Mathematical Methods book PDF Free download By SM Yousaf
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B.Sc Mathematical Methods book by SM Yusuf students study guide in pdf Format with Solution of all Chapter and exercise.
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Mathematical Method Book by S M Yousuf
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Content
PREFACE
CHAPTER 1
TRIGONOMETRY 1
Section I
Complex Numbers 1
The Argand’s Diagram 7
EXERCISE 1.1 20
De Moivre’s Theorem 21
Roots of a Complex Number 31
EXERCISE 1.2 35
Basic Elementary Functions 37
EXERCISE 1.3 41
Logarithmic Function 43
Inverse Hyperbolic Functions 45
Inverse Trigonometric Functions48
Complex Powers 50
EXERCISE 1.4 53
Summation of Series 54
EXERCISE 1.5 59
CHAPTER 2
GROUPS 61
Definition and Examples
Properties of Groups 65
EXERCISE 2.1 69
Subgroups 71
Cyclic Groups 75
Cosets – Lagrange’s Theorem 77
EXERCISE 2.2 80
Permutations 82
Cycles 87
Transpositions 90
Order of a Permutation
EXERCISE 2.3
Rings and Fields 98
EXERCISE 2.4 105
CHAPTER 3
MATRICES 120
Introduction 107
Algebra of Matrices 110
Partitioning of Matrices
EXERCISE 3.1 126
Inverse of a Matrix 130
Elementary Row Operations
Elementary Column Operations
EXERCISE 3.2 144
CHAPTER 4 SYSTEMS OF LINEAR EQUATIONS 149
Preliminaries 149
Equivalent Fractions 150
CHAPTER 4 SYSTEMS OF LINEAR EQUATIONS 149
Preliminaries 149
Equivalent Equations 150
Gaussian Elimination Method 152
Gauss-Jordan Elimination Method 158
Consistency Criterion
Network Flow Problems 170
EXERCISE 4 174
CHAPTER 5 DETERMINANTS
Determinant of a Square Matrix
Axiomatic Definition of a Determinant 185
Determinant as Sum of Products of Elements
Determinant of the Transpose
An Algorithm to Evaluate Det A 195
Determinants and Inverses of Matrices
EXERCISE 5.1 209
Miscellaneous Results 216
EXERCISE 5.2 219
CHAPTER 6
VECTOR SPACES
223
Definition and Examples 223
Subspaces 230
Linear Combinations and Spanning Sets
233
EXERCISE 6.1 236
Linear Dependence and Basis 239
EXERCISE 6.2 251
Row and Column Spaces 253
Rank-Alternative Method 255
Proofs of Theorems in Chapter 4
Linear Transformations 264
EXERCISE 6.3 272
Matrix of a Linear Transformation 274
EXERCISE 6.4 279
CHAPTER 7
INNER PRODUCT SPACES 281
Definitions and Examples 281
Orthogonality 286
EXERCISE 7.1 294
Orthogonal Matrices 295
EXERCISE 7.2 299
Eigenvalues and Eigenvectors
EXERCISE 7.3 306
Similar Matrices 307
Symmetric Matrices 310
Diagonalization of Matrices
EXERCISE 7.4 323
CHAPTER 8
INFINITE SERIES
Sequences 325
EXERCISE 8.1 330
Infinite Series 331
The Basis Comparison Test 339
The Limit Comparison Test
The Integral Test 343
EXERCISE 8.2 347
The Ratio Test 349
Cauchy’s Root Test 352
EXERCISE 8.3 354
Alternating Series 356
Absolute and Conditional Convergence 358
EXERCISE 8.4 362
Power Series 363
Convergence of Power Series 364
Differentiation and Integration of Power Series 370
Addition and Multiplication of Power Series 373
EXERCISE 8.5 375
CHAPTER 9
FIRST-ORDER DIFFERENTIAL
EQUATIONS 377
D.E. and Their Classifications377
Formation of Differential Equations 380
Initial and Boundary Conditions 381
EXERCISE 9.1 384
Separable Equations 386
EXERCISE 9.2 388
Homogeneous Equations 388
D.E. Reducible to Homogeneous Form
EXERCISE 9.3 393
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