Syllabus for MATH102 Mathematics Foundation Module III
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Taylor polynomials and Taylor series, Taylor's Theorem
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 (4 lectures)
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Ordinary Differential equations. Separation of variables. Integral 
curves. The integrating factor method for linear first order 
differential equations. Reduction to separale form for homogeneous 
equations. Initial conditions. Linear second order ODE's with 
constant coefficients. Particular solutions  and complementary 
functions. Simple harmonic motion.
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 (8 lectures)
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Functions of several variables. Domain, range, limits, continuity. 
Partial derivatives. Linearisation. The chain rule, implicit 
differentiation. Directional derivatives, gradients of functions, 
tangent planes. Maxima, minima, saddles for functions of two variables. 
Constrained extrema. Lagrange multipliers. Taylor series in several 
variables.
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(15 lectures)
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Double integrals over reions in the plane. Change of order of 
integration. Area. 
Centroid and centre of mass of a 2-dimensional body. Change of 
variable. Jacobians. Double integration in polar coordinates.
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 (6 lectures)