# MA8151 – Engineering Mathematics – I – Regulation 2017 Syllabus

## 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.

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