工程數學

●Revised Problem Sets: This edition includes a revision of the problem sets, making them even more effective, useful, and up-to-date.
●Sustainability and Ethics in Engineering: Each chapter now features a dedicated section on how mathematical modeling and engineering can address environmental and societal challenges, promoting sustainability and ethical practices.
●Update Examples: Updated examples with modern applications to enhance relevance and understanding.
●Open-Source Software Integration: Included problems that utilize open-source mathematical software, such as Python with NumPy, SciPy, and SymPy libraries, or MATLAB.
●Appendix on Emerging Topics: A new appendix covers emerging areas in applied mathematics, such as data science, machine learning, and network theory, and their engineering applications.

●Use of Simple Examples: Opt for straightforward examples instead of complex ones, as they can be just as, if not more, effective for teaching purposes.
●Independent Chapters: Allow for adaptable course design to meet specific educational needs.
●Comprehensive Content: Ensure the material is self-contained, with only a few instances where a proof is beyond the book's scope, clearly marked, and referenced.
●Contemporary Notation: Adopt modern standard notation to assist students in other courses and when reading current books, as well as mathematical and engineering journals.

Erwin Kreyszig

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 Analysis
CHAPTER 12 Partial Differential Equations (PDEs)
PART D Complex Analysis
CHAPTER 13 Complex Numbers and Functions. Complex Differentiation
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 
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
PART G Probability, Statistics (available online)
CHAPTER 24 Data Analysis. Probability Theory
CHAPTER 25 Mathematical Statistics
APPENDIX 1 References
APPENDIX 2 Answers to Selected Problems (available online)
APPENDIX 3 Auxiliary Material
APPENDIX 4 Additional Proofs
APPENDIX 5 Tables
APPENDIX 6 Emerging Topics in Applied Mathematics