New PDF release: Advanced Mathematics Personal Study Notes

By Mohamed F. El-Hewie

the concept of publishing my own learn notes that coated fifteen years of undergraduate, graduate, and postdoctoral studying and examine dates to the yr 1969. the one distinction among my 40 12 months outdated suggestion and the current is the exceptional invention and progress of the net and software program. Then, our replica machines have been run through ammonia deposits on chemically handled paper. The stencil tissues and engravers have been the typical instruments for small measurement e-book. None of these was once economically possible in the course of my years as pupil with overall dependency on scholarships and kinfolk aid.

In 1986, after settling in Colorado Springs, Colorado, my elder sister volunteered to send all my belonging from Egypt to the united states. 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 large issues in facing the Egyptian bureaucratic exporting corporations used to be paralleled with the same kindness of the the USA truck motive force who needed to force via a residential house advanced with an 18-wheeler, but to determine that his truck was once no longer built with a boost which may decrease the half-ton box at the flooring of the house complicated. the driving force allowed me an additional day to prepared and leased fork carry from a neighborhood condominium 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 accrued extra sleek and chic books in arithmetic. yet, my own notes embodied a technique of engraving the mathematical pondering into my neurons. My cursive writings and photograph illustrations in the course of interactive studying with teachers and self sufficient domestic looking out and education are vividly recorded into 40 12 months previous notes. these contain the theoretical material, the examples that undefined, and the tough difficulties for workout. I strove to maintain the notes as whole as they constructed through the studying approach. My picture method of the translation of mathematically summary thoughts illustrates the psychological improvement of my studying.

The current learn notes include linkable subject matters with bitmapped snips intermingled with searchable textual content and canopy the next issues:

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


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

6. The gradient of a scalar function
6.1. course of gradient vector
6.2. useful program 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. program 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 continuing 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. substitute 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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