Differential Equations & Linear Algebra by Allen Gehret
Differential Equations & Linear Algebra - Table of Contents
1. Linear Algebra
2. Calculus Review
3. First Order Differential Equations
4. Linear Algebra II
5. Second Order Linear Differential Equations
6. Linear Algebra III
7. Systems of Differential Equations
8. Special Functions
What You Will Learn in Differential Equations & Linear Algebra
"Differential Equations?&?Linear Algebra" by Allen?Gehret and Mikhail?Hlushchanka is a well-structured set of "undergraduate lecture notes" that blends the core ideas of "linear algebra" with the theory and methods of "ordinary differential equations (ODEs)". It was written for the Math33B course at UCLA and revised in 2020.
The book begins by introducing systems of equations and matrix techniques, then reviews calculus basics to prepare you for solving ODEs. It guides you through "first-order" and "second-order" linear differential equations, explores solution methods, and explains key concepts like eigenvalues and vector spaces — showing how linear algebra tools help solve systems of differential equations.
Designed for students with prior calculus, these notes emphasize "conceptual understanding and practical problem-solving". You’ll learn to solve many exact equations by hand, understand how matrix methods simplify systems, and see how differential equations model real-world dynamics. The material is clear and educational, making complex topics approachable for self-study or course revision.
Book Details & Specifications
Title:
Differential Equations & Linear Algebra by Allen Gehret
Publisher:
Allen Gehret
Year:
2020
Pages:
165
Type:
PDF
Language:
English
ISBN-10 #:
0980232791
ISBN-13 #:
978-0980232790
License:
University Educational Resource
Amazon:
Amazon
About the Author: Allen Gehret
The author
Allen Gehret
is a mathematician specializing in "differential algebra", "linear algebra", and "model theory". He completed his "Ph.D." with a focus on logarithmic transseries and has taught "differential equations" at UCLA. His work bridges advanced algebraic concepts with practical applications in mathematics education. "Mikhail Hlushchanka" is an expert in "dynamical systems", "fractal geometry", and analysis. He earned his Ph.D. from Jacobs University Bremen and has held research positions at universities including UCLA and the University of Amsterdam. His contributions combine "complex dynamics" with mathematical theory, making him a notable figure in modern pure mathematics.
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