Syllabus & Course Curriculam
Course Type: ME-2
Semester: 2
Course Code: BMTMMEB12T
Course Title: Algebra and Analytical Geometry in 2D & 3D
(L-P-Tu): 4-0-0
Credit: 4
Practical/Theory: Theory
Course Objective: To be done.
Learning Outcome: Course Outcomes (CO): The whole course will have the following outcomes: Upon successful completion, the students will be able to CO1: learn concepts of complex numbers, De’Movire’s theorem and its application, theory of equations CO2: Group theory is
Syllabus:
Complex Numbers: De-Moivre’s theorem (Statement only) and its applications, Polynomial equations with real coefficient, Multiple roots, Descartes’ rule of sign, Relation between roots and coefficients, Transformation of equations, Reciprocal equation, solution of cubic equations-Cardan’s method
Inverse of a matrix, Rank of a matrix, Solution of system of m-linear equations with n- variables by matrix methods, Eigen values and Eigen vector of a matrix, Cayley-Hamilton theorem (Statement only) and its use
Group: Definition and examples, Abelian group, Subgroup,
Ring and Field: Definition and examples
Analytical Geometry in 2D:
Transformation of Rectangular axes: Translation, Rotation and Rigid body motion, Theory of Invariants, General equation of second degree in two variables, reduction into canonical forms and classification of conics
Pair of straight lines: Condition that the general equation of second degree in two variables may represent two straight lines, Point of intersection, Angle between pair of lines, Angle bisectors
Polar co-ordinate system: polar equation of Straight lines, circles.
Analytical Geometry in 3D:
Plane, Straight line,
Sphere: General Equation, Circle, Sphere through circle
Basic Features
Undergraduate degree programmes of either 3 or 4-year duration, with multiple entry and exit points and re-entry options, with appropriate certifications such as:
Note: The eligibility condition of doing the UG degree (Honours with Research) is- minimum75% marks to be obtained in the first six semesters.
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