Updated Daily - The STEM Major's Guide to the University

Student: This is an ongoing title. I will be adding updates to it daily. It comes with access to old editions of my crash course series as well. 

The Ultimate Junior-Year STEM Preparation Guide

This book is carefully designed for students who must complete Linear Algebra, Differential Equations, and Electromagnetism (E&M) before entering the junior year of a modern STEM degree.

Beginning with precalculus, the text focuses on the advanced problem-solving foundations required for higher mathematics and physics. It then progresses through calculus, differential equations, and linear algebra, presenting raw, textbook-connected problem solving so students learn not only the answers, but the method behind every solution.

Alongside mathematics, Jonathan guides students through 44 chapters of essential physics problems, hand-selected to ensure true readiness for junior-level coursework. The journey concludes with an introduction to tensor mathematics and higher math/physics concepts, providing a smooth transition into advanced university study.

Subjects Covered

Mathematics Foundations

• Algebra

• Trigonometry

• Precalculus

Calculus Sequence

• Differential Calculus

• Integral Calculus

• Sequences and Series

• Multivariable Calculus

• Vector Calculus

Core Advanced Mathematics

• Linear Algebra

• Differential Equations

• Differential Equations with Linear Algebra for Engineers and Physicists

Physics Preparation

• Mechanics

• Optics and Waves

• Thermodynamics

• Electromagnetism

• Modern Physics

Advanced Readiness

• Index and Tensor Notation

• Introduction to Higher Mathematics and Physics

Purpose of This Book

• Walk students through everything that must be understood before junior year in a STEM major

• Demonstrate clear solution structure and logical problem-solving strategy

• Teach how to study directly from textbooks, the most important skill for long-term academic success

• Build confidence and readiness for upper-division university courses

This is not just a review—it is a step-by-step bridge into junior-level STEM mastery.