Pi Aim academy mathematics study materials:

Pi Aim academy mathematics study materials:

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*Abstract Algebra*

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*Linear Algebra*

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*Complex Analysis*

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*Real Analysis Part-1*

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*Real Analysis Part-2*

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*Topology & Metric Space*

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*Ordinary Differential Equations*

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*Partial Differential Equations*

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*Integral Equations*

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*Calculus of Variation*

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*Numerical Analysis*

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Lecture notes14 : Double Integrals, Applilcations to Areas and Volumes Change of variables

Lecture notes14 : Double Integrals, Applilcations to Areas and Volumes Change of variables

40

Double integrals over rectangular domains Click here

41.

Triple integrals Click here

42. 

Change of variables Click here

Lecture notes18 : Stokes's theorem and applications

Lecture notes18 : Stokes's theorem and applications

52. 

Orienting the boundary of an orientable surface Click here

53.

Stokes' theorem for general domains Click here

54.

Application of Stokes' theorem Click here

Lecturer notes 17 : Surfaces, Surface Area, Surface integrals, Divergence Theorem and applications

Lecturer notes  17 : Surfaces, Surface Area, Surface integrals, Divergence Theorem and applications

49.

Surfaces and parameterizations [ Click here

50. 

Surface Integrals Click here

51.

Divergence theorem Click here

Lecture notes16 : Line Integrals, Conservative fields Green's Theorem and applications

Lecture notes16 : Line Integrals, Conservative fields Green's Theorem and applications

46. 

Line integrals Click here

47.

Fundamental Theorems of Calculus for Line integrals Click here

48. 

Green's Theorem Click here

Lecture notes 15:Vector fields, Gradient, Divergence and Curl

Lecture notes 15:Vector fields, Gradient, Divergence and Curl

43 . 

Vector fields and their properties Click here

44. 

Gradient Divergence and Curl Objectives Click here

45. 

Curves in space Click here

Lecture notes 13:Maxima, Minima and Saddle Points, Constrained maxima and minima

Lecture notes 13:Maxima, Minima and Saddle Points, Constrained maxima and minima

37 . 

Maxima and Minima Click here

38.

Second derivative test for local maxima / minima & saddle points Click here

39.

Absolute maxima / minima Click here

Lecture notes12: Total differential, Tangent planes and normals

Lecture notes12: Total differential, Tangent planes and normals

34.

Gradient of a scaler field Download here
35.

Tangent plane and normal Download here

36.

Mean value theorem and Linearization Download here

Lecturer notes 11: Partial derivatives, Chain rules, Implicit differentiation, Gradient, Directional derivatives

Lecturer notes 11: Partial derivatives, Chain rules, Implicit differentiation, Gradient, Directional derivatives

31.

Partial derivatives Download here

32.

Chain rules Download here

33.

Implicit differentiation Download here

Lecturer notes 10 : Scaler fields, Limit and Continuity

Lecturer notes 10 :   Scaler fields, Limit and   Continuity

 28.

Series of functions   Download here

29.

 Limit of scaler fields Download here

30. 

Continuity of scaler fields   Download here

Lecture notes 9 : Infinite Series, Tests of Convergence, Absolute and Conditional Convergence, Taylor and Maclaurin Series:

Lecture notes 9  :   Infinite  Series,  Tests  of  Convergence,  Absolute  and  Conditional  Convergence,  Taylor and  Maclaurin  Series:

25 .

Series  of  numbers Download here

26 .

Absolute  convergence Download here

27 .

Series  of  functions Download here

Lecture notes 8 : Applications of Integration - II

Lecture notes 8 :  Applications  of  Integration  - II 

22.

Arc  Length  of  a  Plane  Curve Download here

23.

Area of Surface of revolution Download here


24.

Volume  of  solids  of  revolution  by  washer  method Download here

Lecture notes 7 : Applications of Integration - I

Lecture notes 7  :  Applications  of  Integration  - I

19 . 

Definition  of  the  natural  logarithmic  function base Download here

20.

Definition of the power function and logarithmic function with positive base Download here

21.

Relative  rate  of  growth  of  functionsDownload here

Lecture notes-6 :Definition of Integral

Lecture notes-6 :Definition  of  Integral:

16. 

Integral  from  upper  and  lower  sums Download here

17. 

Fundamental theorem of calculus Download here

18. 

Approximating Integral : Trapezoidal Rule Download here