1. Sets, Relation and Function

1. Introduction to set
2. Subset and power set
3. Intersectoin of sets
4. Union of sets
5. Difference of sets
6. Complement of sets
7. Properties of Operations on Sets
8. Subsets Of Set Of Real Numbers . Intervals
9. Cardinal number of set
10. Cartesian Product Of Sets
11. Cartesian product and relation
12. Function. definition

2. Inequalities. Domain and Range of Elementary Functions

1. Linear inequalities in one variable
2. Values Of X^2 From Values Of X
3. Values Of Reciprocal Of X From Values Of X
4. Sign Scheme (Wavy Curve) Method For Solving Inequalities_ I
5. Sign Scheme (Wavy Curve) Method For Solving Inequalities_ II
6. Range Of Elementary Functions_ I
7. Range Of Elementary Functions_ II

3. Absolute value of Real Number

1. Absolute Value (Modulus) Of Real Number. Introduction
2. Properties Of Modulus Of Real Number
3. Inequalities Of Modulus Of Real Numbers
4. Modulus Of Any Expression
5. Modulus Of Sum Of Real Numbers

4. Logarithm

1. Exponential Function
2. Logarithm And Logarithmic Function
3. Properties Of Logarithm Part I
4. Properties Of Logarithm Part II
5. Logarithmic Equations
6. Logarithmic Inequalities

5. Theory of Equations

1. Polynomial Expression And Equation
2. Graph Of Polynomial Expression
3. Polynomial Equations Reducible To Quadratic Equation
4. Remainder And Factor Theorem
5. Identity
6. Important Points In Solving The Equation
7. Real And Non-Real Roots_ I
8. Real And Non-Real Roots_ II
9. Rational And Irrational Roots Of Quadratic Equation
10. Applications Of Discriminant
11. Relation Between Roots And Coefficients Of Quadratic Equation_ I
12. Relation Between Roots And Coefficients Of Quadratic Equation_ II
13. Relation Between Roots And Coefficients Of Quadratic Equation_ III
14. Polynomial Equations Of Higher Degree
15. One Common Root_ I
16. One Common Root_ II
17. Two Common Roots
18. Graph Of Quadratic Function
19. Graphical Analysis Of Quadratic Function. Theory
20. Graphical Analysis Of Quadratic Function Problems Discussion_ I
21. Graphical Analysis Of Quadratic Function Problems Discussion_ II
22. Location Of Roots Of Quadratic Equation. Theory
23. Location Of Roots Of Quadratic Equation. Problems Discussion

6. Complex Numbers

1. Imaginary Number
2. Complex Number Structure And Plogtting
3. Algebraic Operations On Complex Numbers
4. Properties Of Conjugate Of Complex Number
5. Equality Of Complex Numbers And Its Applications
6. Cube Roots Of Unity_Part I
7. Cube Roots Of Unity_Part II
8. Polar Form Of Complex Number _Theory
9. Polar Form Of Complex Number_Problems Discussion
10. Problems Based On Modulus And Argument Of Complex Number_Part I
11. Problems Based On Modulus And Argument Of Complex Number_Part II
12. Multiplication And Division Of Complex Numbers In Polar Form_Part I
13. Multiplication And Division Of Complex Numbers In Polar Form_Part II
14. Demoivres Theorem
15. Product Of Complex Number And Its Conjugate Equals The Square Of Modulus Of Complex Number
16. Problems Based On Unimodular Complex Number
17. Collinearity Of Two Non-Zero Complex Numbers And Origin
18. Inequalities Involing Complex Nummbers
19. Locus_Line Segement, Rays, Ellispe And Hyperbola
20. Equation Of Circle Using Modulus _Part I
21. Equation Of Circle Using Modulus _Part II
22. Locus Based On Argument Of Complex Number_Equation Of Ray
23. Angle Between Two Lines In Argand Plane
24. Rotation Formula_Part I
25. Rotation Formula_Part II
26. Equation Of Straight Line In Complex Numbrer
27. Nth Roots Of Unity_Theory
28. Nth Roots Of Unity_Problems Discussion

