Calculus and Differential Equations - VISTAS
Course Instructor
Promath
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Course Overview
Schedule of Classes
Course Curriculum
5 Subjects
Unit - I: Calculus (VelsM1EEE)
100 Learning Materials
1.1 Evolute
1.1.1 Introduction
PDF
1.1.2 Solved Problem 1
Video
9:20
1.1.3 Solved Problem 2
Video
9:20
1.1.4 Solved Problem 3
PDF
1.1.5 Solved Problem 4
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1.1.6 Solved Problem 5
PDF
1.1.7 Exercises
PDF
1.2 Beta Function
1.2.1 Beta function
PDF
1.2.2 Solved problem 1
Video
4:17
1.2.3 Solved problem 2
Video
4:5
1.2.4 Solved problem 3
Video
3:43
1.2.5 Solved problem 4
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1.2.6 Solved problem 5
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1.2.7 Solved problem 6
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1.2.8 Exercises
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1.3 Gamma Function
1.3.1 Gamma function
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1.3.2 Properties of Gamma Function
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1.3.3 Solved problem 1
Video
1:50
1.3.4 Solved problem 2
Video
2:19
1.3.5 Solved problem 3
Video
4:6
1.3.6 Solved problem 4
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1.3.7 Solved problem 5
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1.3.8 Solved problem 6
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1.3.9 Solved problem 7
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1.3.10 Solved problem 8
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1.3.11 Solved problem 9
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1.3.12 Exercises
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1.4 Relation Between Gamma and Beta Function
1.4.1 Relation between beta and gamma functions
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1.4.2 Solved problem 1
Video
3:30
1.4.3 Solved problem 2
Video
3:15
1.4.4 Solved problem 3
Video
5:13
1.4.5 Solved problem 4
Video
5:6
1.4.6 Solved problem 5
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1.4.7 Solved problem 6
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1.4.8 Solved problem 7
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1.4.9 Solved problem 8
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1.4.10 Solved problem 9
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1.4.11 Solved problem 10
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1.4.12 Solved problem 11
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1.4.13 Solved problem 12
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1.4.14 Solved problem 13
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1.4.15 Solved problem 14
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1.4.16 Solved problem 15
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1.4.17 Exercises
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1.5 Rolle’s Mean value Theorem
1.5.1 Introduction
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1.5.2 Solved Problem 1
Video
4:52
1.5.3 Solved Problem 2
Video
6:14
1.5.4 Solved Problem 3
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1.5.5 Solved Problem 4
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1.5.6 Solved Problem 5
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1.5.7 Solved Problem 6
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1.5.8 Exercises
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1.6 Taylor's and Maclaurin's theorems
1.6.1 Introduction
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1.6.2 Maclaurin's series expansion of some elementary functions
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1.6.3 Solved Problem 1
Video
8:53
1.6.4 Solved Problem 2
Video
10:13
1.6.5 Solved Problem 3
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1.6.6 Solved Problem 4
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1.6.7 Solved Problem 5
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1.6.8 Solved Problem 6
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1.6.9 Solved Problem 7
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1.6.10 Solved Problem 8
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1.6.11 Solved Problem 9
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1.6.12 Solved Problem 10
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1.6.13 Solved Problem 11
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1.6.14 Solved Problem 12
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1.6.15 Solved Problem 13
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1.6.16 Exercises
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1.7 Indeterminate forms
1.7.1 Introduction
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1.7.2 Indeterminate forms of the type
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1.7.3 Solved Problem 1
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12:14
1.7.4 Solved Problem 2
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11:42
