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Mathematics Paper II-Calculus and Differential Equations
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Mathematics Paper II-Calculus and Differential Equations
Topic outline
Lecture 1-Linear Differential Equation
Lecture 2-Differential Equation Reducible to Linear Form
Lecture 13-Asymptotes
Lecture 22-CENTRE OF CURVATURE
Lecture 23-Chord of Curvature
Lecture 19-CURVATURE PEDAL FORMULAE
Lecture 18-Curvature-Cartesian and Parametric Formulae
Lecture 17-Curvature-Definitions and Intrinsic Formula
Lecture 10-Examples on Leibnitz's theorem
EXPONENTIAL SINE AND COSINE FUNCTIONS
Lecture 9-Leibnitz's theorem Proof and Example
Lecture 11-Maclurin's Theorem Proof and examples
Lecture 16-Method of linear factors to find asymptotes
Lecture 25-MULTIPLES POINTS TYPES OF DOUBLE POINTS
Lecture 14-Oblique Asymptotes
Lecture 15-Parallel Oblique Asymptotes
Lecture 26-PROCEDURE FOR CARTESIAN CURVE TRACING
Lecture 21-RADIUS OF CURVATURE AT ORIGIN
Lecture 20-RADIUS OF CURVATURE POLAR FORM
Lecture 8-SUCCESSIVE DIFFERENTIATION II
Lecture 7-SUCCESSIVE DIFFERENTIATION-Applications of De-Moivre's Theorem
Lecture 6-Successive differentiation-Use of Partial Fraction
SUCCESSIVE DIFFERENTIATION
Lecture 12-Taylor's Theorem Proof and examples
Lecture 24-Test of Concavity, Convexity and Point of Inflexion
Lecture 34-Procedure for Polar Curve Tracing
Lecture 31-Tracing of Astroid
Lecture 32-Tracing of Infinite Damaru
Lecture 33-Tracing of Teardrop Curve
Lecture 30-Tracing of Witch of Agnesi
Lecture 5-Successive Differentiation (ax+b)^m special case
Lecture 29-Tracing of Cissoid of Diocles
Lecture 28-Tracing of Cubical Parabola
Lecture 35-Polar Curve Tracing
Lecture 38-Tracing of Folium of Descartes
Lecture 36-Tracing of Lemniscate of Bernoulli
Lecture 37-Tracing of n-Leaved Rose
Lecture 39-Sine and Cosine
Lecture 27-Tracing of Semi-cubical Parabola
Lecture 40- Reduction Formulae- Integration of nth power of tanx and cotx,
Lecture 41- Reduction Formulae for integration of nth power of secx a
Lecture 42- Reduction Formulae for integration of sin^mx cos^nx, n and m are pos
Lecture 43- Integration of sin^mxcos^nxfrom 0 to half Pi
Lecture 44-Reduction_formulae-Integration of xsin^nx and x^nsinmx
Lecture 45-Reduction formulae-Integration of e^axsin^nbx and x^ne^axsinbx
Lecture 46-Reduction Formulae for (x^2+a^2)^-n, (x^2+a^2)^n2, etc
Lecture 47- Quadrature- Cartesian Formula
Lecture 48-Quadrature- Polar Formula
Lecture 49-Rectification- Cartesian and Parametric Formulae
Lecture 50-Rectification- Polar Formulae
Lecture 51- Exact Differential Equations Recording
Lecture 52- Rules for Finding Integrating Factor-1, 2 and 3
Lecture 53-Rules 4 and 5 to find I.F. for Exact D.E.
