#49 Introduction of Complex Number | Applied Maths 1st all India polytechnic |

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Syllabus:-
1. Algebra -I
1.1 Series : AP and GP; Sum, nth term, Mean
1.2 Binomial theorem for positive, negative and fractional index (without proof).
Application of Binomial theorem.
1.3 Determinants : Elementary properties of determinant of order 2 and 3,
Multiplication system of algebraic equation, Consistency of equation,
Crammer's rule

2. Algebra- II
2.1 Vector algebra : Dot and Cross product, Scaler and vector triple product.
2.2 Complex number.
Complex numbers, Representation, Modulus and amplitude Demoivre
theorem, its application in solving algebraic equations, Mod. function
and its properties..

3. Trigonometry
3.1 Relation between sides and angles of a triangle : Statement of various formulae
showing relationship between sides and angle of a triangle.
3.2 Inverse circular functions: Simple case only

4. Differential Calculus - I
4.1 Functions, limits, continuity, - functions and their graphs, range and domain,
elementary methods of finding limits (right and left), elementary test for
continuity and differentiability.
4.2 Methods of finding derivative, Trigonometric functions, exponential function,
Function of a function, Logaritimic differentiation, Differentiation of Inverse
trigonometric function, Differentiation of implicit functions.

5. Differential Calculus - II
5.1 Higher order derivatives, Leibnitz theorem (without proof). Simple
applications.
5.2 Application - Finding Tangents, Normal, Points of Maxima/Minima,
Increasing/Decreasing functions, Rate, Measure, velocity, Acceleration,
Errors and approximation.

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