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

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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.

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