1
Stage 1
Engineering Calculus
Calculus with engineering applications and computational focus.
Key Topics
Single variable calculusMultivariable calculusVector calculusLine and surface integralsStokes and divergence theorems
3 books
~12 weeks
Engineering Mathematics
Mathematics that builds the world
Intermediate
5 stages
~40 weeks
13 books
Applied mathematics for engineers: differential equations, complex analysis, and numerical methods.
Prerequisites: Complete the foundations path first.
Skill Tree
Visualize your learning journey. Click on any stage (branch) to see the recommended books for that subject. Topics are shown as leaves on each branch.
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Learning Stages
This path is divided into 5 stages covering 25 topics. Work through each stage in order for the best learning experience.
Recommended Books for Stage 1
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Calculus
Larson & Edwards
Intermediate
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Calculus
James Stewart
Intermediate
Thomas' Calculus
Thomas
Intermediate
2
Stage 2
Differential Equations
ODEs and PDEs for modeling physical systems.
Key Topics
First and second order ODEsSystems of ODEsLaplace transformsFourier seriesHeat and wave equationsBoundary value problems
4 books
~10 weeks
Recommended Books for Stage 2
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Fundamentals of Differential Equations
Nagle, Saff & Snider
Intermediate
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A First Course in Differential Equations
Dennis Zill
Intermediate
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Partial Differential Equations: An Introduction
Strauss
Intermediate
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Partial Differential Equations
Miller
Intermediate
3
Stage 3
Linear Algebra for Engineers
Matrix methods for solving systems and analyzing data.
Key Topics
Matrix operationsLinear systemsDeterminantsEigenvalue problemsNumerical methods
2 books
~6 weeks
Recommended Books for Stage 3
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Elementary Linear Algebra
Howard Anton
Beginner
Schaum's Outline of Linear Algebra
Schaum's
Intermediate
4
Stage 4
Complex Analysis
Complex numbers and their applications in engineering.
Key Topics
Complex functionsAnalytic functionsContour integrationResidue calculusConformal mapping
3 books
~8 weeks
Recommended Books for Stage 4
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Complex Variables and Applications
Brown & Churchill
Intermediate
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Fundamentals of Complex Analysis
Saff & Snider
Intermediate
Schaum's Outline of Complex Variables
Schaum's
Intermediate
5
Stage 5
Advanced Engineering Math
Comprehensive coverage of advanced topics for engineers.
Key Topics
Special functionsTransform methodsNumerical analysisOptimization
1 book
~4 weeks
Recommended Books for Stage 5
Advanced Engineering Mathematics
Kreyszig
Advanced
All Books in This Path
Complete list of 13 recommended books across all stages. You don't need to buy them all — pick what works for you.
Calculus
by Larson & Edwards
Used to teach Calc 1, 2, and 3. Great exercises and content. Everything you need.
Calculus
by James Stewart
Perhaps the most popular calculus book in the world. Same author as the precalc books.
Thomas' Calculus
by Thomas
Legendary book used for decades. 13th edition. Incredible with tons of exercises and great explanations.
Fundamentals of Differential Equations
by Nagle, Saff & Snider
Used as undergrad. Great book with solid examples, tons of content, answers to odd problems.
A First Course in Differential Equations
by Dennis Zill
Used to teach DE for many years. Easier than Nagle. Great beginner DE book.
Partial Differential Equations: An Introduction
by Strauss
Standard modern textbook on PDEs.
Partial Differential Equations
by Miller
Dover reprint, very affordable. Great for getting started with PDEs.
Elementary Linear Algebra
by Howard Anton
Best for beginners! Very standard problems that often show up on tests. Highly recommended.
Schaum's Outline of Linear Algebra
by Schaum's
Very comprehensive with lots of examples and topics. Great reference and source of problems.
Complex Variables and Applications
by Brown & Churchill
Perhaps the most popular complex variables book in the world. Used for decades. Introductory level.
Fundamentals of Complex Analysis
by Saff & Snider
Used as undergrad. Very similar to Brown & Churchill. Both are excellent choices.
Schaum's Outline of Complex Variables
by Schaum's
Considered by many to be THE BEST Schaum's ever written! Has everything you need. A must-have!
Advanced Engineering Mathematics
by Kreyszig
Legendary! SO much math: DEs, Calc 3, Linear Algebra, Fourier, PDEs, Complex Analysis. Essential for engineers!
What's Next?
Complete this path and continue your mathematical journey.