As of today, these books sell for:

• Measure and Integral by Weeden and Zygmund: $91
  
• Partial Differential Equations by Evans: $88
  
• Linear and Nonlinear Functional Analysis with Applications by Ciarlet: $95
  
  At $274, this is probably the most expensive tofu presser I've ever seen.

Ordinary Differential Equations and Dynamical Systems by Gerald Teschl is a really good intro to ODE theory on the first-year graduate level. It also has the benefit of being freely available online. At the undergrad level, I haven't used this book personally but Differential Equations, Dynamical Systems, & and Introduction to Chaos by Hirsch, Smale, and Devaney seems to be a common choice.

For PDE, there are lots of standard texts that don't take the "toolbox" approach: at the undergrad level you have Walter Strauss, and at the begininning graduate level you've got Evans and Folland. For a slightly more advanced treatment, I like John Hunter's PDE notes, also free online.

Prerequisites: you should have a firm grasp of introductory analysis, say at the level of Baby Rudin, before diving into either of these subjects. You should also know your undergraduate linear algebra well.

/u/another_user_name posted this list a while back. Actual aerospace textbooks are towards the bottom but you'll need a working knowledge of the prereqs first.

Non-core/Pre-reqs:

Mathematics:

Calculus.

1-4) Calculus, Stewart -- This is a very common book and I felt it was ok, but there's mixed opinions about it. Try to get a cheap, used copy.

1-4) Calculus, A New Horizon, Anton -- This is highly valued by many people, but I haven't read it.

1-4) Essential Calculus With Applications, Silverman -- Dover book.

More discussion in this reddit thread.

Linear Algebra

3) Linear Algebra and Its Applications,Lay -- I had this one in school. I think it was decent.

3) Linear Algebra, Shilov -- Dover book.

Differential Equations

4) An Introduction to Ordinary Differential Equations, Coddington -- Dover book, highly reviewed on Amazon.

G) Partial Differential Equations, Evans

G) Partial Differential Equations For Scientists and Engineers, Farlow

More discussion here.

Numerical Analysis

5) Numerical Analysis, Burden and Faires

Chemistry:

1. General Chemistry, Pauling is a good, low cost choice. I'm not sure what we used in school.
   
   

   Physics:
   

   
   2-4) Physics, Cutnel -- This was highly recommended, but I've not read it.
   
   

   Programming:
   

   
   

   Introductory Programming
   

   
   Programming is becoming unavoidable as an engineering skill. I think Python is a strong introductory language that's got a lot of uses in industry.
   
   

2. Learning Python, Lutz
   
   
3. Learn Python the Hard Way, Shaw -- Gaining popularity, also free online.
   
   

   Core Curriculum:
   

   
   

   Introduction:
   

   
   

4. Introduction to Flight, Anderson
   
   

   Aerodynamics:
   

   
   

5. Introduction to Fluid Mechanics, Fox, Pritchard McDonald
   
   
6. Fundamentals of Aerodynamics, Anderson
   
   
7. Theory of Wing Sections, Abbot and von Doenhoff -- Dover book, but very good for what it is.
   
   
8. Aerodynamics for Engineers, Bertin and Cummings -- Didn't use this as the text (used Anderson instead) but it's got more on stuff like Vortex Lattice Methods.
   
   
9. Modern Compressible Flow: With Historical Perspective, Anderson
   
   
10. Computational Fluid Dynamics, Anderson
    
    

    Thermodynamics, Heat transfer and Propulsion:
    

    
    

11. Introduction to Thermodynamics and Heat Transfer, Cengel
    
    
12. Mechanics and Thermodynamics of Propulsion, Hill and Peterson
    
    

    Flight Mechanics, Stability and Control
    

    
    5+) Flight Stability and Automatic Control, Nelson
    
    5+)[Performance, Stability, Dynamics, and Control of Airplanes, Second Edition](http://www.amazon.com/Performance-Stability-Dynamics-Airplanes-Education/dp/1563475839/ref=sr_1_1?ie=UTF8&qid=1315534435&sr=8-1, Pamadi) -- I gather this is better than Nelson
    
    

13. Airplane Aerodynamics and Performance, Roskam and Lan
    
    

    Engineering Mechanics and Structures:
    

    
    3-4) Engineering Mechanics: Statics and Dynamics, Hibbeler
    
    

14. Mechanics of Materials, Hibbeler
    
    
15. Mechanical Vibrations, Rao
    
    
16. Practical Stress Analysis for Design Engineers: Design & Analysis of Aerospace Vehicle Structures, Flabel
    
    6-8) Analysis and Design of Flight Vehicle Structures, Bruhn -- A good reference, never really used it as a text.
    
    
17. An Introduction to the Finite Element Method, Reddy
    
    G) Introduction to the Mechanics of a Continuous Medium, Malvern
    
    G) Fracture Mechanics, Anderson
    
    G) Mechanics of Composite Materials, Jones
    
    

    Electrical Engineering
    

    
    

18. Electrical Engineering Principles and Applications, Hambley
    
    

    Design and Optimization
    

    
    

19. Fundamentals of Aircraft and Airship Design, Nicolai and Carinchner
    
    
20. Aircraft Design: A Conceptual Approach, Raymer
    
    
21. Engineering Optimization: Theory and Practice, Rao
    
    

    Space Systems
    

    
    

22. Fundamentals of Astrodynamics and Applications, Vallado
    
    
23. Introduction to Space Dynamics, Thomson -- Dover book
    
    
24. Orbital Mechanics, Prussing and Conway
    
    
25. Fundamentals of Astrodynamics, Bate, Mueller and White
    
    
26. Space Mission Analysis and Design, Wertz and Larson

If you're looking for the "bible" of PDE - Evans is typically considered the standard at the graduate level. For an undergraduate exposition of differential equations (ODE), then my professor liked to use Zill for ODE and Haberman for PDE.

​

If you're a little more specific I might be able to direct you to better sources - hope you enjoy the above, I have them all and really like them.

In order to understand the modern approach to PDEs in full generality you must have a minimum background of ODEs, basic topology, complex analysis, and basic differential geometry.
Many of the foundational theorems for these fields are directly applicable to the study of PDEs and it would be fruitless to try to study PDEs in full generality without that basic understanding. That being said, Evans ( http://www.amazon.com/Partial-Differential-Equations-Graduate-Mathematics/dp/0821849743 ) is an excellent well-rounded introduction to the general theory.
If this is too difficult for you to tackle at the moment, you will need to work your way through the above topics first. PDEs, studied in full generality instead of in particular cases, is not a light topic.

Depending on your level, i have used PDEs by Evans which is very well written, and the most recommended book i know of on the subject. It is pretty advanced though.

I am no expert (undergrad applied maths), but from what I have heard, Evans is the go to text. I have also heard good things about Salsa as a general overview/ course on PDEs.

Graduate or undergraduate level?


If graduate, this is THE book to get.

This is much more applied.

Evans for PDEs. There are many rigorous books for ODEs since its a little bit easier to be rigorous without over-complicating the subject matter.

As an undergrad physics major, I would recommend this as well. If you're going to continue and do graduate PDE work, I would just jump into Evans after that.