Advanced Engineering Mathematics(SI Edition)(8版)

PART I: ORDINARY DIFFERENTIAL EQUATIONS 
Ch 1 First-Order Differential Equations 
Ch 2 Second-Order Differential Equations
Ch 3 The Laplace Transform 
Ch 4 Sturm-Liouville Problems and Eigenfunction Expansions 

PART II: PARTIAL DIFFERENTIAL EQUATIONS 
Ch 5 The Heat Equation 
Ch 6 The Wave Equation 
Ch 7 Laplace’s Equation 
Ch 8 Special Functions and Applications 
Ch 9 Transform Methods of Solution 

PART III: MATRICES AND LINEAR ALGEBRA 
Ch10 Vectors and the Vector Space Rn 
Ch11 Matrices, Determinants, and Linear Systems 
Ch12 Eigenvalues, Diagonalization, and Special Matrices 

PART IV: SYSTEMS DIFFERENTIAL EQUATIONS 
Ch13 Systems of Linear Differential Equations
Ch14 Nonlinear Systems and Qualitative Analysis 

PART V: VECTOR ANALYSIS 
Ch15 Vector Differential Calculus 
Ch16 Vector Integral Calculus 

PART VI: FOURIER ANALYSIS 
Ch17 Fourier Series 
Ch18 Fourier Transforms 
Ch19 Complex Numbers and Functions 
Ch20 Integration 
Ch21 Series Representations of Functions 
Ch22 Singularities and the Residue theorem 
Ch23 Conformal Mappings