The tenth edition of this bestselling text includes examples in more detail and more applied exercises; both changes are aimed at making the material more relevant and accessible to readers. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. It goes into the following topics at great depth differential equations, partial differential equations, Fourier analysis, vector analysis, complex analysis, and linear algebra/differential equations.

PART A Ordinary Differential Equations (ODEs).

 CHAPTER 1 First-Order ODEs.
 CHAPTER 2 Second-Order Linear ODEs.
 CHAPTER 3 Higher Order Linear ODEs.
 CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods.
 CHAPTER 5 Series Solutions of ODEs. Special Functions.
 CHAPTER 6 Laplace Transforms.

 PART B Linear Algebra. Vector Calculus.

 CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems.
 CHAPTER 8 Linear Algebra: Matrix Eigenvalue Problems.
 CHAPTER 9 Vector Differential Calculus. Grad, Div, Curl.
 CHAPTER 10 Vector Integral Calculus. Integral Theorems.

 PART C Fourier Analysis. Partial Differential Equations (PDEs).

 CHAPTER 11 Fourier Series, Integrals, and Transforms.
 CHAPTER 12 Partial Differential Equations (PDEs).

 PART D Complex Analysis.

 CHAPTER 13 Complex Numbers and Functions.
 CHAPTER 14 Complex Integration.
 CHAPTER 15 Power Series, Taylor Series.
 CHAPTER 16 Laurent Series. Residue Integration.
 CHAPTER 17 Conformal Mapping.
 CHAPTER 18 Complex Analysis and Potential Theory.

 PART E Numeric Analysis.

 Software.

 CHAPTER 19 Numerics in General.
 CHAPTER 20 Numeric Linear Algebra.
 CHAPTER 21 Numerics for ODEs and PDEs.

 PART F Optimization, Graphs.

 CHAPTER 22 Unconstrained Optimization. Linear Programming.
 CHAPTER 23 Graphs. Combinatorial Optimization.

 INDEX I1.
 PHOTO CREDITS P1.