R16 CP Lab Manual

B.TECH_I Year  - II Semester  

COMPUTER PROGRAMMING LAB MANUAL

(COMMON FOR ALL ECE STUDENTS)

 

Note: a) All the Programs must be executed in the Linux Environment. (Mandatory)  

b) The Lab record must be a print of the LATEX (.tex) Format.

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MATHEMATICS-III Unit Wise Question Bank

I Year - II Semester

MATHEMATICS-III 

Unit Wise Question Bank

UNIT I: Linear systems of equations:

Rank-Echelon form-Normal form – Solution of linear systems – Gauss elimination - Gauss Jordon-

Gauss Jacobi and Gauss Seidal methods.Applications: Finding the current in electrical circuits.

Click Here To Download Unit_1 Question Bank

 UNIT II: Eigen values - Eigen vectors and Quadratic forms:

Eigen values - Eigen vectors– Properties – Cayley-Hamilton theorem - Inverse and powers of a matrix by
using Cayley-Hamilton theorem- Diagonalization- Quadratic forms- Reduction of quadratic form to
canonical form – Rank - Positive, negative and semi definite - Index – Signature.
Applications: Free vibration of a two-mass system.

Click Here To Download Unit_2 Question Bank

 

UNIT III: Multiple integrals:

Curve tracing: Cartesian, Polar and Parametric forms.
Multiple integrals: Double and triple integrals – Change of variables – Change of order of integration.
Applications: Finding Areas and Volumes.

Click Here To Download Unit_3 Question Bank

 

UNIT IV: Special functions:

Beta and Gamma functions- Properties - Relation between Beta and Gamma functions- Evaluation of
improper integrals.
Applications: Evaluation of integrals.

Click Here To Download Unit_4 Question Bank

 

UNIT V: Vector Differentiation:

Gradient- Divergence- Curl - Laplacian and second order operators -Vector identities.
Applications: Equation of continuity, potential surfaces

Click Here To Download Unit_5 Question Bank

UNIT VI: Vector Integration:

Line integral – Work done – Potential function – Area- Surface and volume integrals Vector integral
theorems: Greens, Stokes and Gauss Divergence theorems (without proof) and related problems.
Applications: Work done, Force.

Click Here To Download Unit_6 Question Bank

 

 

Click Here To Download All Documents Into a Single File In .ZIP 

 

MATHEMATICS-III Lesson PLan All_Units

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MATHEMATICS-III

Course Objectives:

1. The course is designed to equip the students with the necessary mathematical skills and
techniques that are essential for an engineering course.
2. The skills derived from the course will help the student from a necessary base to
develop analytic and design concepts.
3. Understand the most basic numerical methods to solve simultaneous linear equations.

Course Outcomes:

 At the end of the Course, Student will be able to:

1. Determine rank, Eigenvalues and Eigen vectors of a given matrix and solve
simultaneous linear equations.
2. Solve simultaneous linear equations numerically using various matrix methods.
3. Determine double integral over a region and triple integral over a volume.
4. Calculate gradient of a scalar function, divergence and curl of a vector function.
Determine line, surface and volume integrals. Apply Green, Stokes and Gauss
divergence theorems to calculate line, surface and volume integrals.

Click Here To Download M_III Lesson Plan For All_Units.

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