Course Descriptions

Hyperbolic functions. Techniques of integration. Integration by parts. Trigonometric integrals. Trigonometric substitutions. Partial fractions. Improper integrals. Sequences. Infinite series. Positive series. Integral test. Comparison tests. The ratio and root tests. Alternating series. Power series. Taylor and Maclaurin series. Parametric equations. Polar coordinates. Vectors in space. The dot and cross products. Lines and planes in space.

Algebraic properties of complex numbers. Polar form of complex numbers. DeMoivre’s formula. Complex roots and powers. Algebraic properties of ma-trix operations. Special types of matrices. Solving linear systems of equa-tions. Elementary row and column operations. Echelon form of a matrix. Gauss and Gauss-Jordan method. Definition and properties of determinants. Cofactor expansion. Finding inverses via cofactors. Real vector spaces. Sub-spaces. Linear independence. Basis and dimension. Coordinates. Eigenval-ues and eigenvectors. Characteristic polynomial and characteristic equation. Eigenvalues and eigenvectors. Diagonalization

Electrical circuits. Kirchhoff's laws, and circuit components. Electrical power and energy. Resistive circuit analysis. Operational amplifiers. Solutions of first and second order dynamic circuits. Sinusoidal steady-state analysis of circuits. Complex, active and reactive powers. Three-phase circuits. Semiconductor elements: diodes, transistors, thyristors and triacs. Amplifier circuits. Magnetic circuits and transformers. Electromechanic energy conversion and electrical machines.

Principles of statics, vectors, force and moment vectors, equilibrium of a rigid body, free body diagrams, friction, structural analysis, trusses and simple machines, geometric properties, distributed loadings, center of gravity, moment of inertia, internal loadings, shear and moment diagrams, stress, strain, factor of safety and basic strength calculations.

Engineering materials and their properties. Atomic bonding and order. Crystal structures and their properties. Crystal defects and their effects on properties of materials. Solid state diffusion. Elastic and plastic deformation of materials. Phase concept and phase diagrams. Fe-Cementite phase diagram. Phase transformations and TTT Diagrams. Basic heat treatments for metals and alloys. Engineering materials: metals, polymers, ceramics and composites. Principles of corrosion and protection.

Microstructural examination of metals, tensile tests, and hardness tests, impact tests, Jominy hardenabity test and other experiments with equipment to be taken to the laboratory.

Functions of several variables. Limits and continuity. Partial derivatives. Chain rule for partial derivatives. Directional derivatives. Local maxima and minima. Lagrange multipliers. Taylor’s formula. Double integrals in Cartesian and polar coordinates. Triple integrals in Cartesian, cylindrical and spherical coordinates. Line integrals. Green’s theorem. Surface integrals. Stokes’ theorem. Divergence theorem.

Introduction to statistics. Sample mean, median and standard deviation. Graphical plots. Probability. Multiplication rule. Permutation and combination. Conditional probability and Bayes’ rule. Random variables. Discrete and continuous probability distributions. Joint probability distributions. Mathematical expectation. Mean, variance, covariance and correlation coefficient of random variables. Some continuous and discrete probability distributions. Normal distribution. Fundamental sampling distributions. Sampling distribution of mean. Interval estimation of mean. Testing a statistical hypothesis. Simple linear regression and correlation.

Communication, items of communication, types of communication, oral and written communication and presentation, effective communication skills. The definition and the importance of language. The relationship between language and society, language and culture. The relationship between language and literature. Spoken language, written language, native language, standard language, dialect, special languages. Features of meaning, sound and style (structure) of Turkish. Rules of writing and punctuation. Features and types of narration. Subject and limitation of the subject. Written language and its features. The layout of written narration (planning of written narration), wording, types of written narration, features of written narration, expressional failure.

Kinematics of a particle, introduction to dynamics, rectilinear motion, curvilinear motion, force, acceleration, work, energy, impulse, momentum, planar Kinematics of a rigid body, moments of inertia, ad angular acceleration, rigid body translation: force and acceleration, work, energy, mechanical vibrations, damped and undamped vibrations