7. Progression and Series

1. Sequence and series
2. Arithmetic progression. Introduction
3. Arithmetic mean of two numbers
4. Selection of terms in AP
5. Properties of AP
6. Arithmetic means
7. Sum of A.P._ I
8. Sum of A.P._ II
9. Geometric Progression. Introduction
10. Geometric mean of two numbers
11. Selection of terms of G.P.
12. Properties of G.P.
13. Geometric means
14. Sum of terms of G.P._ I
15. Sum of terms of G.P._ II
16. Applications of sum of GP
17. Infinite G.P. and its sum
18. Harmonic Progression_ I
19. Harmonic Progression_ II
20. Harmonic Means
21. Relations between AM, GM and HM
22. Sum Of Series Using Sigma Notation Part I
23. Sum Of Series Using Sigma Notation Part II
24. Arithmetico-Geometric Progression
25. Multiple Sigma Of Multiple Variables
26. Sum Of Series By Method Of Cancellation Part I
27. Sum Of Series By Method Of Cancellation Part II

8. Permutation and Combination

1. Counting Principle_Part I
2. Counting Principle_Part II
3. Factorial Notation
4. Exponent Of Prime In Factorial
5. Permutation Formula
6. Permutations With Restrictions_Part I
7. Permutations With Restrictions_Part II
8. Permutations With Identical Objects
9. Combinations Formula
10. Properties Of Combinations Formula
11. Problems Based On Combinations_Part I
12. Problems Based On Combinations_ Part II
13. Combination And Arrangement
14. Problems Based On Chessboard
15. Selection From Objects Which Are Not All Distinct
16. Circular Permutations
17. All Possible Selection From Distinct Objects
18. All Possible Selection From Identical Objects
19. Divisors Of Natrual Number
20. Division And Distribution Of Distinct Objects_Unequal Fiixed Group
21. Division And Distribution Of Distinct Objects_Mix Of Equal And Unequal Fixed Groups
22. Distribution Of Distint Objects In Any Way
23. Distrbition Of Identical Objects_Theory
24. Distribution Of Identical Objects _Problems Discussion
25. Distribution Of Identical Objects_Applications
26. Principle Of Inclusion And Exclusion
27. Derangement
28. Multinomial Theorem

9. Binomial Theorem

1. Binomial Theorem_Introduction
2. Binomial Theorem Problems Discussion_Part I
3. Binomial Theorem Problems Discussion_Part II
4. Conjugate Binomials
5. Middle Term In Binomial Expansion
6. Finding Coefficient Of The Term In The Expansion_Part I
7. Finding Coefficient Of The Term In The Expansion_Part II
8. Finding Coefficient Of The Term In The Expansion_Part III
9. Greatest Term In Binomial Expansion
10. Applications Of Binomial Theorem_Part I
11. Applications Of Binomial Theorem_Part II
12. Multinomial Theorem
13. Sum Of Coefficients In Binomial Expansion
14. Binomial Theorem With Complex Numbers
15. Sum Of Coefficients In Any Expansion
16. Series Based On Binomial Coefficients_Part I
17. Series Based On Binomial Coefficients_Part II
18. Series Of Coefficients Resulting From Product Of Two Expansions_Part I
19. Series Of Coefficients Resulting From Product Of Two Expansions_Part II
20. Sum Of Special Series
21. Binomial Theorem For Any Index_Theory
22. Binomial Theorem For Any Index_Problems Discussion

10. Probability

1. Experiment And Sample Space
2. Event
3. Axiomatic Approach To Probability
4. Probability Based On Permutation And Combination Part I
5. Probability Based On Permutation And Combination Part II
6. Probability Based On Permutation And Combination Part III
7. Addition Theorem Of Probability

