Chapter 1
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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
De
Chapter 2: Review of one-variable integration
Indefinite Integrals: differentiate
F ( x)
integrate
f ( x) = F '( x)
y = f ( x)
F ( x) = f ( x)dx
b
Definite Integrals:
f ( x)dx
a
Area under the curve a b
F ( x) = F (a) + f ( x)dx
a
x
Examples of useful in
Chapter 3: Multivariate Calculus Only the Basics
Derivative of a single variable function:
df f ( x + x) f ( x) = f '( x) lim x 0 dx x
Derivatives of a two-variable function:
f ( x, y ) f ( x + x , y ) f ( x , y ) lim = f x ( x, y ) x 0 x x f ( x , y + y