Stage 4 Further Calculus

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