1.7.5 Solved Problem 3
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1.7.6 Solved Problem 4
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1.7.7 Solved Problem 5
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1.7.8 Solved Problem 6
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1.7.9 Solved Problem 7
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1.7.10 Solved Problem 8
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1.7.11 Solved Problem 9
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1.7.12 Solved Problem 10
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1.7.13 Solved Problem 11
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1.7.14 Solved Problem 12
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1.7.15 Solved Problem 13
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1.7.16 Solved Problem 14
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1.7.17 Solved Problem 15
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1.7.18 Solved Problem 16
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1.7.19 Solved Problem 17
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1.7.20 Solved Problem 18
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1.7.21 Solved Problem 19
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1.7.22 Solved Problem 20
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1.7.23 Solved Problem 21
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1.7.24 Solved Problem 22
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1.7.25 Solved Problem 23
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1.7.26 Solved Problem 24
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1.7.27 Solved Problem 25
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1.7.28 Solved Problem 26
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1.7.29 Solved Problem 27
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1.7.30 Solved Problem 28
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1.7.31 Solved Problem 29
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1.7.32 Exercises
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Unit - II: Sequences and Series (VelsM1EEE)
41 Learning Materials
2.1 Sequences
2.1.1 Introduction.pdf
PDF
2.1.2 Operation on Sequence
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2.1.3 Convergence, Divergence and Oscillation of a Sequence
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2.1.4 Solved Problem 1
Video
3:48
2.1.5 Solved Problem 2
Video
4:30
2.1.6 Solved Problem 3
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2.1.7 Solved Problem 4
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2.1.8 Solved Problem 5
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2.1.9 Exercises
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2.2 Infinite series
2.2.1 Introduction
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2.2.2 Properties of series
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2.2.3 Necessary condition for convergence of a series
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2.2.4 Series with positive terms
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2.2.5 Solved Problem 1
Video
3:23
2.2.6 Solved Problem 2
Video
4:25
2.2.7 Solved Problem 3
Video
1:47
2.2.8 Solved Problem 4
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2.2.9 Exercises
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2.3 Comparison test
2.3.1 Introduction
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2.3.2 Solved Problem 1
Video
5:9
2.3.3 Solved Problem 2
Video
5:3
2.3.4 Solved Problem 3
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2.3.5 Solved Problem 4
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2.3.6 Solved Problem 5
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2.3.7 Solved Problem 6
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2.3.8 Solved Problem 7
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2.3.9 Solved Problem 8
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2.3.10 Exercises
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2.4 Integral test
2.4.1 Introduction
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2.4.2 Solved Problem 1
Video
4:5
2.4.3 Solved Problem 2
Video
4:48
2.4.4 Solved Problem 3
Video
4:26
2.4.5 Solved Problem 4
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2.4.6 Solved Problem 5
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2.4.7 Exercises
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2.5 Logarithmic test
2.7.1 Introduction
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2.7.2 Solved Problem 1
Video
9:7
2.7.3 Solved Problem 2
Video
6:19
2.7.4 Solved Problem 3
Video
10:52
2.7.5 Solved Problem 4
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2.7.6 Exercises
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Unit - III: Multivariable Calculus: Differentiation (VelsM1EEE)
16 Exercises • 68 Learning Materials
3.1 Function of two or more variable
