Advanced Calculus

高微應該學到甚麼程度 有點困惱 至少要能處理微分幾何的問題與一點物理現象

R.Courant and D.Hilbert是數學物理的書肯定很有水準 下冊在說ODE與PDE 有空應該慢慢看

要看懂Riemann Conjecture 必須讀一點複變(complex analysis) 例如解析函數

Exercises 001 清大108博士班高微考題

  1. Vector Calculus(div grad curl and all that )                  H. M. Schey
  2. Understanding Multivariable Calculus(初等微積分)   Bruce H. Edwards
  3. Methods of Mathematical Physics (1)  (2)PDE             R.Courant   D.Hilbert
  4. Math Problems [Putnam Newman IMC]                      John Scholes
  5. Mathematical Analysis(I)(II)                                       Zorich V.A.

以下是台大數學系建議

  1. Introduction to calculus and analysis      Richard Courant,Fritz John
  2. Real analysis : modern techniques and their applications     Gerald B. Folland
  3. A first course in real analysis                 Murray H. Protter , Charles B. Morrey
  4. Principles of Mathematical Analysis 探馬建議           Walter Rudin