Calculus Topics - GATE CE Syllabus

1

Functions of single variable

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📌 Key Formulaf(x) domain and range

2

Limit

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📌 Key Formulalim x→a f(x)

3

Continuity

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📌 Key Formulalim x→a f(x) = f(a)

4

Differentiability

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📌 Key Formulaf'(x) exists

5

Mean value theorems

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📌 Key FormulaRolle's, Lagrange's, Cauchy's MVT

6

Maxima and minima

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📌 Key Formulaf'(x)=0, second derivative test

7

Taylor series (in one and two variables)

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📌 Key Formulaf(x) ≈ f(a) + f'(a)(x-a) + ...

8

Evaluation of definite integrals

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📌 Key Formula∫_a^b f(x) dx = F(b) - F(a)

9

Evaluation of indefinite integrals

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📌 Key Formula∫ f(x) dx = F(x) + C

10

Application of definite integral to obtain area and volume

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📌 Key FormulaArea = ∫ y dx, Volume by disk/shell

11

Partial derivatives

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📌 Key Formula∂f/∂x, ∂f/∂y

12

Total derivative

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📌 Key Formuladf = (∂f/∂x)dx + (∂f/∂y)dy

13

Gradient

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📌 Key Formula∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)

14

Divergence

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📌 Key Formula∇·F

15

Curl

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📌 Key Formula∇×F

16

Vector identities

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📌 Key Formula∇·(∇×F)=0, ∇×(∇f)=0, etc.

17

Line, surface and volume integrals

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📌 Key Formula∫_C F·dr, ∬_S F·dS, ∭_V f dV