Shivaji University, Maharashtra, Civil Engineering Semester 3, Engineering Mathematics - III Syllabus

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Unit - 1 Linear Differential equations with constant coefficients

Unit–1

Linear differential equations with constant coefficients

1.1. Linear differential equations with constant coefficients and their methods of solution

1.2. Applications of linear differential equations with constant coefficients to civil engineering problems Beam cantilever and strut

Unit - 2 Vector differential calculus

UNIT–2

Vector differential calculus

2.1. Differentiation of vectors Consistency of linear system equations

2.2. Gradient of scalar point function and directional derivative

2.3. Divergence and curl of vector point function and solenoidal vector fields

2.4.Irrotational vector field

Unit - 3 Probability Distribution

UNIT–3

Probability Distribution

3.1. Random variable

3.2. Binomial distribution

3.3. Poisson distribution

3.4. Normal distribution

Unit - 4 Laplace Transform

UNIT–4

Laplace Transform

4.1. Definition and transform of elementary functions

4.2. Properties of Laplace transform

Unit - 5 Inverse Laplace Transform

UNIT–5

Inverse Laplace Transform

5.1. Inverse Laplace transform formulae

5.2. Inverse Laplace transform by using partial fraction and convolution theorem

5.3. Solution of linear differential equation with constant coefficients

Unit - 6 Complex Variable

UNIT–6

Complex variable

6.1. Function of complex variable

6.2. Analytic function

6.3. Necessary and sufficient condition for fz to be analytic

6.4. CauchyRiemann equation in Cartesian and polar coordinates

6.5. MilneThomson theorem

6.6 Harmonic function

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Other Subjects of Semester-1
Surveying-i
Fluid mechanics-i
Strength of materials
Building construction and materials
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