11. Statistics

1. Measures Of Dispersion Introduction
2. Measures Of Dispersion Of Ungrouped Data
3. Measures Of Dispersion Of Discrete Frequency Distribution
4. Measures Of Dispersion Of Continuous Frequency Distribution And Coefficient Of Variation

12. Mathematical Reasoning

1. Mathematical Reasoning Introduction
2. Compound Statement Using Logical Connective And
3. Logical Connective Or Logical Equivalence Distributive Property Of Basic Logical Connective
4. Tautology And Fallacy
5. Negation Of Compound Statement
6. Conditional Statement
7. Converse, Inverse, Contrapositive, And Bicondional Statement

1. Trigonometric functions

1. Trigonometric Ratios Of Acute Angles Part I
2. Trigonometric Ratios Of Acute Angles Part II
3. Problems Based On Trigonometric Identities
4. Degree And Radian Measure Of An Angle
5. Angle In Trigonometry
6. Trigonometric Ratios Of Angles Exceeding Right Angle
7. Trigonometric Ratios Of Allied Angles Theory
8. Trigonometric Ratios Of Allied Angles Problems Discussion
9. Graphs Of Sinx And Cos X
10. Graphs Of Secx, Cosecx, Tanx And Cotx
11. Range Of Functions Involving Trigonometric Functions

2. Trigonometric ratios and transformation formulas

1. Compound Angle Formulas Of Sine An Cosine Part I
2. Compound Angle Formulas Of Sine And Cosine Part II
3. Expression Acos X + Bsin X
4. Compound Angle Formulas Of Tangent
5. Transformation Formulas Product To Addition And Difference
6. Transformation Formulas Sum And Difference To Product
7. Trigonometric Ratios Of Multiple Angles Part I
8. Trigonometric Ratios Of Multiple Angles Part II
9. Trigonometric Ratios Of Multiple Angles Part III
10. Trigonometric Ratios Of Multiple Angles Part IV
11. Conditional Identities Cengage
12. Values Of Sine And Cosine For 18 Degrees And 36 Degrees
13. Important Results Using Trig. Ratios Of Multiple Angles
14. Sum Of Series In Sine And Cosine Having Angles In A.P.
15. Finding Range Of Expression Using Trigonometric Substitution
16. Trigonometric Inequalities In Triangle

3. Trigonometric Equations

1. Elementary Trigonometric Equations Part I
2. Elementary Trigonometric Equations Part II
3. Precautionary Things In Solving Trigonometric Equations
4. Trig. Equations Whose Solution Set Contain Quadrant Angles
5. General Solution Of The Equation Cos X = K
6. General Solution Of The Equation Sin X = K
7. General Solution Of The Equation A Cos X + B Sin X = C
8. General Solution Of The Equation Tan X = K
9. General Solution Of The Equation Square Of The Trig. Function Equals Constant
10. Solving Trig. Eq. Using Maximum And Minimum Values Of Functions
11. Graphical Approach To Solve Equations And Inequalities

4. Properties of Triangle

1. Properties Of Triangle And Solutions Of Triangle Introduction
2. Sine Rule Part I
3. Sine Rule Part II
4. Cosine Rule Part I
5. Cosine Rule Part II
6. Projection Rule
7. Tangent Rule And M-N Theorem
8. Half Angle Formulas
9. Area Of Triangle Part I
10. Area Of Triangle Part II
11. Relation Between Area And Inradius Of The Triangle
12. Angles And Lengths Associated With The Circumcenter Of The Triangle
13. Angles And Lengths Associated With The Incenter Of The Triangle Part I
14. Angles And Lengths Associated With The Incenter Of The Triangle Part II
15. Angles And Lengths Associated With The Incenter Of The Triangle Part III
16. Angles And Lengths Associated With The Orthocener Of The Triangle Part I
17. Angles And Lengths Associated With The Orthocener Of The Triangle Part II
18. Properties Of Medians And Centroid Of Triangle
19. Geometry Related To Excenters Of Triangle
20. Exradii And Excenters Of Triangle Problems Discussion
21. Regular Polygon

