Class XII : Mathematics Lecture Plan
|Lecture Plan : Mathematics|
|S.N.||Name of Chapter||No. of Lectures|
(Lec. Duration : 1hr 45min)
|3.||Inverse Trigonometric Function||02|
|4.||Relation & Function||07|
|6.||Continuity & Differentiability||03|
|8.||Derivative as a Rate Measurer & Tangents, Normals||03|
|10.||Monotonicity, Maxima & Minima||05|
|13.||Application of the Integrals||03|
|Total : ||67|
1. Matrices :
- L1 = Algebra of matrices, Transpose of a matrix, symmetric & skew symmetric matrix, properties of Transpose, symmetric and skew symmetric matrices. Trace of a matrices, types of matrices.
- L2 = Addition, multiplication, adjoint & Inverse of a square matrix, properties of adjoint and inverse matrix. Concept of elementary row and column operation.
- L3 = Rank of a matrix, echlon form of a matrix. Consistency, inconsistency and solution of non-Homogeneous and homogeneous system of equations by (i) inverse of a matrix (ii) rank (echlon form).
2. Determinants :
- L4 = Definition, Minors & cofactors, properties of determinants. Evaluation of determinants using factor theorem. Product of two determinants. Application of determinants to coordinate geometry.
- L5 = Solution of system of equation by Cramer’s Rule & Test of consistency. Differentiation & Integration of determinants.
3. Inverse Trigonometric Function :
- L6 = Definition of inverse trigonometric functions, principal value, graphs of inverse trigonometric functions, Formulae for sum, difference of inverse trigonometric function. Properties of inverse trigonometric functions.
- L7 = Problem discussion.
4. Relation & Function :
- L8 = Relation, types of relations: empty, universal, symmetric, transitive & equivalence relation.
- L9 = Graphical Transformation. Domain & Range, Types of functions (Polynomial, Algebraic, Modulus, Signum, Logarithmic, Exponential, Greatest Integer Function.
- L10 = Classification of functions. (One-one (injective), many-one, onto (surjective), into function). Composite function, properties of composite functions Composition of uniformly & non-uniformly defined function.
- L11 = Problem discussion.
- L12 = Even and Odd function, periodic function. Inverse of a function, Properties of Inverse Function. Equal or identical functions.
- L13 = Functional Equation & Problem discussion.
- L14 = Problem Discussion.
5. Limit :
- L15 = Indeterminate forms. L'Hospital's Rule. Expansion method, sandwich theorem.
- L16 = Newton - Leibnitz's formula for Differentiation (DUIS), Limit of a sum by definite integral.
6. Continuity & Differentiability :
- L17 = Continuity, reasons of discontinuity, Types of Discontinuity, Continuity in an interval [a,b]. Continuity of composite function, Intermediate value theorem, Some continuous and discontinuous functions.
- L18 = Differentiability (RHD & LHD), Differentiability in open & closed interval. Algebra of differentiability.
- L19 = Problem Discussion.
7. Differentiation :
- L20 = Derivative of composite function, chain rule, derivatives of inverse trigonometric function, Differentiation by using trigonometrical substitutions. derivatives of implicit function.
- L21 = Derivatives of exponential & logarithmic function. Differentiation of infinite series. Derivatives of function in parametric forms, Differentiation of a function w.r.t. another function, Differentiation of determinants. Second order derivatives.
- L22 = Rolle's & Lagrange's, Mean value theorem & their application.
- L23 = Problem discussion.
8. Derivative as a Rate Measurer & Tangents, Normals :
- L24 = Derivative as Rate of change.
- L25 = Slope of the tangent and Normal, Equation of tangent and Normal. Angle of intersection of two curves. Length of the tangent, sub tangent, normal and subnormal.
- L26 = Problem discussion.
9. Approximation :
- L27 = Error & Approximation.
10. Monotonicity, Maxima & Minima :
- L28 = Monotonic Increasing & Decreasing, Method of testing monotonicity.
- L29 = Critical points, Comparison of functions using calculus.
- L30 = Concept of Local & Global Maxima / Minima. First & Second Derivative test with words problem.
- L31 = Maxima & minima in discontinuous functions. Point of inflection.
- L32 = Problem Discussion.
11. Indefinite Integrals :
- L33 = Integration of a function, Basic integration Formulae, Integration by substitution.
- L34 = Integration by partial fractions & by parts, integrals of the form ,
- L35 = Integration of the form , , , , .
- L36 = Integration of Trigonometric functions and , and where k is constant.
- L37 = Integration of and some particular Integrals.
- L38 = Problem discussion.
- L39 = Problem discussion.
12. Definite Integrals :
- L40 = Basic Properties of Definite integral & evaluation of definite integrals.
- L41 = Definite integral as a limit of a sum, Periodic Property.
- L42 = Newton-Leibnitz’s formula for definite integral, Maxima/Minima value of definite integral. Definite integral dependent on Parameter,
- L43 = (Walli’s formula). Gamame & Reduction formula.
- L44 = Problem discussion.
- L45 = Problem discussion.
13. Application of the Integrals :
- L46 = Simple tracing of curves like, lines, circles, parabola, Ellipse, Cubic, Trigionometric, Inverse, Trigonometric curves & Exponential & Logarithmic Curves and some more curves which occur frequently in standard forms.
- L47 = Concept of area bounded by a curve and Area between two curves.
- L48 = Problem discussion.
14. Differential Equation :
- L49 = Definition, order & degree of differential Equation. Formation of different equation whose general solution is given.
- L50 = Solution of Differential Equation, By method of separation of variables, Homogeneous equation of first order & first degree.
- L51 = Exact differential equation, Linear Differential eqution. Bernoullie’s diff equation.
- L52 = Application of differential equation: Rate of disintegration, Orthogonal trajectory, electricity, Heat transfer etc.
- L53 = Problem discussion.
15. Vector :
- L54 = Vectors & Scalars, magnitude & direction, Direction cosines & direction ratios of a vector. Types of Vectors. Postion vector of a point, components of a vector, addition of vectors.
- L55 = Multiplication of a vector by a scalar, postition vector of a point dividing a line segment in the given ratio. Scalar product, cross product.
- L56 = Projection of a vector on a line, scalar & vector Product of 3-vectors.
16. 3D :
- L57 = Direction cosines and direction ratios of a line joining two points; Cartesian & vector equation of line, Angle between two lines. Skew lines, Shortesst distance between the lines,Condition for coplanarity.
- L58 = Problem discussion.
- L59 = Concept of plane, Equation of plane in vector & Cartesian form. angle between two planes. Angle between line & plane.
- L60 = Distance of a plane from a point, Distance between parallel planes.
- L61 = Problem discussion.
17. Probability :
- L62 = Conditional probability, Multiplication theorem on probability, Independent events.
- L63 = Total theorem, Baye's theorem.
- L64 = Random variable & probability Distribution, Mean, Variance of random variable, Bernoulli's Trials & Binomial Distribution.
- L65 = Problem Discussion.
- L66 = Problem Discussion.
18. L.P.P. :
- L67 = Terminology such as constraints, objective function, optimization, Different types of L.P. problem, Mathematical formulation of L.P. problems, Graphical method of solution for problem in two variables, feasible and infeasible region and solution.(Upto 3-non-trial constant).