__MT-332 ADVANCED CALCULUS & LINEAR ALGEBRA__

__CREDIT HOURS__

Theory = 3

Practical = 0

**COURSE LEARNING OUTCOMES (CLOs)**

S. No. |
CLOs |
PLO |
Taxonomy |

1 | Describe formation of system of linear equations and vector calculus to explain physical situations | PLO-1 |
Coginitive |

2 | Apply appropriate methods to solve system of linear equations in relevant engineering problems | PLO-2 | Coginitive Level 3* |

3 | Use of vector calculus in relevant engineering problems | PLO-2 | Coginitive Level 3* |

**COURSE CONTENT**

Linearity and linear dependence of vectors basis dimension of a vector space, field matrix and type of matrices (singular. non- singular, symmetric, non- symmetric, upper, lower, diagonal tri-diagonal matrix), Rank of a matrix using row operations and special method, echelon and reduced echelon forms of a matrix, determination of consistency of a system of linear equation using rank, transitions matrix, basic concept of tensors, eigen value and eigen vectors of a matrix, Diagonalization, Cayley-Hamilton theorem. Applications of linear algebra in Engineering.__Linear Algebra:__Geometric representation of vector, norm of vector, Euclidean inner product, projections and orthogonal projections, Euclidean n spaces n properties Cauchy-Schwarz inequality, Euclidean transformations, apply geometric transfom 1 ations to plane figure, composition or transformations.__Euclidean Spaces and Transformation:__Define a stationary point of a function of several variables, define local maximum and saddle point for a function of two variables the stationary points of a several variables, obtain higher partial derivatives of simple functions of two or more variables, iterated integrals, double and triple integrations with applications (area, centroid, moment of inertia, surface area, and volume, use multiple integrals in solutions of engineering problems.**Advance Calculus:**Vector differential operator, directional derivative, gradient, divergence, curl of a vector field, and Laplacian operators with applications. (Solenoid, conservative, etc.). Vector Integrations; Evaluate line integrals along simple paths, apply line integrals to calculate work done, apply Green's theorem in the plane to simple examples, evaluate surface integrals over simple surface, use the Jacobean to transform a problem a new co-ordinate system, apply Gauss' divergence theorem to simple problems, apply Stokes theorem to simple examples.**Vector Calculus:**

**RECOMMENDED BOOKS**

*(01) Elementary Linear Algebra by Howard Anton*

*(02) Calculus and Analytical Geometry by Howard Anton*

*(03) Advance Engineering Mathematics by Erwin Kreyszig*

*(04) Elementary Linear Algebra by Bernaid Kolman*

*For details of Taxonomy Levels **CLICK HERE!**