5. Height and Distance

1. Height And Distance Problems Based On Right Angled Triangle
2. Height And Distance Problems Based On Trig. Ratios Of Compound Angles And Multiple Angles
3. Height And Distance Problems Based On Sine And Cosine Rule

1. Coordinate System

1. Two Dimensional Coordinate System
2. Distance Formula
3. Shifting Of Origin Translation Of Axes
4. Rotation Of Axes
5. Section Formula Part I
6. Section Formula Part II
7. Area Of Polygon
8. Coordinates Of Centroid Of Triangle
9. Coordinates Of Circumcenter Of Triangle
10. Coordinates Of Orthocenter Of Triangle
11. Coordinates Of Incenter Of Triangle
12. Slope Of Line
13. Angle Between Two Lines
14. Equation Of Locus Of Point I
15. Equation Of Locus Of Point II
16. Equation Of Locus Of Point Part III
17. Equation Of Locus Of Point Part IV
18. Division Of Plane By Straight Line

2. Straight Lines    

1. Equation Of Straight Line In Different Forms
2. Equation Of Line_Problems Discussion_Part I
3. Equation Of Line_Problems Discussion_Part II
4. Equation Of Line_Problems Discussion_Part III
5. Equation Of Straight Line_Paramteric Form
6. Distance Of Point From The Line_Part I
7. Distance Of Point From The Line_Part II
8. Distance Between Parallel Lines
9. Positions Of Points W.R.T. Line On The Plane
10. Coordinates Of Image Of Point In The Line
11. Concurrency Of Three Lines
12. Equations Of Angle Bisectors_Part I
13. Equations Of Angle Bisectors_Part II
14. Family Of Straight Lines_Part I
15. Family Of Straight Lines_Part II

3. Pair of Straight Lines

1. Pair Of Straight Lines Introduction
2. Standard Second Degree Equation Of Pair Of Striaght Lines
3. Pair Of Straight Lines Through Origin
4. Equation Of Angle Bisectors And Homogenization

4. Circles

1. Equation Of Circle In Center-Radius Form
2. General Equation Of Circle
3. Equation Of Circle In Two Points-Angle Form
4. Equation Of Circle In Parametric Form
5. Locus Problems Based On Circle
6. Equation Of Chord Biseted At A Given Point
7. Position Of Point W.R.T. Circle
8. Lenght Of Tangent To Circle
9. Position Of Line W.R.T. Circle
10. Equation Of Tangent To Circle At A Given Point On It
11. Equation Of Tangent To Circle Having Given Slope
12. Tangents To Circle From External Point
13. Chord Of Contact Of Circle
14. Director Circle Of A Given Circle
15. Radical Axis Of Two Circles
16. Two Non-Intersecting Circles
17. Two Circles Touching Each Other
18. Two Intersecting Circles
19. Angle Of Inetersection Of Circles
20. Family Of Circles

5. Parabola

1. Parabola_Definition
2. Standard equation of parabola
3. Paramteric equations of parabola
4. Parabola having its axis parallel to y-axis
5. Parabola having its axis parallel to x-axis
6. Division of plane by parabola
7. Equation of midpoint chord of parabola
8. Focal chord of parabola and its properties
9. Tangent to parabola having equation y^2=4ax_Part I
10. Tangent to parabola having equation y^2=4ax_Part II
11. Tangent to parabola having eq.n other than y^2=4ax
12. Point of intersection of tangents to paraboya y^2=4ax
13. Locus problems of pt. of interesection of tangents to parabola
14. Tangent to parabola from a point not lying on the curve
15. Chord of contact of parabola
16. Normal to parabola at a point on it or having given slope
17. Normal to parabola from a point not lying on it
18. Properties of normal to parabola
19. Conormal points of parabola and its properties

