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Course Contents
Complex Numbers: Basic Operations, Graphical Representations, Polar and Exponential Forms of Complex Numbers, De’Moivre’s Theorem with Applications.
Functions: Hyperbolic Functions and their Graphical representation, Hyperbolic and Trigonometric identities and their relationship, Exponential Functions.
Differentiation: Differentiation and Successive Differentiation and its Application to Rate, Speed and Acceleration, Leibritze’s Theorem and its Applications, Equations of Tangents and Normals, Curvature, Radius and Centre of Curvature, Maxima and Minima of Function of one Variable and its Applications, Convexity and Concavity, Points of Inflexion, Concept of Infinite Series, Taylor’s and Mclaurin’s Series and Expansion of Functions, Errors and Approximations and Limiting Values of Functions.
Partial Differentiation: Partial Differential Coefficient and Chain Rule, Partial Differentiation of an Implicit Function, Total Differential, Euler’s Theorem, Applications to Small Errors and Approximations, Statement of Taylor’s Theorem of Two Independent Variable and its Applications.
Integral Calculus: Standard Integrals, Function of a Linear Function, Integration by Substitution, by Partial Fractions and by Parts, Integration of Trigonometric Functions, Definite Integrals and their Properties and Reduction Formulae, Curve Tracing in Rectangular and Polar Coordinates.
Integration Applications: Volumes of Solids Of Revolution, Centroid of a Plane Figure, Centre of Gravity of a Solid of Revolution, Lengths of Curves, Surface Revolution, Rules of Pappus, Moment of Inertia, Radius of Gyration, Parallel Axes Theorem, Perpendicular Axes Theorem, Second Moment of Area, Composite Figures, Centres of Pressure and Depth of Centre of Pressure.
Analytical Solid Geometry: Rectangular Co-ordinate Systems in Three Dimensions, Direction Cosines, Plane (Straight Line) and Sphere.
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