3.1.1 Introduction
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3.1.2 Limit
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3.1.3 Continuity
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3.1.4 Solved Problem 1
Video
3:25
3.1.4 Quiz
Exercise
3.1.5 Solved Problem 2
Video
6:14
3.1.5 Quiz
Exercise
3.1.6 Solved Problem 3
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3.1.7 Solved Problem 4
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3.1.8 Solved Problem 5
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3.1.9 Solved Problem 6
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3.1.10 Solved Problem 7
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3.1.11 Exercise
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3.2 Partial Differentiation
3.2.1 Introduction
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3.2.2 Solved Problem 1
Video
000
3.2.2 Quiz
Exercise
3.2.3 Solved Problem 2
Video
000
3.2.3 Quiz
Exercise
3.2.4 Solved Problem 3
Video
000
3.2.4 Quiz
Exercise
3.2.5 Solved Problem 4
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3.2.6 Solved Problem 5
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3.2.7 Solved Problem 6
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3.2.8 Solved Problem 7
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3.2.9 Solved Problem 8
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3.2.10 Solved Problem 9
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3.2.11 Exercises
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3.3 Homogeneous Function and Euler's Theorem
3.3.1 Introduction
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3.3.2 Euler's Theorem
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3.3.3 Solved Problem 1
Video
000
3.3.3 Quiz
Exercise
3.3.4 Solved Problem 2
Video
000
3.3.4 Quiz
Exercise
3.3.5 Solved Problem 3
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000
3.3.5 Quiz
Exercise
3.3.6 Solved Problem 4
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3.3.7 Solved Problem 5
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3.3.8 Solved Problem 6
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3.3.9 Solved Problem 7
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3.3.10 Solved Problem 8
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3.3.11 Solved Problem 9
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3.3.12 Exercises
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3.4 Total Derivative
3.4.1 Introduction
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3.4.2 Solved Problem 1
Video
000
3.4.2 Quiz
Exercise
3.4.3 Solved Problem 2
Video
000
3.4.3 Quiz
Exercise
3.4.4 Solved Problem 3
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3.4.5 Solved Problem 4
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3.4.6 Solved Problem 5
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3.4.7 Solved Problem 6
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3.4.8 Solved Problem 7
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3.4.9 Solved Problem 8
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3.4.10 Exercises
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3.5 Tangent and normal to a surface
3.5.1 Introduction
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3.5.2 Tangent plane and normal to a surface
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3.5.3 Solved Problem 1
Video
6:50
3.5.4 Solved Problem 2
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3.6 Maxima and minima of functions of two variables
3.6.1 Introduction
PDF
3.6.2 Solved Problem 1
Video
9:7
3.6.2 Quiz
Exercise
3.6.3 Solved Problem 2
Video
17:17
3.6.3 Quiz
Exercise
3.6.4 Solved Problem 3
Video
12:24
3.6.4 Quiz
Exercise
3.6.5 Solved Problem 4
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3.6.6 Solved Problem 5
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3.6.7 Solved Problem 6
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3.6.8 Solved Problem 7
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3.6.9 Solved Problem 8
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3.6.10 Solved Problem 9
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3.6.11 Solved Problem 10
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3.6.12 Solved Problem 11
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3.6.13 Exercises
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3.7 Lagrange's method of undetermined multipliers
3.7.1 Introduction
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3.7.2 Solved Problem 1
Video
9:50
3.7.2 Quiz
Exercise
3.7.3 Solved Problem 2
Video
10:25
3.7.3 Quiz
Exercise
3.7.4 Solved Problem 3
Video
7:55
3.7.4 Quiz
Exercise
3.7.5 Solved Problem 4
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3.7.6 Solved Problem 5
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3.7.7 Exercises
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Unit - IV: Multivariable Calculus: Integration (VelsM1EEE)