6. Ellipse

1. Ellipse Definition
2. Standard Equation Of Ellipse
3. Problems Based On Standard Equation Of Ellipse Part I
4. Problems Based On Standard Equation Of Ellipse Part II
5. Equation Of Ellipse Having Axes Parallel To Coordinate Axes
6. Problems Based On Focal Property Of Ellipse
7. Equation Of Ellipse Having Any Two Perpendicular Lines As Its Axes
8. Equation Of Ellipse In Parametric Form Part I
9. Equation Of Ellipse In Parametric Form Part II
10. Properties Of Ellipse
11. Equation Of Tangent To Ellipse Theory
12. Equation Of Tangent To Ellipse Problems Discussion Part I
13. Equation Of Tangent To Ellipse Problems Discussion Part II
14. Director Circle Of Ellipse
15. Properties Of Tangent To Ellipse
16. Normal To Ellipse

7. Hyperbola

1. Hyperbola Definition 1
2. Hyperbola Definition 2
3. Standard Equation Of Hyperbola
4. Problems Based On Standard Equation Of Hyperbola
5. Equation Of Hyperbola Having Axes Parallel To Coordinate Axes
6. Eq. Of Hyperbola Having Given Two Lines As Its Axes
7. Rectangular Hyperbola xy=C^2
8. Equation Of Hyperbola In Parametric Form
9. Parametric Equations Of Hyperbola xy=C^2
10. Chords Of Hyperbola
11. Tangent To Hyperbola At A Point On It
12. Asymptotes To Hyperbola
13. Tangent To Hyperbola Having Given Slope Part I
14. Tangent To Hyperbola Having Given Slope Part II
15. Tangents To Hyperbola From A Point Not Lying On The Curve
16. Normal To Hyperbola Part I
17. Normal To Hyperbola Part II
18. Properties Of Tangent To Hyperbola
19. Orthogonal Intersection Of Ellipse And Hyperbola

+2_Algebra

1. Determinant

1. Determinant Definition And Expansion Part I
2. Determinant Definition And Expansion Part II
3. Sarrus rule of expansion
4. Properties Of Determinant Theory Part I
5. Properties Of Determinant Theory Part II
6. Problems Based On Properties Of Determinant Part I(Ncert Based)
7. Problems Based On Properties Of Determinant Part Ii(Ncert Based)
8. Problems Based On Properties Of Determinant Part III
9. Problems Based On Properties Of Determinant Part I
10. Problems Based On Properties Of Determinant Part V
11. Product Of Determinants Part I
12. Product Of Determinants Part II
13. Differentiation Of Determinant Cengage-1
14. System Of Linear Equations In Three Variables Part I Cengage-1
15. System Of Linear Equations In Two Variables Cengage-1
16. System Of Linear Equations In Three Variables Part II

2. Matrices

1. Matrix_Introduction
2. Classification Of Matrices
3. Important Things About Matrix
4. Addition Of Matrices
5. Multiplication Of Matrix By Scalar
6. Product Of Matrices_Theory
7. Product Of Matrices_Problems Discussion
8. Elementary Properties Of Product Of Matrice
9. Associative Property Of Matrix Multiplication
10. Commutative Property Of Product Of Matrices
11. Transpose Of Product Of Matrices
12. Determinant Of Product Of Matrices
13. Some Special Matrices
14. Adjoint of matrix
15. Properties Of Adjoint Of Matrix
16. Inverse Of Matrix
17. Properties Of Inverse Of Matrix_Part I
18. Properties Of Inverse Of Matrix_Part II
19. Inverse Of Matrix Using Elementary Transformations
20. Solving System Of Equations Using Matrix

3. Probability

1. Conditional Probability
2. Multiplication Rule Of Probability
3. Independent Events
4. Total Probability Theorem
5. Bayes Theorem
6. Random Variable And Its Probability Distribution

