Chap1 - Chapter 1 Nakanishi Office Hours for Week 2 only:...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 1 Nakanishi Office Hours for Week 2 only: PHYS Rm. 264, M (8/30) and F (9/3), 11:30 am – 12:20 pm From Week 3 onward: Grader (Mr. Shen) Office Hour: PHYS Rm. 105, Th. 3 – 4 pm Nakanishi Office Hour: PHYS Rm. 264, F 11:30 am – 12:20 pm f '( x) ≡ lim ∆x → 0 Derivative of f(x): f ( x + ∆x) − f ( x) ∆x • Simple and explicitly given f(x) • Not-so-simple, but explicitly given f(x) • Composite function f(u(x)) • Implicitly given f(x), e.g., x=g(y), g(x)+h(y)=0, or g(x,y)=0 • Parametrically given function: x=g(t), y=h(t) logarithm and exponential: y = ln x and y = ex Chapter 1 More general power laws: y = x−n , y = x p / q , y = xa Taylor series for f(x): x2 x3 f ( x) = f (0) + f '(0) x + f ''(0) + f '''(0) + ... 2! 3! ∞ For example, xn ex = ∑ n=0 n ! Trigonometric and Hyperbolic Functions: ∞ ∞ (−1) n x 2 n (−1) n x 2 n +1 cos x = ∑ , sin x = ∑ (2n)! n=0 n = 0 (2n + 1)! e x + e− x e x − e− x cosh x = , sinh x = 2 2 Chapter 1 L’Hôspital’s Rule: • If [f(x)→∞ and g(x) →∞] or [f(x)→0 and g(x) →0] as x→a, then f ( x) f '( x) lim x →a g ( x) x→a ≡ lim g '( x) • If f’(x) and g’(x) still tends to infinity or zero, keep taking the derivatives until they will have a definite limiting ratio. Differential of f(x) at x=x0: df ≡ df dx dx x0 df dx ...
View Full Document

This note was uploaded on 11/26/2010 for the course PHYS 290 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

Page1 / 3

Chap1 - Chapter 1 Nakanishi Office Hours for Week 2 only:...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online