MA8151 – ENGINEERING MATHEMATICS – I SYLLABUS (REGULATION 2017) AFFILIATED TO ANNA UNIVERSITY (SEMESTER 1)

UNIT I DIFFERENTIAL CALCULUS 

Representation of functions – Limit of a function – Continuity – Derivatives – Differentiation rules. Maxima and Minima of functions of one variable (ma8151).

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.

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