## MySkill Academy |

11thMat-3 Course Topics

Matrices - definition, concept and types of matrices,operations of transpose, scalar multiplication, multiplying a row or column by a number, adding two rows/columns,reducing a matrix into triangular and echelon form | addition and multiplication of matrices, solving simultaneous linear equations by Gaussian Elimination Method; Determinants - definition of a determinant and its evaluations | properties of determinants, using properties of determinants to evaluate the value, product of determinants, determinant of a square matrix, singular and non-singular matrices | |

Vectors –I | Scalars and Vector, Concept of scalars and vectors, Magnitude and direction of a general vector, fre vectors, localized vectors, zero vector, unit vector, negative of a vector, algebra of vectors, resolution of a vector, vector Arithmetic in space (3D) using i,j,k direction ratios and direction cosines | Vector Algebra-equality of vectors, collinear vectors, co-planar vectors, co-initial vectors , like vectors, unlike vectors, triangle law, parallelogram law, Polygon law, Applications of Vector Algebra-position vector of a point, distinction between position vectors and free vectors, section formulae, problems | Product of two vectors-angle between two vectors, definition of dot product , geometrical meaning, properties, definition of cross product, geometrical meaning, properties, applications to geometry, trigonometry and physica. |

Unit 9 : Limits,Continuity and Differentiability | Limits - approximations and errors, intuitive understanding of limit as an extension of approximation,Left hand limits and Right hand limits, definition of Limit,properties of limit, Limit theorems, Standard limits | Evaluation of limits; Continuity - graphical meaning of continuity of a function, visual identification of continuity and discontinuity, formal definition of continuity , examples, points of discontinuity, kinds of discontinuity, algebra of continuous functions, composite function theorem, standard problems | Slope as Limits - finding the slope of straight lines and curves, definition of a derivative as limit, evaluation of simple derivatives; Differentiability - graphical understanding of differentiability and nondifferentiability, formal definition of differentiability and examples, relation between continuity and differentiability,formal definition of differentiability and examples, relation between continuity and diffentiability , evlauaion of derivatives using first principle, properties of derivatives, derivatives as a rate of change, slope of a straight line. |

Unit 10 : Differential Calculus | Methods of differentiation - differentiation formulae:addition, product, quotient rules, derivative of composite functions, power functions, trigonometric functions, | derivative of implicit functions, parametric differentiation, meaning of second, third and higher order derivatives (with problems restricted to second order), | derivative of implicit functions, parametric differentiation, meaning of second, third and higher order derivatives (with problems restricted to second order), |

Unit 11 : Integral Calculus | Indefinite integral as Anti-derivative - integration as antiderivative, properties of integrals and integrals of standard functions and also functions of the form | Methods of Integration - properties of integration, indefinite integrals: decomposition, substitution, partial fractions and integration by parts methods |

11thMat-3 Course Plan