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ADDITIONAL MATHEMATICS – I

Semester :  III

Course Code : 18MATDIP31

CIE Marks : 40                       SEE Marks : 60

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ADDITIONAL MATHEMATICS – I

SYLLABUS

Module-1

Complex Trigonometry: Complex Numbers: Definitions and properties. Modulus and amplitude of a complex number, Argand’s diagram, De-Moivre’s theorem (without proof).
Vector Algebra: Scalar and vectors. Addition and subtraction and multiplication of vectors- Dot and Cross products, problems. 

Module-2

Differential Calculus: Review of successive differentiation-illustrative examples. Maclaurin’s series expansions-Illustrative examples. Partial Differentiation: Euler’s theorem-problems on first order derivatives only. Total derivatives-differentiation of composite functions. Jacobians of order two-Problems.

Module-3

Vector Differentiation: Differentiation of vector functions. Velocity and acceleration of a particle moving on a space curve. Scalar and vector point functions. Gradient, Divergence, Curl-simple problems. Solenoidal and irrotational vector fields-Problems. 

Module-4

Integral Calculus: Review of elementary integral calculus. Reduction formulae for sinnx, cosnx (with proof) and sinmx cosnx (without proof) and evaluation of these with standard limits-Examples. Double and triple integrals-Simple examples. 

Module-5

Ordinary differential equations (ODE’s): Introduction-solutions of the first order and first-degree differential equations: exact, linear differential equations. Equations are reducible to exact and Bernoulli’s equation.