Mathematics-I
Mathematics-I
Lectures : Monday and Friday at 12:00 noon.
Lab: Wednesday at 2:00 PM
Office Hours : Tuesday at 12:00 noon
Minor Examination - 25%
Major Examination - 45%
Quizzes - 20% (Best Two will be considered)
Lab performance - 10%
A student is expected to have full attendance in the course unless student takes leave of absence for valid medical or bonafide reasons. In any case, at least 75% attendance in the course is mandatory.
Objectives
Learning Outcomes
Contents
Review of Set Theory : Sets and Set operations, Finite and infinite sets, Power set, Partition of a set, Algebra of sets, Cardinality of a set, Countable and uncountable sets.Relations : Equivalence relation, Equivalence classes and partitions, Partial order relation, Poset, Linear order relation, Axioms of choice, Zorn’s lemma.Functions : Injective, Surjective, and Invertible functions, composition of functions, relation between composition of functions and various set theoretic operations. Two Dimensional Geometry : Review of Conic Sections in 2D, General equation of conic, Tangent, Normal, Chord of contact, Diameter, Special properties of Parabola, Ellipse and Hyperbola.Three Dimensional Geometry : Review of lines and planes in 3D, Change of axes, Shift of origin, Rotation of axes, Sphere, Section of a sphere by a plane, Sphere through a given circle. Intersection of a line and sphere, tangent line, tangent plane, Angle of intersection of two spheres and condition of orthogonality, Equations of ellipsoid, hyperboloid, paraboloid in the standard form, Tangent plane, and Normal. Polar Coordinates : Polar equations of straight line, circle and conics. Polar equation of Chord of contact, Tangent, and Normal.Calculus : Epsilon-Delta definition of the limit of a function, Basic properties of limits, Continuous functions and classification of discontinuities, Differentiability, Applications of Derivatives, Integration of a function.Books