Savitribai Phule Pune University, Maharashtra (SPPU), Civil Engineering Semester 3, Engineering Mathematics III Syllabus

Unit - 1 Linear Differential Equations (LDE) and Applications

1.1 LDE of nth order with constant coefficients

1.2 Complementary Function

1.3 Method of variation of parameters

1.4 Cauchy’s and Legendre’s DE

1.5 Simultaneous and Symmetric simultaneous DE

Unit - 2 Numerical Methods

2.1 Numerical solutions of system of linear equations Gauss elimination method

2.2 Cholesky

2.3 Jacobi and GaussSeidel methods

2.4 Numerical solutions of ordinary differential equations Euler’s

2.5 Modified Euler’s

2.6 Runge Kutta 4th order and PredictorCorrector methods

Unit - 3 Statistics and Probability

3.1 Measures of central tendency

3.2 Standard Deviation

3.3 Coefficient of Variation

3.4 Moments

3.5 Skewness and Kurtosis

3.6 Correlation and Regression

3.7 Reliability of Regression Estimates

3.9 Probability Density function

3.10 Probability distributions Binomial

3.11 Poisson

3.12 Normal

3.13 Test of Hypothesis ChiSquare test and t – test

Unit - 4 Vector Differential Calculus

4.1 Physical interpretation of Vector differentiation

4.2 Vector differential operator

4.3 Gradient

4.4 Divergence and Curl

4.5 Directional derivative

4.6 Solenoidal

4.7 Irrotational and Conservative fields

4.8 Scalar potential

4.9 Vector identities

Unit - 5 Vector Integral Calculus and Applications

5.1 Line

5.2 Surface and Volume integrals

5.3 Workdone

5.4 Green’s Lemma

5.5 Gauss’s Divergence theorem

5.6 Stoke’s theorem

5.7 Applications to problems in Fluid Mechanics

5.8 Streamlines

5.9 Continuity equations

5.10 Bernoulli’s equation

5.11 Equations of motion

Unit - 6 Applications of Partial Differential Equations (PDE)

6.1 BASIC CONCEPTS

6.2 MODELLING OF VIBRATING STRING

6.3 WAVE EQUATION

6.4 ONE AND TWO DIMENSIONAL HEAT FLOW EQUATIONS

6.5 Applications of P.D.E to general problem