Isaak’s current tutoring subjects are listed at the left. You
can read more about
Isaak’s qualifications in specific subjects below.
As an engineer, I routinely use the skills and principles taught in Algebra 2! Exponents, logarithms and roots come up all the time because many relationships between important factors in a design or description of a natural principle can only be treated as if they were linear, or that is, adequately described using straight lines, to the roughest of approximations. Not having these mathematical tools would make engineering work rather crude. Imagine how the drawings of a Corvette would look if the artist were restricted to use only straight lines!
Similarly, complex numbers are very useful for describing periodic waveforms, predicting natural resonances in systems, designing control systems and many other things.
I enjoy helping students understand and master the challenge of solving equations involving one or more of these non-linear equations, systems of linear equations.
I love calculus because it reveals great truths about the world we live in that would be very difficult (or at least much more tedious and time-consuming) to realize without it. How else could you figure out the volume of a sphere, Maxwell's equations of electromagnetism, the center of mass and the moment of inertia of a complicated structure, the modes of vibration of a structure, the amount of deflection expected in a beam, the fundamental modes of a plant under feedback control? You'd have to resort to using a gagillion more empirically determined formulas, and design possibilities would be slow, tedious and handicapped. It would be more difficult to minimize waste, maximize health and safety, control processes and systems, maximize quality, optimize profit, etc.
My calculus background began in high school, I studied calculus on my own in study hall by correspondence because there were only three students in my tiny rural Alberta school opting to take it to justify having a class. AP courses were not available.
The first two semesters of calculus in college were the first time I had the privilege of studying calculus at the level of those of you high school students fortunate enough to be able to take AP calculus in high school.
I took a third semester of calculus which got into vector calculus, volumes of revolution, and the Stokes and Green's theorems. Following that I took a course on ordinary differential equations, which is a branch of calculus involving equations where both a derivative of a variable and the variable itself are in the same equation. After that I took a course on partial differential equations, involving the study of equations in which derivatives of multiple variables are involved in a single equation, and (where known) the techniques of finding their solutions. The final course was the calculus of complex variables, which involves the exploitation of line integrals evaluated along curves traversing paths through the complex plane (the plane encompassing both real and imaginary numbers).
I passed all of these courses except the first with above class-average marks (the first was average but was also my first time in a large school setting where I was no longer one of the 'smartest' kids).
In the last couple of years, as I discovered my enjoyment of tutoring, I have gone back and refreshed myself on the introductory college/AP calculus. With the perspective combined experience of all the courses, I can help you do your best to learn calculus as well as you can while you are taking the course, it can be a handy tool to have in the rest of your coursework and career.
Differential equations are equations that include both a variable of the derivative or anti-derivative (possibly higher-ordered) of the same variable.
We engineering types often become very familiar with the Laplace transforms techniques for solving these equations in particular, so much so that the fact that the equations we solve algebraically by these techniques correspond to ordinary differential equations fades into the background of distant memory.
But the general student studying differential equations must learn to deal with a more diverse swath of differential equation-types, some of which are not amenable to solution by Laplace transform.
I could immediately help any student struggling with the Laplace transform techniques, and
with a couple days notice, offer some less expert assistance with some of the other techniques, such as variation of parameters, the method of Frobenius.
My memory of the details of how to approach solving some of these other types of differential equations, up to and including an entire course covering various partial differential equations is very faint.
Some of the fruits of electrical engineering are ubiquitous throughout modern society, while other aspects of it play behind-the-scenes.
Electrical/electronic engineering includes the analysis of circuits, motors, transmission lines, semiconductor devices, digital circuits, analog circuits, control systems, power conversion, microprocessing, control theory (classical, modern, and digital), electrostatis, electrodynamics and others.
Each of these topics is deep enough to make up one or more courses all by itself. I am well-qualified to teach introductory circuit analysis of AC/DC circuits; it is the basic glue that every electrical engineering -related degree-holder knows like the back of their hand.
With a little review, I could surely help anyone struggling with digital circuit theory and boolean algebra. I was top of the class, but haven't used it lately.
I may be able to help with other courses to a limited extent.
Linear algebra is the study of systems of equations described using matrix and vector notation.
It can seem like a chore before you realize the practical applications of it, but it is a chore worth doing well, as it has myriad applications throughout engineering theory.
The knowledge of linear algebra simplify the task of solving simultaneous equations. This is ginormous! Why? Because simultaneous equations arise that need to be solved to do structural design in civil engineering, circuit design in electrical, lens design in optics, control systems design. Aspects of it are used in physics to solve quantum mechanical equations, in mechanics to find torque vectors or moments, .... etc.
In short, there are untellable numbers of applications, but you'll run into applications of linear algebra time and time again, so learn it thoroughly the first time!
The study of the physical world around us and the nature of the interactions between all of the forms of matter and energy in it.
My bachelor's degree in engineering physics from the University of Alberta helped me develop strong problem-solving skills and an understanding of both classical and modern physics. I also have the engineering and philosophical background to be able to support my answer when a student asks "But why should I care about this?"
Physics-principles are vital for every student because they shape and bound the technologies that shape our world, play critical roles in elements of public and international policy, and cull implausible investment opportunities from consideration. It is essential for mankind's success in the future that everyone who votes with their ballot or their dollar to have an understanding of physics principles in order to reason soundly with respect to these issues.
I enjoy working with students up to and including introductory college-level physics to help them develop their physics brain and educate them on why they should.
Precalculus is an important and interesting part of every student's life if they are considering taking calculus, arguably the most useful mathematical tool ever invented (and by reputation, perhaps the most intimidating).
Building a solid foundation in the trigonometric relations, the relations between the manipulations of an equation and its graph, inverse functions, composite functions, domains, ranges, roots of polynomials, and the like ensures that the study of calculus will not become far more difficult and intimidating than it needs to be. Focus on doing well in precalculus so that you can get through calculus without a headache!
The SAT Math test is typical of many standardized math tests in that often as not, two or more of the typically four offered answers can be eliminated if one knows some of the most important math shortcuts -- simple facts and observations that can save time or improve accuracy.
In most cases, I coach students to put their calculators away. Most SAT questions can be answered correctly without pressing a single key. Only after all questions have been attempted would I normally consider checking work with a calculator.
To improve SAT math scores, I work with a student to make sure their understanding of the subject is strong, and help work the kinks out of any identified weaknesses in the tested skills. Solid understanding is a prerequisitie of sane confidence, a prerequisite to keeping exam stress within healthy and helpful bounds.
Trigonometry involves the study of angles, lines, and especially many of the characteristics of various two-dimensional shapes, in some detail.
The ability to solve triangles is extremely important for, and can be immediately applied to, the act of making measurements.
For example, the best methods for finding out the distance to a star, the height of a tree or tall building, the maximum height safely reached via a ladder of a given height.
It also comes into play in the study of calculus, and a huge number of other subjects that depend on calculus, and almost always depend on a solid background in trigonometry.
In short, if you are having trouble in trigonometry and considering any occupation (or even a hobby, like say, quilting) where you might have to measure, design, or build anything, it would be far easier to get your troubles with trigonometry taken care of than it would be to find a way to get by without it. There is simply no way to angle around that.