Differential Equations STEM Math – Tiers 1-6
Tier 1. The TI 30XA is an inexpensive, yet powerful, calculator. The lessons in Tier 1 teach your student how to get the most out of this calculator, covering topics ranging from basic operations (addition, subtraction, etc.) and storing numbers in memory to working with fractions and trigonometry operations (SIN, COS, TAN). Pre-Algebra is a great foundation for your student to create a solid future in mathematics. This course explains the basic rules for addition, multiplication, and the distributive law, as well as explaining fractions, squares, square roots, reciprocals, exponents, and other topics crucial to understanding higher level mathematics.
Tier 2. Tier 2 is made up of three topics: Algebra, Geometry, and Trigonometry.
Algebra teaches students to apply a process, and students learn how to approach a mathematical problem. Students learn how to solve linear equations by applying topics learned in Tier 1 – addition, subtraction, multiplication, division, the distributive law, reciprocal, and exponents – as well as The Rule of Algebra. Students are also introduced to the SIN and COS functions, and how they are dealt with in linear equations.
Students already use geometry in their lives and most don’t even realize it. This course teaches students that when they understand the rules of straight lines and angles, parallel lines, triangles, and the Pythagorean Theorem, they can figure out a lot when given only a little bit of information. Algebra and Geometry are combined in utilizing similar triangles to solve a variety of problems, which is one of the most useful tools in industrial practical math. Geometry lessons teach students about polygons and their perimeters, area, volume, and surface area, as well as the formulas that govern them.
Some students are intimidated by the trigonometry functions SIN, COS, and TAN, but this intimidation is unnecessary! The trigonometry lessons clearly and concisely explain that these functions are simply ratios, and when given a little bit of information, your student can learn a lot about the triangles that use them. In addition, the Pythagorean Theorem, and the Laws of Sines and Cosines, aid in a student’s understanding of trigonometry.
Tier 3. This course, divided into three parts, prepares students for the SAT. Part 1 relies heavily upon George F. Simmons’ textbook, Precalculus Mathematics in a Nutshell, and covers real numbers, polynomials, linear equations, the quadratic equation, inequalities, functions, graphs, and straight parallel, and perpendicular lines, and other topics. Part 2 covers additional topics seen on the SAT, including percentages, markups and discounts, means, medians, and averages, as well as ratios, logic, progressions, series, probabilities, permutations and combinations. Part 3 deals with preparation for the test itself – how often you should practice, get a good night’s sleep before the test, etc. This part also contains many practice problems so that your student will be familiar with the types of questions the test may ask.
Tier 4. This course uses notes and George F. Simmons’ wonderful book, Precalculus Mathematics in a Nutshell, and delves further into geometry, algebra, and trigonometry. The geometry section covers triangles, polygons, circles, angles, cylinders, cones, and spheres. The algebra section conducts a review of Tier 3, then covers functions, graphs, polynomials, exponential functions, logarithms, analytic geometry, and the conic sections, circles, parabolas, ellipses, and hyperbolas, infinite series and much more. The trigonometry section covers trig functions and their graphs, frequency and phase, identities and their proofs, inverse trig functions, and the Laws of Sines and Cosines. Complex Numbers are now treated properly in the appropriate modern mode where Euler’s Equation is the center piece of their development and geometric explanation. For example, ii = e-Pi/2 will be very easy to understand. The modern tool Wolfram Alpha is introduced early in Tier 4 and revolutionizes the way most Algebra and Trigonometry problems are solved. This serves as a great preparation for Calculus where Wolfram Alpha truly revolutionizes how Calculus problems are solved.
Tier 5. Tier 5 is made up of two topics: differential calculus and integral calculus.
This course introduces students to calculus, then covers functions, derivatives and their rules, inverse functions, and series expansions. Applications to graphing include methods for understanding what the graph of a function looks like, including whether it is increasing or decreasing, finding maximums and minimums, points of inflection, and concavities. This courses also introduces your student to the powerful tool, Wolfram Alpha, which makes time-consuming calculations used to discover this information obsolete.
Integral calculus causes more students to abandon mathematical studies than any other topic. The powerful tool, Wolfram Alpha, eliminates the obstacles that cause many students to give up. This course uses Wolfram Alpha to learn applications of integration, including areas, arc length, volumes, and surface areas. The course also covers parametric functions and improper integrals while teaching your student the easy to understand commands that Wolfram Alpha uses. Wolfram Alpha requires NO understanding of programming languages, simply tell Wolfram Alpha what you want to know and it will return the answer as well as show you for future reference the syntax that it uses.
Tier 6. This course teaches the student Linear & Differential Equations, Polynomial Approximations of Functions, the use of Math Models, Orthogonal Curves, Polar Coordinates and ODE’s.