Bridge course for Biology Students
Algebra: Functions, mapping, one-one function or injection, onto function or surjection, bijection, identity function, constant function, inverse function, composite function, real valued function.
Quadratic expressions in one variable, extreme values change in sign and magnitude, quadratic expressions in two variables, summation series involving A.p., G.P., H.P. expression of npr and ncr and their definitions, fundamentals of matrices.
Trigonometry: Fundamentals of trigonometry, general definition of trigonometric ratios, sign of the trigonometric ratios as the angle varies from 0 to 2x. trigonometric ratios of the angles of 0,90 - 0, 190, 270, 0 in terms of those of 0. Graphs and periodicity of trignometric ratios. Inverse trigonometric functions. Hyperbolic functions. Expressions for sin2x, cos2x, tan2x in terms of those of x and y. Inverse hyperbolic functions.
Co-ordinate Geometry: Translation and rotation of axis, locus and its equation, straight-line point-slope form, slope-intercept form, perpendicular form, two-point form, intercept form, symmetric form, the equation to a straight line. The straight line and the equation a+bx = 0. Families of lines (one parameter), point of intersection of two straight lines, angle of intersection of two straight lines, conditions of parallelism and perpendicularity of lines. Pair of straight lines, homogenous equation of the second degree in X and Y. Angle between the lines and the combined equation of the bisectors of the angles between the lines respectively by the above equation. General equation second degree in X and Y, point of intersection and the angle between the lines.
Calculus: Notation of limit and continuity of a function, derivatives of composite, implicit, parametric, inverse circular, hyperbolic functions, logarithemic differentiation, derivative of a function with reference to another function, application of differentiation, partial differentiation, computation of the first and second order partial derivatives.
Integration: Integration as the inverse processes of differentiation, indefinite and definite integral, standard integral covering algebraic, trigonometric exponential and hyperbolic functions. Measures of integration, substitution methods, integration by parts, properties of definite integral and its equations, trapezoidal and simpson's rules for approximation integration area under the curves, formation of differential equations.
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