Introductory Applicable Analysis
appendix to Yoshi Oono’s official site
To download the whole Part I use 
Individual Sections may be downloaded from below.
Part I
Read this first AMI-i.pdf
1 Introduction - Three representative linear PDE - 1 AMI-1.pdf
Appendix al Physical Examples AMI-1a.pdf
Appendix alA Balance Equation 24
Appendix alB Diffusion Equation and Laplace Equation 26
Appendix a1C Diffusion and Brownian Motion 28
Appendix aID Equatin of Motion of Continuum Body 30
Appendix alE Fluid Dynamics: Navier-Stokes Equation 35
Appendix alF Electrodynamics 39
2 Differentiation Revisited AMI-2.pdf
2A Elementary Review 47
2B Partial Differentiation Revisited 55
2C Vector Analysis Revisited 62
2D Curvilinear Coordinates 71
3 Calculus of Variation 77 AMI-3.pdf
4 Complex Functions 87 AMI-4.pdf
Appendix a4 Complex Numbers 95
5 Differentiation of Complex Functions 98 AMI-5.pdf
6 Integration on Complex Plane 102 AMI-6.pdf
7 Analytic Continuation 114 AMI-7.pdf
8 Contour Integration AMI-8.pdf
8A Singularities 124
8B Contour Integration 131
9 Gamma-function 142 AMI-9.pdf
10 Conformality and Holomorphy 153 AMI-10.pdf
11 Ordinary Differential Equation: General AMI-11.pdf
llA General Theory 163
llB Elementary Solution Methods 170
12 Constant Coefficient Linear ODE 181 AMI-12.pdf
Appendix a12 Decomposition of eAt 189
13 Quasilinear First-Order PDE AMI-13.pdf
13A General Theory 190
13B Homogeneous Functions 194
13C Application to Constant Coefficient Linear PDE 197
14 Generalized Functions 201 AMI-14.pdf
15 Green's Functions for ODE 213 AMI-15.pdf
16 Green's Functions for PDE Elementary Approach AMI-16.pdf
16A Green's Function for Laplace Equation
16B Green's Function for Diffusion Equation
16C Green's Function for Wave Equation
16D Laplace Equation in 2-Space
17 Fourier Expansion AMI-17.pdf
18 Separation of Variables Rectangular Domain AMI-18.pdf
Part II to download the whole Part II use 
19 Integration Revisited AMII-19.pdf
Appendix a19 What is measure?
20 Hilbert Space AMII-20.pdf
21 Orthogonal Polynomials AMII-21.pdf
22 Numerical Integration AMII-22.pdf
23 Separation of Variables - General Consideration - AMII-23.pdf
24 General Linear ODE AMII-24.pdf
25 Asymptotic Expansion AMII-25.pdf
26 Spherical Harmonics AMII-26.pdf
27 Cylinder Functions AMII-27.pdf
28 Diffusion Equation: How irreversibility is captured AMII-28.pdf
29 Laplace Equation: Consequences of spatial moving average AMII-29.pdf
30 Wave Equation: Finiteness of propagation speed AMII-30.pdf
31 Numerical Solution of PDE AMII-31.pdf
32 Fourier Transformation AMII-32.pdf
33 Laplace Transformation AMII-33.pdf
Appendix a33 Mellin Transformation
34 Linear Operators AMII-34.pdf
35 Spectrum of Sturm-Liouville Problem AMII-35.pdf
36 Green's Function: Laplace Equation AMII-36.pdf
37 Spectrum of Laplacian AMII-37.pdf
38 Green's Function: Diffusion Equation AMII-38.pdf
39 Green's Function: Helmholtz Equation AMII-39.pdf
40 Green's Function: Wave Equation AMII-40.pdf
Appendix A Rudiments of Analysis AMII-Appendix.pdf
Index AMII-Index.pdf