comparison Test
- The Limit Comparison Test
- The Integral Test
- The Ratio Test
- Cauchys Root Test
- Alternating Series
- Absolute and Conditional Convergence
- Power Series
- Convergence of Power Series
- Differentiation and integration of Power Series
- Addition and Multiplication of Power Series
CHAPTER 9 FIERST-ORDER DIFFERENTIAL EQUATIONS
- D.E and Their Classifications
- Formation of Differential Equations
- Initial and Boundary Conditions
- Separable Equations
- Homogeneous Equations
- D.E Reducible to Homogeneous Form
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One of the strengths of Mathematical Methods by SM Yousaf is its focus on applications, which helps students to see the practical applications of mathematical methods and understand how the concepts covered in the book can be used in real-world situations. Additionally, the book includes numerous examples and exercises, which provide opportunities for students to practice what they have learned and apply the concepts covered in the book to new problems.
Whether you are a student looking to build a solid foundation in mathematical methods or a professional seeking to refresh your knowledge of the subject, Mathematical Methods by SM Yousaf is an excellent resource that is sure to meet your needs. With its comprehensive coverage of the subject and its focus on applications, this textbook is sure to provide a valuable resource for anyone interested in learning about mathematical methods.