Lecture 54-D.E. of I order and Higher Degree-Equation Solvable for p
Lecture 55-D.E. Solvable for y
Lecture 56-D.E. of I Order and Higher Degrees- DE Solvable for x-Recording
Lecture 57-D.E. of I Order and Higher Degrees- Clairaut's Equations and Singular Solution
Lecture 58-D.E. of I Order and Higher Degrees- Geomertical Meaning
Lecture 59- Orthogonal Trajectories-Cartesian Curves
Lecture 60- Orthogonal Trajectories-Polar Curves
Mathematics Paper II-Calculus and Differential Equations
Lecture 1-Linear Differential Equation
Lecture 2-Differential Equation Reducible to Linear Form
Lecture 13-Asymptotes
Lecture 22-CENTRE OF CURVATURE
Lecture 23-Chord of Curvature
Lecture 19-CURVATURE PEDAL FORMULAE
Lecture 18-Curvature-Cartesian and Parametric Formulae
Lecture 17-Curvature-Definitions and Intrinsic Formula
Lecture 10-Examples on Leibnitz's theorem
EXPONENTIAL SINE AND COSINE FUNCTIONS
Lecture 9-Leibnitz's theorem Proof and Example
Lecture 11-Maclurin's Theorem Proof and examples
Lecture 16-Method of linear factors to find asymptotes
Lecture 25-MULTIPLES POINTS TYPES OF DOUBLE POINTS
Lecture 14-Oblique Asymptotes
Lecture 15-Parallel Oblique Asymptotes
Lecture 26-PROCEDURE FOR CARTESIAN CURVE TRACING
Lecture 21-RADIUS OF CURVATURE AT ORIGIN
Lecture 20-RADIUS OF CURVATURE POLAR FORM
Lecture 8-SUCCESSIVE DIFFERENTIATION II
Lecture 7-SUCCESSIVE DIFFERENTIATION-Applications of De-Moivre's Theorem
Lecture 6-Successive differentiation-Use of Partial Fraction
SUCCESSIVE DIFFERENTIATION
Lecture 12-Taylor's Theorem Proof and examples
Lecture 24-Test of Concavity, Convexity and Point of Inflexion
Lecture 34-Procedure for Polar Curve Tracing
Lecture 31-Tracing of Astroid
Lecture 32-Tracing of Infinite Damaru
Lecture 33-Tracing of Teardrop Curve
Lecture 30-Tracing of Witch of Agnesi
Lecture 5-Successive Differentiation (ax+b)^m special case
Lecture 29-Tracing of Cissoid of Diocles
Lecture 28-Tracing of Cubical Parabola
Lecture 35-Polar Curve Tracing
Lecture 38-Tracing of Folium of Descartes
Lecture 36-Tracing of Lemniscate of Bernoulli
Lecture 37-Tracing of n-Leaved Rose
Lecture 39-Sine and Cosine
Lecture 27-Tracing of Semi-cubical Parabola
Lecture 40- Reduction Formulae- Integration of nth power of tanx and cotx,
Lecture 41- Reduction Formulae for integration of nth power of secx a
Lecture 42- Reduction Formulae for integration of sin^mx cos^nx, n and m are pos
Lecture 43- Integration of sin^mxcos^nxfrom 0 to half Pi
Lecture 44-Reduction_formulae-Integration of xsin^nx and x^nsinmx
Lecture 45-Reduction formulae-Integration of e^axsin^nbx and x^ne^axsinbx
Lecture 46-Reduction Formulae for (x^2+a^2)^-n, (x^2+a^2)^n2, etc
Lecture 47- Quadrature- Cartesian Formula
Lecture 48-Quadrature- Polar Formula
Lecture 49-Rectification- Cartesian and Parametric Formulae
Lecture 50-Rectification- Polar Formulae
Lecture 51- Exact Differential Equations Recording
Lecture 52- Rules for Finding Integrating Factor-1, 2 and 3
Lecture 53-Rules 4 and 5 to find I.F. for Exact D.E.
Lecture 54-D.E. of I order and Higher Degree-Equation Solvable for p
Lecture 55-D.E. Solvable for y
Lecture 56-D.E. of I Order and Higher Degrees- DE Solvable for x-Recording
Lecture 57-D.E. of I Order and Higher Degrees- Clairaut's Equations and Singular Solution
Lecture 58-D.E. of I Order and Higher Degrees- Geomertical Meaning
Lecture 59- Orthogonal Trajectories-Cartesian Curves
Lecture 60- Orthogonal Trajectories-Polar Curves
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