+2_Vector and 3D Geometry

1. 3D coordinate system

1. 3D coordinate system
2. Understanding 3d coordinates
3. Problems based on 3D coordinate system
4. Distance formula
5. Section formula_Part I
6. Section formula_Part II
7. Equation of sphere_Part I
8. Equation of sphere_Part II

2. Introduction to Vectors

1. Introduction to Vectors
2. Direction of vector
3. Algebra of Vectors & Angle between Vectors
4. Section Formula
5. Problems based on algebra of vectors_Part I
6. Problems based on algebra of vectors_Part II
7. Components of vector on axes
8. Problems_Components of vector on axes_Part I
9. Problems_Components of vector on axes_Part II
10. Linear combination of vectors
11. Problems based on linear combintion of vectors_Part I
12. Problems based on linear combintion of vectors_Part II

3. Different Product of Vectors

1. Dot Product_Theory
2. Problems based on dot product
3. Dot product_Square of sum of vectors
4. Solving Vector equations using dot product
5. Cross product_Theory
6. Problems based on cross product_Part I
7. Problems based on cross product_Part II
8. Cross product as area of parallelogram
9. Cross product_JEE problames
10. Scalar triple product_definition
11. Problems based on STP
12. Properties of STP
13. STP as volume of parallelepiped
14. Vector triple product_Part I
15. Vector triple product_Part II
16. Vector triple product_Part III
17. Solving vector equations using VTP
18. Reciprocal system of vectors

4. Line and Plane

1. Direction of line in space
2. Equation of line_theory
3. Equation of line_Problems discussion_Part I
4. Equation of line_Problems discussion_Part II
5. Distance of point from the line
6. Coplanar and non-coplanar lines
7. Angle between two lines
8. Shortest distance between non-intersecting lines
9. Equation of plane_Part I
10. Equation of plane_Part II
11. Normal and intercept form of plane
12. Family of planes
13. Line of intersection of planes
14. Distance of point from the plane
15. Different sides of plane
16. Angle between two planes
17. Angle bisectors of planes
18. Foot of perpendicular from a point on the plane_reflection of a point in the plane
19. Different Cases Of Line And Plane

1. Functions

1. Function_definition
2. Different types of relations
3. Cartesian product and relation
4. Sign Scheme (Weavy Curve) Method for Solving Ineqalities Part_I
5. Sign Scheme (Weavy Curve) Method for Solving Ineqalities Part_II
6. Applications of Sign Scheme Method
7. Concept of Squaring in Inequalities
8. Concept of Reciprocal in Inequalities
9. Functions Involving Quadratic Expressions
10. Functions Involving Quadratic Expressions Part_II
11. Trigonometric Functions Part_I
12. Trigonometric Functions Part_II
13. Functions involving ITF
14. Exponential Function
15. Logarithmic Functions_Part I
16. Logarithmic Functions_Part II
17. Applications of Logarithmic Inequalities
18. Greatest Integer Function
19. Properties of GIF
20. Graph of GIF and its applications
21. Fractional part function
22. Graph of Fractional Part Function and its Applications
23. Signum Function
24. Function max. of and min. of
25. Identical Functions
26. Identifying Injective and Surjective Nature of the Function_Part I
27. Identifying Injective and Surjective Nature of the Function_Part II.11924.121761
28. Odd and Even functions
29. Properties of odd and even functions
30. Functional Equations of Odd and Even Functions
31. Periodic Functions
32. Period of Transformed and Composite Functions
33. Period of Function Obtained by Algebraic Operations of Functions
34. Functional Equations of Periodic Functions
35. Inverse Function Part_I
36. Inverse function_Part II
37. Properties of inverse functions
38. Composite functions
39. Definition of composite functions
40. Injectivity and surjectivity of composite functions
41. Finding function from funcational equations
42. Transformation of graphs
43. Transformation of graphs involving modulus
44. Function based on max.-min value in variable interval

