Rajiv Gandhi Prodoyogiki Vishwavidyalaya, MP, Civil Engineering Semester 1, Mathematics - I Syllabus

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Unit - 1 Calculus

Module 1

Calculus

1.1 Rolle’s theorem

1.2 Mean Value theorems

1.3 Expansion of functions by Mc

1.4 Taylor’s theorem for function of two variables

1.5 Partial Differentiation Maxima Minima two and three variables

1.6 Method of Lagranges Multipliers

Unit - 2 Calculus

Module 2

Calculus

2.1 Definite Integral as a limit of a sum and Its application in summation of series

2.2 Beta and Gamma functions and their properties

2.3 Applications of definite integrals to evaluate surface

2.4 Areas and volumes of revolutions

2.5 Multiple Integral

2.6 Change the order of the integration

2.7 Applications of multiple integral for calculating area and volumes of the curves.

Unit - 3 Sequences and series

Module 3

Sequences and series

3.1 Convergence of sequence and series

3.2 Tests for convergence

3.3 Power series

3.4 Taylors series

3.5 Series for exponential

3.6 Trigonometric and logarithm functions

3.7 Fourier series Half range sine and cosine series

3.8 Parseval’s theorem.

Unit - 4 Vector Spaces

Module 4

Vector Spaces

4.1 Vector Space

4.2 Vector Sub Space

4.3 Linear Combination of Vectors

4.4 Linearly Dependence and independence of vectors

4.5 Basis of a Vector Space

4.6 Linear Transformations

Unit - 5 Matrices

Module 5

Matrices

5.1 Rank of a Matrix

5.2 Solution of Simultaneous Linear Equations by Elementary Transformation

5.3 Consistency of Equation

5.4 Eigen Values and Eigen Vectors

5.5 Diagonalization of Matrices 

5.6 CayleyHamilton theorem and its applications to find inverse

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Other Subjects of Semester-1
Engineering physics
Basic computer engineering
Basic mechanical engineering
Basic civil engineering & mechanics
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