Ayanaw’s current tutoring subjects are listed at the left. You
can read more about
Ayanaw’s qualifications in specific subjects below.
Algebra I and II for High School or College Math: Operations on Whole Numbers, Addition and Subtraction Using Fractional Notation, Addition and Subtraction Using Decimal Notation, Multiplication and Division Using Fractional Notation, Multiplication and Division Using Decimal Notation, Ratio and Proportion, Percent Notation, The Real Number System, Dimensional analysis, Number systems other than base 10, Order of Operations, Exponents, Set Operations, Venn diagrams, Logic; Truth tables, Conditionals and Bi-conditionals.
Single Variable (Calculus I and II): Limits, limit theorems, L'Hopital's Rule, Continuity; intermediate value theorem, Derivatives, chain rule, implicit differentiation, Applications of Derivatives; Analysis of Graphs, mean value theorem, max/min, Related rates, Integrals, Integration techniques; polynomials, exponential and logs, trigonometric, substitution, trig substitution, parts, partial fractions, Applications of Integrals, length of curves, work, volume, surface area - Parametric equations, Polar coordinates, Sequences and Series, Convergence test, Power series, and Taylor series.
Multivariable Calculus (Calculus III): Vectors, dot product, cross product, lines, planes, Vector-Valued Functions, limits, derivatives, curves, tangents, curvature, Partial Derivatives, chain rule, directional derivatives, gradient, Lagrange multipliers, Multiple Integrals, surface area, polar & cylindrical coordinates, moments and center of gravity, Vector Calculus, vector fields, line integrals, Green's theorem, surface integrals, Stokes Theorem, and Divergence Theorem.
I have taken two Differential Equations courses and one Applied Mathematics using Differential Equation to earn my Applied Mathematics Degree. Since then, I have been tutoring some students. It is very critical to learn the concepts of Differential Equation and know how to use it and when to use it. Many laws leading natural phenomena are equations involving rates at which derivatives. Basically, Equations containing derivatives are differential equations.
I took multiple Linear Algebra courses to earn my Applied Mathematics degree. Linear Algebra was one of my specialties while studying. Since then, I have been tutoring undergraduate and graduate level Linear algebra courses. Linear algebra is very rich subject and central to both pure and applied mathematics, concerning vector spaces, often finite or infinite dimensional, as well as Linear Mappings between such spaces.
Algebra, College Algebra, or Pre-calculus: Linear equations, Absolute value, Inequalities, Nonlinear Functions, Function notation, Polynomials, Translations, Shifting, reflecting graphs, Composition, Inverse functions - Roots of polynomials, Quadratic equation, Factoring, Complete square, Quadratic formula, Complex Numbers, Higher Degree, Factoring special cases, Exponentials and Logarithmic function and Graphs, 2 equations 2 unknowns, Matrix algebra, Gaussian elimination, Inverses, Mathematics of finance, Simple/compound interest, Linear programming, and Geometric approach.
Statistics or probability: Descriptive Statistics, Data Analysis, Graphic Representations, Measures of Central Tendency, Dispersion, Position, Regression and Correlation, Probability, Random Variables, Probability Distributions for Discrete and Continuous Random Variables, Inferential Statistics, Sampling and Sampling Distributions, Central Limit Theorem, Confidence Intervals, Hypothesis Testing, Inference Concerning Correlation and Regression, Analysis of Variance, Categorical Data Analysis, Chi-square, Contingency Tables, Homogeneity tests, Decision Theory, Process, and Quality Control (Control Charts)
I have been teaching Trigonometry as Pre-calculus requirement in Prep School for the last two years. Trigonometry is my favorite subject of all, because it is a branch of mathematics that studies only triangles and the relationships between the lengths of their sides and the angles between those sides.