Advanced Engineering Mathematics Book

Pt. I	Ordinary Differential Equations
1	Introduction to Differential Equations	1
2	Equations of First Order	18
3	Linear Differential Equations of Second Order and Higher	73
4	Power Series Solutions	173
5	Laplace Transform	247
6	Quantitative Methods: Numerical Solution of Differential Equations	292
7	Qualitative Methods: Phase Plane and Nonlinear Differential Equations	337
Pt. II	Linear Algebra
8	Systems of Linear Algebraic Equations; Gauss Elimination	391
9	Vector Space	412
10	Matrices and Linear Equations	465
11	The Eigenvalue Problem	541
12	Extension to Complex Case (Optional)	599
Pt. III	Scalar and Vector Field Theory
13	Differential Calculus of Functions of Several Variables	613
14	Vectors in 3-Space	683
15	Curves, Surfaces, and Volumes	714
16	Scalar and Vector Field Theory	757
Pt. IV	Fourier Methods and Partial Differential Equations
17	Fourier Series, Fourier Integral, Fourier Transform	844
18	Diffusion Equation	943
19	Wave Equation	1017
20	Laplace Equation	1058
Pt. V	Complex Variable Theory
21	Functions of a Complex Variable	1108
22	Conformal Mapping	1150
23	The Complex Integral Calculus	1182
24	Taylor Series, Laurent Series, and the Residue Theorem	1209
	References	1260
App. A	Review of Partial Fraction Expansions	1263
App. B	Existence and Uniqueness of Solutions of Systems of Linear Algebraic Equations	1267
App. C	Table of Laplace Transforms	1271
App. D	Table of Fourier Transforms	1274
App. E	Table of Fourier Cosine and Sine Transforms	1276
App. F	Table of Conformal Maps	1278
	Answers to Selected Exercises	1282
	Index	1315