By Mohamed F. El-Hewie

the idea of publishing my own learn notes that coated fifteen years of undergraduate, graduate, and postdoctoral studying and study dates to the yr 1969. the one distinction among my 40 12 months previous proposal and the current is the exceptional invention and development of the web and software program. Then, our reproduction machines have been run through ammonia deposits on chemically taken care of paper. The stencil tissues and engravers have been the typical instruments for small dimension ebook. None of these used to be economically attainable in the course of my years as pupil with overall dependency on scholarships and relations aid.

In 1986, after settling in Colorado Springs, Colorado, my elder sister volunteered to send all my belonging from Egypt to the us. A half-ton wood field traveled from Alexandria, Egypt, to Houston, Texas, wearing all my handwritten notes and faculty textbooks. Then, the customized clearance and transportation among Texas and Colorado ran lower than $500. The kindness of my sister for risking the big problems in facing the Egyptian bureaucratic exporting firms was once paralleled with the same kindness of the the USA truck motive force who needed to force via a residential residence complicated with an 18-wheeler, but to determine that his truck used to be now not outfitted with a boost that may decrease the half-ton box at the flooring of the residence complicated. the driving force allowed me an additional day to prepared and leased fork raise from a neighborhood apartment store. riding a forklift at the streets of Colorado Springs was once one of the adventures I loved in such appealing Rocky town.

By 1986, I already collected extra sleek and chic books in arithmetic. yet, my own notes embodied a strategy of engraving the mathematical pondering into my neurons. My cursive writings and photograph illustrations in the course of interactive studying with academics and self sustaining domestic looking and guidance are vividly recorded into 40 yr outdated notes. these comprise the theoretical subject material, the examples that undefined, and the hard difficulties for workout. I strove to maintain the notes as whole as they constructed in the course of the studying strategy. My photo method of the translation of mathematically summary innovations illustrates the psychological improvement of my studying.

The current examine notes contain linkable issues with bitmapped snips intermingled with searchable textual content and canopy the subsequent themes:

1: Gradient, Divergence and Curl
2: Gauss's and Stokes' Theorems
3: common Orthogonal Curvilinear Coordinates
4: Tensor Analysis
5: The targeted concept of Relativity
6: Matrices
7: designated capabilities
8: Fourier transforms

....
CHAPTER 1: GRADIENT, DIVERGENCE AND CURL

1. Scalar and Vector fields
1.1. Definitions of scalar and vector fields
2. Continuity
3. Partial derivatives
4. Increments in element functions
5. Directional derivatives

6. The gradient of a scalar function
6.1. course of gradient vector
6.2. sensible software of the gradient
6.2.1. Electrostatic box
6.2.2. Equipotential floor or point surface
6.2.3. Interpretation of the importance and path of the gradient of a scalar field
6.2.4. instance of the gradient derivation

7. Line integrals
7.1. software of linear integrals

8. Conservative Fields
8.1. software on electrostatic field
8.2. Gradient of a unmarried valued differentiable function
8.3. Gradient of a relentless vector

9. The divergence of a vector
9.1. Interpretation of divergence of a vector

10. The curl of a vector
10.1. Interpretation of curl of a vector
10.2. replacement definition of the curl of a vector

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Advanced Mathematics Personal Study Notes by Mohamed F. El-Hewie


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