PUC 1st Year Sem-2 Mathematics Syllabus - Course Learning Objectives:

1. To study the Trigonometric Relations and the Solutions of Trigonometric Equations.

2. To study the basic concepts of Complex numbers, De Moviers Theorem, Quadratic equations,

expressions and their solutions, maximum and minimum values of quadratic equations.

3. To study the concept of the limit and formal definition of the limit, and discuss of continuity of

various functions.

4. To study the concept of differentiability of a given function on a given interval and higher order

derivatives.

5. To study the chain rule in differentiation and to find the derivative implicitly defined functions.

6. To study the strategy of graphing a curve on its domain and optimize a given function.

PUC 1st Year Sem-2 Mathematics Syllabus

Course Content:

Unit- I (12 Hours)

TRIGONOMETRIC RELATIONS: Transformation Formulas, Conditional Trigonometric Identities, Trigonometric Equations, Relation between the Angles and Sides of a triangle, Properties of triangles.

Unit – II (12 Hours)

COMPLEX NUMBERS & QUADRATIC EQUATIONS: Concept of Complex Numbers, Algebra of Complex Numbers, Complex Plane, Polar Form, De Moivre‟s Theorem, Quadratic equations in one variable, Equations reducible to quadratic equations, Forming quadratic equations with given roots and quadratic expressions.

PUC 1st Year Sem-2 Mathematics Syllabus

Unit- III (16 Hours)

LIMITS AND CONTINUITY: Rates of change, Concept of a limit, Rules for finding limit, Formal definition of limit, Extension of the limit concept, Infinite limits, some special limits, Continuity at a point, Rules of continuity, Continuity on intervals, Tangent lines.

Unit - IV (10 Hours)

DIFFERENTIATION: The Derivative of a function, Derivatives and continuity, Differentiation rules – Sums and Differences, Differentiation rules – Products and Quotients, Second and higher order derivatives, Derivatives of trigonometric functions, Continuity of trigonometric functions.

PUC 1st Year Sem-2 Mathematics Syllabus

Unit - V (09Hours) CHAIN RULE AND IMPLICIT DIFFERENTIATION: The chain rule, Differentiation formulas that include the chain rule, Implicit differentiation, Tangent and normal lines, Rational powers of differentiable functions, Related rates of change.

PUC 1st Year Sem-2 Mathematics Syllabus

Unit - VI (16 Hours)

APPLICATIONS OF DERIVATIVES: Extreme values of functions, Finding extrema, Rolle's Theorem, Mean value Theorem, Increasing and Decreasing functions, The first Derivative test, Curve Sketching, The second Derivative Test, Strategy for Graphing, Asymptotes and dominant terms, Optimization, Differentials.

PUC 1st Year Sem-2 Mathematics Syllabus

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