Harcourt Butler Technical University, UP, Computer Engineering Semester 1, Mathematics-I Syllabus

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Unit - 1 Functions of One Real Variable

Unit1

Functions of One Real Variable

1.1 Successive differentiation

1.2 Leibnitz test

1.3 Mean value theorems

1.4 Sequences and Series.

1.5 Expansion of function

1.6 Improper integrals and their convergence

Unit - 2 Functions of Several Real Variables

Unit2

FUNCTIONS OF SEVERAL VARIABLES

2.1 Limits and Continuity

2.2 Partial differentiation

2.3 Total differentiation and approximation

2.4 Jacobian and Euler’s theorem expansion of functions.

2.5 Beta and Gamma functions

2.6 Multiple integral Change of order and Change of variables.

2.7 change of variables in applications to area volumesurface area etc.

2.8 Dirichlet’s Integral and applications.

Unit - 3 Vector Calculus

Unit 3

Vector calculus

3.1 point functions

3.2 Differentiation Gradient Directional derivative.

3.3 Divergence.

3.4 Curl of a vector and their physical interpretations.

3.5 Solenoidal and irrotational derivative.

3.6 Integration line surface and volume integrals

3.7 Green’s Stroke’s and Gauss Divergence theorems without proof and applications.

Unit - 4 Matrices and Linear Algebra

Unit 4

Matrices and Linear Algebra

4.1 Vector space and subspace

4.2 Linear dependence

4.3 Dimensions and basis

4.4 Linear transformation and its matrix representation.

4.5 Elementary transformations and Echelon form

4.6 Rank and nullity

4.7 Consistency of linear system of equations and their solutions charactestic equation.

4.8 Cayley Hamilton theorem.

4.9 Real and complex Eigen values Eigen vectors diagonalization.

4.10 Quadratic forms complex orthogonal and unitary matrices.

4.11 Application to cryptography discrete compartmental models and stability.

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Other Subjects of Semester-1
Physics
Engineering mechanics
Electrical engineering
Professional communication
English language & composition
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