I am a very patient tutor that will repeat any part of a lesson that you need until it is understood. I always appreciate everyone that supports me with his or her business. I like to tutor subject matter that is very advanced as well as high school and beginners level mathematics and science. I tutored throughout my whole life. There have been many success stories with many of my students eventually completing a graduate degree. My teaching experience includes teaching many subjects of ... [more]

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Differential Equations

At the University of Tennessee Knoxville my specialization for a PhD degree in mathematics was in the field of differential equations. I did several additional years of advanced graduate study in the area of partial differential equations and their numerical solution by finite difference and finite element methods. I have taught differential equations at a number of military academies and served as an editor for research articles on differential equations. I have tutored students at the University of Tennessee in the differential equations area for over 20 years. I strongly encourage all those studying science or engineering to study differential equations. Since this field is so important, a lengthy description of the subject matter you would study is included. Differential equations are equations that relate the values of a function and it's derivatives. Differential equations arise in the study of virtually every area of science and engineering. In physics they explain the motion of particles and other objects. In chemistry they help analyze rates of reaction and the behavior of thermodynamic systems. In biomathematics they describe growth and relationships between the populations of an ecosystem. In engineering differential equations model the behaviors of electric circuits, mechanical systems, deformations of elastic materials, and heat transfer, just to mention some of their uses. There are too many uses of differential equations to include them all in any short discussion. There are several different ways in which differential equations are classified. One of which is as an ordinary or partial differential equation. An ordinary differential equation is an equation relating a function of one variable with it's first, and possibly second, third, and forth derivatives. A partial differential equation, on the other hand, involves partial derivatives of a function of more than one variable. In pure mathematics arbitrary differential equations with derivatives of any order are studied, for the sake of argument, even if applications are not always known. Another classification is as a linear or non-linear differential equation. A linear differential equation takes it's name from ordinary linear equations where the sums and constant multiples of solutions are also solutions. Other common classifications include separable, exact, and homogeneous equations. Separable equations can be solved by algebraic separation of the terms that involve different variables. Exact equations are ones that can be shown to be the result of the implicit differentiation of an expression. Homogeneous equations are of a kind that are easily transformed into a separable equation. The highest order of the derivatives occurring in an equation is often used in their classification. Second order partial differential equations are sometimes classified as elliptical, hyperbolic, or parabolic based on an analogy to the quadratic surfaces of analytic geometry. An introduction to the study of differential equations usually begins with a survey of the most commonly used ordinary differential equations that can be solved to obtain an explicit formula for their solution. This study is expanded to include equations that are solved by series solutions or implicit relations between the variables. Many interesting applications of differential equations to science and engineering are used for illustration. As this study continues the second order partial differential equations that describe heat transfer or wave propagation are covered. Material about the existence, uniqueness, and behavior of the solutions to differential equations is also included. Several techniques of solution including integration, methods for constant coefficients, separation of variables, variation of parameters, and the use of Laplace transforms are always covered. Many numerical techniques to approximate the solution of a differential equation are used when solution by a formula can not easily be found. There are many specialized and advanced topics regarding differential equations.

C

I have tutored many computer science majors at the University of Tennessee over the last 15 years in C/C++ language programming. C and C++ programming is required for all computer science majors and most of their assignments are done in C/C++. Anyone with a computer could learn elementary C language programming with my tutoring. C language is where you want to start if you want to be a computer science major or a computer programmer. C language and it's advanced extension C++ are the premier programming languages that most system software is written in. A C language compiler is a translator to assembly language and an assembler and linker all built into one. Compiled C language is equivalent to highly optimized assembly language, but does not require the tremendous effort that programming directly in assembly language does. I served as the chairman of the ANSI (American National Standards Institute) committee for the standardization of C language during the 1980's, when C language was still in it's development. I also served during these years as the head of the Unix Group. Unix was written in C language together with assembly language and we worked hard to develop the compilers and linkers used by everyone in the world. Additionally, I edited how to books at SAMS publishing on self study of C language and conducted many post doctorate seminars on C language compiling at the University of Tennessee Knoxville. A large number of other contributors from the military, Bell Telephone, DEC, Scott Paper Company, Microsoft, IBM, Packard Bell, Sun Microsystems, Tandy Computer, NBC News, the University of Berkeley, a variety of academic professionals, and many other companies that produce devices such as printers, scanners, and modems provided some of the content of C language.

MATLAB

I have been tutoring MATLAB programming for 15 years. Many of the students I have tutored were engineering majors at the University of Tennessee. At the University of Tennessee, as well as at most colleges, MATLAB is the language that homework assignments given to engineering majors, that require a computer program, are usually done in. Due to this I have a great deal of experience in teaching MATLAB programming. Also, I use MATLAB on a regular basis for much of my own programming and have a considerable amount of knowledge about using the more advanced features of MATLAB. MATLAB is considered a high-performance language for technical computing. It is recommended for both beginner level programmers as well as experienced professionals. MATLAB has an extensive library of functions that calculate all of the common mathematical functions and perform the most widely used matrix algebra operations. Functions available in MATLAB provide support for many statistical procedures and number theoretical calculations. One of the best features of Matlab is that it has easy to use functions that plot both 2 and 3 dimensional graphs, while the other widely used programming languages lack this feature entirely. Simulink is another feature of MATLAB that allows the construction and execution of block diagram simulations of multi-component systems. For the beginner it uses a core language that does not require type casting or knowledge of any technical matters involving the representation of numbers and text by computer language defined variables. The syntax to use complex numbers and arrays is easier in this language than in the alternatives available to a novice programmer. For the experienced professional MATLAB has many extensions (toolboxes) containing specialized functions useful in many ares of engineering and science. This eliminates the need to locate references on the many algorithms used and the time needed to develop one's own source code. Since MATLAB has become so widely used by engineers it is almost a must for anyone studying to become a professional in the engineering field.

Electrical Engineering

Over the years, of the many college students I have tutored most of them were engineering majors. Mechanical and electrical engineering are about equally popular so I have had around the same number of students in these two fields, although some of my students were in civil, aero-nautical, or nuclear engineering. The curriculum in engineering includes mathematics, with calculus, numerical analysis, matrix algebra, and differential equations being required for electrical engineers. Also, general physics, general chemistry, thermodynamics, signal analysis, and a variety of specialized engineering courses on electric circuits, power generation and transmission, digital electronics, and so forth are taken. I have tutored all of these subjects and served as a college faculty instructor in all of the science and math requirements. My faculty advising included supervising theses work in the area of magnetism and electrodynamics. Besides my experience in the teaching of engineering I had a great deal of experience in computer and consumer electronics at Packard Bell and Tandy Computers. In the practical trade area I completed the electrician's certification with the State of Tennessee and completed the training program for a Electric Utility Linesman with a specialty in high voltage power lines. I worked several years, in the younger part of my life, as a construction electrician and as an electrical utility worker. My experience includes the design and construction of both coal burning and nuclear powered electric generating plants. The engineering students that hired me for a tutor at the University of Tennessee were very successful receiving A's in most of their courses.