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Class prep · TJ Advanced Mathematical Techniques

Match the technique,then check the model.

An independent course in mathematical techniques used in physics and chemistry. Special functions, generating functions, models, waves and complex amplitudes, each tied to a calculation you can finish by hand. Every problem has a full worked solution. Built by Neil Kothari, a TJ alumnus.

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$395 covers the full school year. The first lesson is free.

Try one. This is a test-level question from the course.

Problem 1

  • Test level
  • Multiple choice
  • No calculator
  • 4 pts

Which number equals Γ(9)/Γ(8)\Gamma(9)/\Gamma(8)?

Choose one answer

original problems, each with a worked answer
624
original problems, each with a worked answer
at test level or beyond
432
at test level or beyond
short lessons, one for every topic
48
short lessons, one for every topic
units, all open now
8
units, all open now

Free lesson

Lesson 1.1: Gamma at Positive Integers

Evaluate Gamma at positive integers by the shifted factorial, and cancel ratios exactly.

Start with the gamma function at the positive integers. Use the factorial identity, then say where the same function shows up in a model.

Problem 2

  • Core
  • True or false
  • No calculator
  • 2 pts

True or false: Γ(7)=7!\Gamma(7)=7!. Justify with the integer definition.

Is the statement true or false?

Problem 3

  • Core
  • Multiple choice
  • No calculator
  • 4 pts

Which number equals Γ(8)\Gamma(8)?

Choose one answer

Open the rest of this lesson, free

The full lesson and all 13 of its problems, with every worked answer.

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How it works

Class prep that works alongside class

A complete techniques course for students who know basic calculus and basic physics. Work alongside your school course or study the material in sequence. Each lesson starts with a formula you can evaluate, develops the identity, and shows the check before you try the practice.

  • Original problems in several formats: true or false, multiple choice, multi-part and free response.
  • Each one is marked core, test level or beyond.
  • Gamma and beta values, generating functions, equilibria, finite probability models, 2 by 2 modes, waves and phasors.
  • A worked answer for every problem, ending with the mistake that most often costs points.
  • Special functions, generating functions, rate models, small physical probability models, linear algebra in applications, waves and complex amplitudes.

What is inside

  1. 1Special functions6 lessons · 78 problems
  2. 2Generating functions6 lessons · 78 problems
  3. 3Modeling with differential equations6 lessons · 78 problems
  4. 4Probability in physical models6 lessons · 78 problems
  5. 5Linear algebra in applications6 lessons · 78 problems
  6. 6Waves6 lessons · 78 problems
  7. 7Complex numbers as a tool6 lessons · 78 problems
  8. 8Synthesis6 lessons · 78 problems
The front entrance of Thomas Jefferson High School for Science and Technology
Neil Kothari, co-founder of EduAvenues

Who built it

Neil Kothari

TJHSST alumnus · Co-founder, EduAvenues · 10+ years in TJ preparation

Neil is a TJ alumnus and has spent more than a decade working with TJ students and their families. He built this course so students can choose a technique, finish the calculation, and name the limit of the model. Every problem is written for the course and every answer is checked before it goes in.

Tuition

$395for the full school year

One tuition covers every unit of the course. All 8 units are open now. The Gamma at Positive Integers lesson stays free for everyone.

  • All 8 units: 48 lessons and 624 original problems
  • A worked answer for every problem
  • Access through the end of the school year
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