11thMat-3 Course Topics
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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 |
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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. |
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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.
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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), |
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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 |
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