COURSE SCHEDULE

Week 01: Introduction To Subject: "Calculus and Analytic Geometry", historical background, Applications of subject in engineering.

Week 02: Complex numbers, polar form of complex numbers, exponential form, D.M Theorem and its applications.

Week 03: Introduction to 2-D coordinate system, Simple Cartesian curves, Functions and graphs, one to one function, onto function, even and odd function, symmetrical properties, curve tracing, shifting of a graph, scaling and reflection of graph.

Week 04: Introduction to Limits of functions, basic definition of limit of a function, calculating limit by definition, finite limit at a finite point, one sided limits; Right hand limit, Left hand limit, uniqueness of limit.

Week 05: Theorems on limit, Infinite limit at a finite point, limits at infinity, limit of a sequence, limit of Rational functions, some useful limits.

Week 06: Introduction to Continuity of Functions, Limit implies continuity, Geometrical significance of continuity at a point, continuity of combinations of functions, Properties of continuous functions.

Week 07: Differentiation of Functions, Introduction, Definition and notation, graphical interpretation of derivative, general Theorems on derivative.

Week 08: Derivative of trigonometric and Inverse trigono... functions, Logarithmic and exponential functions, Hyperbolic and Inverse hyper... functions. Implicit differentiation, Chain Rule.

Week 09: Derivative as a Slope of Tangent to a curve, as Rate of Change, Applications to Tangent and Normal. Properties of the first and second order derivative, higher order derivatives.

Week 10: Differentials and approximation, Linearization,

Week 11: Maxima/Minima of a Function, Definitions to Global and local extrema, How to calculate Local extrema; By definition, First derivative test, 2nd derivative test, how to find out Absolute extrema.

Week 12: Taylor and Maclaurin Expansions and their convergence.

Week 13: Integral as Anti-derivative, Indefinite Integration of simple functions, Methods of Integration: Integration by substitution, by Parts, by partial Fraction, Integration of Rational and Irrational functions.

Week 14: Definite Integral, Properties of definite Integral, definite Integral as Limit of a Sum, Fundamental Theorem of Calculus, Applications to Area, Arc length, Volume and Surface of Revolution.

Week 15: Improper Integrals, definition, All types of Improper Integrals with solution methods.

Week 16: Presentations