Mohamed F. El-hewie

College Level Mathematics Personal Study Notes: Solved Examples & Exercises Mohamed F. El-hewie

College Level Mathematics Personal Study Notes This book comprises three hundred and thirty solved examples in college mathematics, a prerequisite for completion of bachelor degree in electrical engineering, nuclear engineering, physics, or mathematics. Each chosen example represents a unique concept in applied mathematics that is essential in preparing the undergraduate student to advance to higher level mathematics and physics. In most chapters, unsolved exercises are added for practicing. Thus, the book represents the essential needs of study of mathematics during the five intense study years of undergraduate college education. A special feature of this ebook is the effort taken to put the solved examples in the simplest form and to limit the number of examples to the absolute minimum that does not cram the memory of the already strained student. Even though redundant examples are believed by some to enhance memorization of mathematical concepts, I opted to follow my instincts supported by my own experience that simplicity and conciseness could lead to long last and clear vision than redundancy. The following syllabus was adapted from my undergraduate study at the Faculty of Engineering between years 1969 and 1974 and the Faculty of Science of the University of Alexandria, Egypt, between the years 1976 and 1978. Matrices, Binomial Theory, Partial Fractions, Theory of Residues, Differential Equations, Particular and Complementary Solutions of Second Order Differential Equations, Properties of the f(D)- Operator, Trigonometry, Analytical Geometry: Straight Line, Circle, Parabola, Ellipse, Hyperbola, Polar Coordinates, Hyperbolic functions, Curvature, Leibniz theory and Nuclear Differentiation, Integration, Maclaurin Series and Taylor limits, Newton?s Method of Numerical Solution of Equations, Partial Differentiation, Applications on Integration and Polar Equations, Multiple Integrals: Green?s Theorem, Spherical Trigonometry: Napier's rules, Numerical Solution of Equations, Graphical Method of Solution of Equation, Newton-Raphson?s iterative method of solution, The Method of False Position (Regula Falsi) Or Inverse Interpolation, Bolzano Method, Roots of Polynomial Equations, Synthetic division, Evaluation of derivatives by synthetic division, Synthetic division by quadratic polynomial, Method of finding the imaginary roots of polynomials, Graeffe?s Root Squaring Method, Simultaneous equations of first degree, Gauss method of elimination, The Gauss-Seidel iteration method, Relaxation methods, Finite difference solution of differential equations, Linear Programming,