**Further Calculus (optional):**

Ordinary Differential Equations:

- Aronld V.I.
*Ordinary Differential Equations* - Ince E.L.
*Ordinary Differential Equations* - Miller R.K. and Michel A.N.
*Ordinary Differential Equations* - Tenenbaum M. and Pollard H.
*Ordinary Differential Equations*

Partial Differential Equation:

Differential equation with several variables, i.e. equations with partial derivatives. Particularly useful in physics, e.g. heat, electrostatics, electrodynamics, etc.

- Arnold V.I.
*Lectures on Partial Differential Equations* - Bass R.F. PDE From a Probability Point of View [.pdf] (FREE!)
- Driver B.
*Analysis Tools with Applications*and PDE Notes (FREE!) - Evans G., Blackledge J. and Yardley P.
*Analytic Methods for Partial Differential Equations* - Evans L.C. Entropy and Partial Differential Equations [.pdf] (FREE!)
- Evans L.C.
*Partial Differential Equations*- As Evans emphasise, PDE is not a branch of functional analysis; many interesting equations are non-linear; understanding generalised solutions is fundamental; good theory is as useful as exact formulas; and this is a textbook, not a reference book. Check out his page for errata. - Jost J.
*Partial Differential Equations* - King A.C., Billingham J. Otto S.R.
*Differential Equations: Linear, Nonlinear, Ordinary, Partial* - Kuttler K. Notes for Partial Differential Equations [.pdf] (FREE!)
- Markowich P.A.
*Applied Partial Differential Equations: A Visual Approach* - Pinchover Y. and Rubinstein J.
*An Introduction to Partial Differential Equations* - Pivato M.
*Linear Partial Differential Equations and Fourier Theory*[.pdf] (FREE!) - Sattinger D.H. Partial Differential Equations of Applied Mathematics [.pdf] (FREE!)
- Sauvigny F.
*Partial Differential Equation Vol 1, 2* - Showalter R.E. A PDE Primer (FREE!)
- Sneddon I.N.
*Elements of Partial Differential Equations* - Strauss W.A.
*Partial Differential Equations: An Introduction*- The author's principle: "Motivate with physics but then do mathematics." - Symes W.W. Partial Differential Equations of Mathematical Physics [.pdf] (FREE!)

Calculus of Variations:

- Dacorogna B.
*Introduction To The Calculus Of Variations* - Gelfand I.M. and Fomin S.V.
*Calculus of Variations* - Jost J. and Li-Jost X.
*Calculus of Variations* - van Brunt B.
*The Calculus of Variations* - Weinstock R.
*Calculus of Variations*

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