2. Limits

1. Introduction to limit of function
2. Problems based on existence of limit_Part I
3. Problems based on existence of limit_Part II
4. Rule of limit of function
5. Indeterminate forms of limit
6. Evaluating limit by cancelling common factor_PArt I
7. Evaluating limit by cancelling common factor_Part II
8. Standard algebraic limit
9. Limit of algebraic functions at infinity_Part I
10. Limit of algebraic functions at infinity_Part II
11. Evaluating limit using expansion of function
12. Standard trigonometric limit_Part I
13. Standard trigonometric limit_Part II
14. Trigonometric limit_Part III
15. Limit of function involving ITF
16. Exponential limit
17. Logarithmic limit
18. One power infinity
19. One power infinity
20. L’Hospital rule
21. L’Hospital rule to evaluate indeterminate forms

3. Differentiation

1. Derivative_Introduction
2. Problems based on first definition of derivative
3. Derivative of some standard functions
4. Product and quotient rule of differentiation
5. Chain rule of differentiation
6. Diff. of function involving ITF
7. Differentiation of inverse of given function
8. Differentiation of implicit functions
9. Differentiation using logarithm
10. Differentiation of parametric form of equations
11. Higher order derivatives
12. Successive differentiation of parametric form of equations
13. Differentiation of functional equations_Part I
14. Differentiation of functional equations_Part II

4. Continuity and Differentiability

1. Continuity Of Function Definition
2. Different types of discontinuity of functions
3. Problems based on missing point discontinuity
4. Finding unknowns using continuity
5. Continuity of functions involving GIF_Part I
6. Continuity of functions involving GIF_Part II
7. Continuity of function sgn(f(x))
8. Continuity of miscellaneous functions_Part I
9. Continuity of Miscellaneous Functions Part II
10. Continuity of functions obtained by alg. operations of functions
11. Differentiability_definition
12. Differentiability using first definition of derivative_Part I
13. Differentiability using first definition of derivative_Part II
14. Differentiability using differentiation
15. Differentiability of functions involving ITF
16. Diff. of functions obtained by algebraic operations of functions

5. Application of Derivatives

1. Slope of tangent and normal
2. Tangent-normal at a given point on the curve
3. Tangent-normal having given slope
4. Tangent-normal from a point not lying on the curve
5. Derivative as Rate of Change
6. Approximation using derivative
7. Rolle’ Theorem
8. Selection of function for Rolle’ theorem
9. Mean value theorem
10. Selection of function for mean value theorem
11. Proving inequalities using mean value theorem
12. Cauchy’s Mean Value Theorem-1

6. Monotonicity an maxima-minima

1. Increasing-decreasing functions
2. Monotonicity of differentiable functions
3. Separatin the intervals of monotonicity of non-monotonic functions_Part I
4. Separatin the intervals of monotonicity of non-monotonic functions_Part II
5. Finding-relating unknowns using monotonicity
6. Proving inequalities using monotonicity_Part I
7. Proving inequalities using monotonicity_Part II
8. Proving inequalities using monotonicity_Part III
9. Concavity of curve
10. Point of inflection
11. Maxima-minima_Definition
12. Maxima-minima of differentiable functions_Part I
13. Maxima-minima of differentiable functions_Part II
14. Maxima-minima of differentiable functions_Part III
15. Maxima-minima of non-differentiable functions_Part I
16. Maxima-minima of non-differentiable functions_Part II
17. Applications of maxima-minima in optimization
18. Applications of maxima-minima in plane geometry-coordinate geometry
19. Use of trigonometry in applications of maxima-minima
20. Applications of maxima-minima in solid geometry

