# RGPV B.E first year Mathematics-1 syllabus

The article will provide you with the RGPV syllabus and reference book details of B.E 1st year for the subject Engineering Mathematics - I.

## RGPV Engineering Mathematics-1 syllabus of B.E first year

Engineering Mathematics-1 is studied by both the groups of branches.

The subject carries a total of 100 marks. Out of which 20 marks of theory is from the average of 2 mid semester exams and 10 marks for the assignment session. The syllabus for Mathematics-1 is as follows:

__Differential Calculus__

This section on differential calculus will deal with expansion of functions by Maclaurin's and Taylor's theorem. Other topics of differential calculus like partial differentiation, Euler's theorem and its application in approximation and errors as well as the maxima and minima of function of two variables will also be included in this course. You will also be taught about curvatures including radius of curvature, centre of curvature and more.

__INTEGRAL CALCULUS :__

This topic includes Definite Integrals as a limit of a sum , its application in Summation of series. Other topics included are Double and Triple Integrals, Change of Order of Integration,Area,Volume and Surfaces using double and triple Integral. This section also includes Beta and Gamma Functions.

__DIFFERENTIAL EQUATIONS :__

Here you would be taught to solve Ordinary Differential Equation of first order and first degree for Exact differential Equations, Solution of Ordinary Differential Equation of first order and higher degree (solvable for p, x and y, Clairauts Equation)and Linear Differential Equations with Constant Coefficients. The other topics taught are Cauchy's Homogeneous differential Equation, Simultaneous differential Equations and Method of Variation of Parameters.

__MATRICES :__

This unit on matrices would include identification of Rank of matrices, Solution of Simultaneous equation by elementary transformation, Consistency of

System of Simultaneous Linear Equation, finding the Eigen Values and Eigen Vectors and explanation of Cayley-Hamilton Theorem and its Application to find the inverse.

__Algebra of Logic__: In this section you would be taught about Boolean Algebra, the Principle of Duality, Boolean Expressions and Functions and other Basic theorems.

This section would also include other topics like Elementary Concept of Fuzzy Logic and

__Graph Theory :__which includes a description about Graphs, Subgraphs, their Degree and Distance, Tree, cycles and Networks.

**Reference Books**

For a detailed description on the reference books that would be required to study the subject, please see Engineering Mathematics reference books and study materials for Madhya Pradesh (MP) Universities