1. Successive Differentiation 1-1 to 1-41
(1) Introduction (2) Derivatives Of 9th Order (3) Leibnitz's Theorem.
2. Reduction Formulae 2-1 to 2-15
(1) Introduction (2) Reduction Formula for [sin" xdx where n is a positive integer > 2 and for [ sin" xdx (3) Reduction Formula for Jcos"xdx where n is a positive integer > 2 and for J cosxdx
(4) Reduction Formulae for Jsinm jccos" xdx (5) Reduction Formulae for sinmxcosnxdx.
3. Expansions Of Functions 3-1 to 3-37
(1) Introduction (2) Maclaurin's Series (3) Some Standard Expansions (4) Expansion's Of Functions In Power Series (5) Taylor's Series.
4. Indeterminate Forms 4-1 to 4-20
(1) Introduction (2) L' Hospital's Rule (3) Other Indeterminate Forms (4) Forms 0 x °° and <*> - °° (5) Exponential Form 1°°, °°°, 0°.
5. Convergence Of Sequences And Series 5-1 to 5-65
(1) Introduction (2) Convergent And Divergent Sequences (3) Divergent Sequences (4) Algebra Of Convergent Sequences (5) Some Important Sequences (6) Methods Of Evaluation of Limits (7) Infinite Series (8) General Properties Of Series (9) Series Of Positive Terms (10) Test For Convergence (Zero Test) (11) Comparison Test (Form I) (12) Limit Comparison Test (13) D'Alembert's Ratio Test (14) Raabe's Test (15) Cauchy's n th Root Test (16) Integral Test (17) Alternating Series (18) Absolute And Conditional Convergence (19) Convergence Of Some Standard Series (20) Interval Of Convergence (21) Summary.
6. Maxima And Minima 6-1 to 6-21
(1) Introduction (2) Global Or Absolute Maxima (3) Local Or Relative Maxima and Minima (4) Global Maxima And Minima (5) A Necessary Condition For An Extrema (6) Conditions For Maxima (7) Conditions For Minima (8) Point Of Inflection (9) Procedure To Solve Problems.
7. Partial Differentiation 7-1 to 7-56
(1) Introduction (2) Limit Of A Function (3) Continuity (4) Partial Derivatives Of The First Order (5) Geometrical Interpretation Of Partial Derivatives (6) Partial Derivatives Of Higher Order (7) Partial Derivatives Of Some Standard Functions (8) Differentiation Of A Function Of A Function (9) Variables To Be Treated As Independent Variables (10) Composite Functions (I I) Differentiation Of Composite Functions
(12) Differentiation Of Two Variable Implicit Function f (x, y) = 0
(13) Differentiation Of Three Variable Implicit Function/(x, y, z)-0.
8. Euler's Theorem And Jacobians 8-1 to 8-30
(1) Introduction (2) Homogeneous Functions (3) Euler's Theorem (4) Jacobians (5) Jacobians Of Composite Functions.
9. Applications of Partial Differentiation 9-1 to 9-35
(1) Introduction (2) Taylor's Expansion Of Functions Of Two Variables (3) Errors And Approximations (4) Maxima And Minima Of z =f(x, y) (5) Lagrange's Method Of Undetermined Multipliers.
10. Integration 10-1 to 10-41
(1) Introduction (2) Partition (3) Upper And Lower Sums (4) Average Value Of A Function (5) Norm Of A Partition (6) Riemann Sums (7) To Evaluate The Sum As An Integral (8) To Evaluate The Definite Integral As The Limit Of A Sum (9) The Mean Value Theorem For Definite Integral (10) Fundamental Theorem Of Calculus (11) Improper Integrals (12) Convergence Of Integrals (13) Absolute Convergence.
11. Tracing Of Curves And
Study Of Some Solids 11-1 to 11-32
(1) Introduction (2) Procedure For Tracing Curves Given In Cartesian Equations (3) Graphs Of y p = x q (4) Graphs Of The Form y=(x-a)(x-b)(x- c) (5) Some Well Known Curves (6) Equations In Parametric Form (7) Procedure For Tracing Curves Given In Polar Equations (8) Curves Of The Form r - a sin nti Or r - a cos nB (9) Some Solids.
12. Rectification 12-1 to 12-17
(1) Introduction (2) Length Of The Arc Of A Curve Given By y -f (x) (3) Length Of The Arc Of A Curve Given By r = /(O).