7. Indefinite Integration

1. Indefinite integration_Introduction
2. Elementary integration problems
3. Integration of f(ax + b)
4. Integrand_(f(g(x)))g'(x)
5. Integrand_f'(x) upon f(x)
6. Integration of tan, cot, sec, cosec
7. Integrand ((f(x))^n)f'(x)
8. Substitution techniques in integration_Part I
9. Substitution techniques in integration_Part II
10. Integration using trigonometric substitution
11. Integrand_Reciprocal of quadratic
12. Integrand involving biquadratic expression
13. Trigo. integrand reducible to reciprocal of quadrtic
14. Integrand_Reciprocal of square root of quadratic
15. Practice problems
16. Integration by partial fractions_Part I
17. Integration by partial fractions_Part II
18. Integration by parts_Part I
19. Integration by parts_Part II
20. Integrand_(e^ax)sinbx or (e^ax)cosbx
21. Integrand_Square root of quadratic
22. Integrand_(e^x)(f(x)+f'(x))
23. Integration by cancellation

8. Definite Integration

1. Definite integration as area function_Part I
2. Definite integration as area function_Part II
3. Elementary properties of definite integration_Part I
4. Elementary properties of definite integration_Part II
5. Definite integration using fundamental theorem
6. Definite integration by substitution_Part I
7. Definite integration by substitution_Part II
8. Definite integration by parts_Part I
9. Definite integration by parts_Part II
10. Definite integration by reciprocal substitution
11. Comparison of definite integrals
12. Definite integral as limit of sum_Part I
13. Definite integral as limit of sum_Part II
14. Function as definite integral
15. Inequalities involving definite integral_Part I
16. Inequalities involving definite integral_Part II
17. Definite integral as limit of sum_Part I
18. Definite integral as limit of sum_Part II
19. Property of DI_Replacing x by sum of limits minus x
20. Properties of D.I._Halving the upper limit
21. D.I. of log(sin x) or log(cos x) between limits 0 and pi by 2
22. D.I. of odd and even functions
23. Definite integration of periodic functions
24. Leibniz rule_Introduction
25. Finding limit of function using leibniz rule
26. Definite integration_Applications of leibniz rule in monotonicity of function
27. Leibniz rule when integrand is function of two independent variables
28. Leibniz rule_Higher level problems
29. Reduction formula in definite integration

9. Area

1. Area bounded by curve and axis_Part I
2. Area bounded by curve and axis_Part II
3. Area bounded by curves_Part I
4. Area bounded by curves_Part II
5. Area involving Trig. Functions
6. Area involvoing logarithmic function
7. Area involving implicit functions
8. Finding area without integration

10. Differential Equation

1. Differential equations_Part I
2. Differential equations_Part II
3. Differential equations of Variable seperable type
4. Homogeneous differential equations_Part I
5. Homogeneous differential equations_Part II
6. General form of variable separable type
7. Linear Differential equations
8. Diff. Equn. reducible to LDE
9. Miscellaneous_Linear Diff. Equations
10. Applications of differential equations_Part I

11. Inverse Trigonometric Functions(ITF)

1. Inverse Trigonometric Functions Definition
2. Graphs Of Inverse Trigonometric Functions
3. Composition Of Trigonometric Function And Its Inverse Function
4. Problems Based On Definition Of Itfs Part I
5. Problems Based On Definition Of Itfs Part II
6. Functions – Sin Inverse Of Sine And Cosec Inverse Of Cosecant
7. Functions Cos Inverse Of Cosine And Sec Inverse Of Secant
8. Functions Tan Inverse Of Tangent And Cot Inverse Of Cotangent
9. Writing One Itf In The Fomr Of Other Itfs
10. Inverse Trigonometric Functions Of Minus X
11. Inverse Trigonometric Functions Of Reciprocal Of X
12. Simplifying Inverse Trigonometric Functions Using Substitution
13. Complimentary Angles In The Form Of Itfs
14. Addition Of Angles In The Form Of Tan Inverse Function Part I
15. Addition Of Angles In The Form Of Tan Inverse Function Part II
16. Addition Of Angles In The Form Of Tan Inverse Function Part III
17. Sum Of Series Involving Tan Inverse Function
18. Addition Of Angles In The Form Of Cos Inverse Function