Matemáticas Avanzadas para Ingeniería – Erwin Kreyszig – 9na Edición

PART A Ordinary Differential Equations (ODEs)

1: First-Order ODEs

2: Second-Order Linear ODEs

3: Higher Order Linear ODEs

4: Systems of ODEs. Phase Plane. Qualitative Methods

5: Series Solutions of ODEs. Special Functions

6: Laplace Transforms

PART B Linear Algebra. Vector Calculus

7: Linear Algebra: Matrices, Vectors, Determinants. Linear Systems

8: Linear Algebra: Matrix Eigenvalue Problems

9: Vector Differential Calculus. Grad, Div, Curl

10: Vector Integral Calculus. Integral Theorems

PART C Fourier Analysis. Partial Differential Equations (PDEs)

11: Fourier Analysis

12: Partial Differential Equations (PDEs)

PART D Complex Analysis

13: Complex Numbers and Functions. Complex Differentiation

14: Complex Integration

15: Power Series, Taylor Series

16: Laurent Series. Residue Integration

17: Conformal Mapping

18: Complex Analysis and Potential Theory

PART E Numeric Analysis

19: Numerics in General

20: Numeric Linear Algebra

21: Numerics for ODEs and PDEs

PART F Optimization, Graphs

22: Unconstrained Optimization. Linear Programming

23: Graphs. Combinatorial Optimization

PART G Probability, Statistics

24: Data Analysis. Probability Theory

25: Mathematical Statistics

APPENDIX 1 References

APPENDIX 2 Answers to Odd-Numbered Problems

APPENDIX 3 Auxiliary Material

APPENDIX 4 Additional Proofs

APPENDIX 5 Tables