BSc Maths - 3 Online MathsTuitions
for IIT - JAM Coaching
Live classes are scheduled on 23 July 2015 at 6:15 am
Part-A
Vector Space
Learnig Objectives
- Binary Operations , vectors ,vector addition and scalar multiplication
- Definition of vector space and Subspaces
- Linear combination , span , LD , LI and basis
- Dimension of vector space , dimension theorem
- Linear transformations and its matrix representation
- Sylvester's law
- Eigen values and vectors , caylay-hamilton theorem , diagonalization
- Inner product , euclidean and unitary spaces , norm of a vector , schwartz's inequality
- orthogonality , orthonormal sets and gram-schmidt process
Syllabus
Vectoer spaces - general properties . Subspaces , linear combination ,spanning , basis , finite dimensional vector space , linear transformations , rank-nullity theorems , matrix representation of linear transformations and its characteristics sylvester's law of nullity,characteristic vlues and vectors , caylay - hamilton theorem ,diagonalization.Inner product spaces ,euclidean and unitary spaces , norm , schwartz's inequality , orthogonality, orthonormal set and gram-schmidt orthogonalization process .
Learning out comes
Student will
- Learn how the binary operations will work on vector spaces , when does the non empty subset of a vector space becomes the subspace of the vector space .
- learn about linear combinations and it spans the vector space and form the basis for vector space , identifying the dimension of the vector space .
- Study about the dimension theorem proof and will verify and get the dimension of the vector spaces .
- learn about linear transformations - properties and characterisrics , matrix representations .Sylvester's law of nullity .
- learn about eigen values and eigen vectors - properties and charecterics eigen values and eigen vectors and caylay hamilton theorem - its verification and finding Inverse of A and powers of A .
- Study and learn about the norm ( length) of the vectors , ineer product spaces , euclidean and unitary spaces -their properties and characteristics -schwartz's inequality .
- Orthogonalization of vectors and orthionormal sets and gran-schmidt's process of orthogonalization .
Part - B Multiple Integrals & Vector Calculus
Learning Objectives :
- Line and multiple integrals , limit form and existance .
- Double integral and defining over the region R , change of order of integration and change of variables , double integrals in polar coordinates .
- Triple integrals and defining over the volume V.
- Applications of double and triple integrals .
- Vector calculus ( differentiation and integration ).
- Vector differential operator , Gradient ,Divergence and Curl and their applications , vector identities .
- Vector integration - Line , Surface and Volume integrals
- Vector integral theorems - Green's , Gauss and Stoke's theorem and their verifications .
Syllabus
Introduction to multiple integrals : concept of plane and curve ,line integrals , sufficient condition for existance of line integrals , The area of a subset of R^2 ,Calculation of double integrals , jordan curve , area , change of order integration and change of variables , lengths of curve , surface areas , integral expression for the length of a curve .
Vector Calculus ( Differentiation and Integration ) :Ordinary derivatives of vectors , space curves , continuity and differentiability . Gradeient , Divergence and curl operators - identities .Vector integral theorems , Green's , Gauss and Stoke's theorems and their verifications .
Learning out comes:
Student will
- Learn about the concept and how to define the double integrals over the region R .
- How to evaluate the double integrals by changing the order of integration and by change of variable .
- Learn to calculate the double integrals in polar coordinates and Areas enclosed by the closed curves .
- How to evaluate the triple integrals over the volumes .
- Learn about the vector differentiation and integration and vector differential operator, Gradient ,Divergence and Curl and vector identities
- Vector integration : Evaluation of Line integrals along the curves , surface interals over the surfaces and volume integrals over the volumes .
- vector integral theorems - Green's , Gauss and Stoke's theorems and their verifications.
Great benifits from BijMathIQ - Online Maths Tuitions
- Get tutoring from well qualified and experianced faculty .
- Get unlimited access to live sessions recording videos at free .
- Clear explanation of concepts using various mathematical tools ( wherever required )
- Covers maximum number of examples
- take online quiz tests ( 10+ with explanation video for each test ) at free
- Access self pace tuitions (30 + videos )
- Handwritten material provided
- PPT's
- Get full support from BijMathIQ - Online Maths Tuitions .
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