MA8151 – NOTES & QP
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MA8151 – SYLLABUS
UNIT I DIFFERENTIAL CALCULUS
Representation of functions — Limit of a function — Continuity — Derivatives — Differentiation rules — Maxima and Minima of functions of one variable.
UNIT II FUNCTIONS OF SEVERAL VARIABLES
Partial differentiation — Homogeneous functions and Euler?s theorem — Total derivative — Change of variables — Jacobians — Partial differentiation of implicit functions — Taylor?s series for functions of two variables — Maxima and minima of functions of two variables — Lagrange?s method of undetermined multipliers.
UNIT III INTEGRAL CALCULUS
Definite and Indefinite integrals — Substitution rule — Techniques of Integration — Integration by parts, Trigonometric integrals, Trigonometric substitutions, Integration of rational functions by partial fraction, Integration of irrational functions — Improper integrals.
UNIT IV MULTIPLE INTEGRALS
Double integrals — Change of order of integration — Double integrals in polar coordinates — Area enclosed by plane curves — Triple integrals — Volume of solids — Change of variables in double and triple integrals.
UNIT V DIFFERENTIAL EQUATIONS
Higher order linear differential equations with constant coefficients — Method of variation of parameters — Homogenous equation of Euler?s and Legendre?s type — System of simultaneous linear differential equations with constant coefficients — Method of undetermined coefficients.