44 Exercises • 78 Learning Materials
4.1 Double Integrals
4.1.1 Introduction
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4.1.2 Applications of Multiple Integral in Engineering
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4.1.3 Evaluation of Double Integration in Cartesian Coordinates
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4.1.4 Evaluation of Double Integration in Polar Coordinates
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4.1.5 Properties of Double integrals
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4.1.6 Problem based on Cartesian Form
Video
2:46
4.1.6 Quiz
Exercise
4.1.7 Solved problem 2
Video
5:13
4.1.7 Quiz
Exercise
4.1.8 Solved problem 3
Video
2:30
4.1.8 Quiz
Exercise
4.1.9 Solved problem 4
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4.1.10 Solved problem 5
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4.1.11 Problem based on Region Given
Video
5:36
4.1.11 Quiz
Exercise
4.1.12 Solved problem 7
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4.1.13 Solved problem 8
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4.1.14 Solved problem 9
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4.1.15 Problem based on Polar Form
Video
2:49
4.1.15 Quiz
Exercise
4.1.16 Solved problem 11
Video
3:49
4.1.16 Quiz
Exercise
4.1.17 Solved problem 12
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4.1.18 Exercises
Exercise
4.2 Triple Integrals
4.2.1 Triple integrals
PDF
4.2.2 Problem based on Cartesian Form
Video
4:41
4.2.2 Quiz
Exercise
4.2.3 Solved problem 2
Video
3:40
4.2.3 Quiz
Exercise
4.2.4 Solved problem 3
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4.2.5 Solved problem 4
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4.2.6 Solved problem 5
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4.2.7 Problem based on Region Given
Video
4:40
4.2.7 Quiz
Exercise
4.2.8 Solved problem 7
PDF
4.2.9 Problem based on Polar Form
Video
4:19
4.2.9 Quiz
Exercise
4.2.10 Exercises
Exercise
4.3 Change of Order of Integration
4.3.1 Change of Order of Integration
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4.3.2 Solved problem 1
Video
4:57
4.3.2 Quiz
Exercise
4.3.3 Solved problem 2
Video
9:15
4.3.3 Quiz
Exercise
4.3.4 Solved problem 3
Video
6:34
4.3.4 Quiz
Exercise
4.3.5 Solved problem 4
Video
11:58
4.3.6 Solved problem 5
PDF
4.3.7 Solved problem 6
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4.3.8 Exercises
Exercise
4.4 Change of Variables (Double Integral)
4.4.1 Change of Variables (Double Integral)
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4.4.2 Changing Cartesian to Polar Coordinates
PDF
4.4.3 Solved problem 1
Video
5:39
4.4.3 Quiz
Exercise
4.4.4 Solved problem 2
Video
5:21
4.4.4 Quiz
Exercise
4.4.5 Solved problem 3
Video
5:20
4.4.5 Quiz
Exercise
4.4.6 Solved problem 4
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4.4.7 Solved problem 5
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4.4.8 Exercises
Exercise
4.5 Change of Variables (Triple Integral)
4.5.1 Change of Variables (Triple Integral)
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4.5.2 Change of Cartesian to Spherical Co-Ordinates
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4.5.3 Change of Cartesian to Cylindrical Co-Ordinates
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4.5.4 Problem based on Cylindrical Co-Ordinates
Video
4:54
4.5.4 Quiz
Exercise
4.5.5 Solved problem 2
Video
5:35
4.5.5 Quiz
Exercise
4.5.6 Solved problem 3
PDF
4.5.7 Problem based on Spherical Co-Ordinates
Video
5:27
4.5.7 Quiz
Exercise
4.5.8 Solved problem 5
Video
6:22
4.5.8 Quiz
Exercise
4.5.9 Solved problem 6
PDF
4.5.10 Exercises
Exercise
4.6 Greens Theorem
4.6.1 Introduction
PDF
4.6.2 Solved Problem 1
Video
6:50
4.6.2 Quiz
Exercise
4.6.3 Solved Problem 2
Video
12:6
4.6.3 Quiz
Exercise
4.6.4 Solved Problem 3
Video
8:55
4.6.4 Quiz
Exercise
4.6.5 Solved Problem 4
Video
9:41
4.6.5 Quiz
Exercise
4.6.6 Solved Problem 5
Video
7:50
4.6.6 Quiz
Exercise
4.6.7 Solved Problem 6
PDF
4.6.8 Solved Problem 7
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4.6.9 Solved Problem 8
PDF
4.6.10 Exercises
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4.7 Gauss Divergence Theorem
4.7.1 Introduction
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4.7.2 Solved Problem 1
Video
15:7
4.7.2 Quiz
Exercise
4.7.3 Solved Problem 2
Video
5:24
4.7.3 Quiz
Exercise
4.7.4 Solved Problem 3
Video
4:15
4.7.4 Quiz
Exercise
4.7.5 Solved Problem 4
Video
6:53
4.7.5 Quiz
Exercise
4.7.6 Solved Problem 5
Video
13:58
4.7.6 Quiz
Exercise
4.7.7 Solved Problem 6
Video
8:16
4.7.7 Quiz
Exercise
4.7.8 Solved Problem 7
Video
10:21
4.7.8 Quiz
Exercise
4.7.9 Solved Problem 8
PDF
4.7.10 Exercises
PDF
4.8 Stokes Theorem
4.8.1 Introduction
PDF
4.8.2 Solved Problem 1
Video
10:3
4.8.2 Quiz
Exercise
4.8.3 Solved Problem 2
Video
9:19
4.8.3 Quiz
Exercise
4.8.4 Solved Problem 3
Video
14:11
4.8.4 Quiz
Exercise
4.8.5 Solved Problem 4
Video
7:31
4.8.5 Quiz
Exercise
4.8.6 Solved Problem 5
Video
6:45
4.8.6 Quiz
Exercise
4.8.7 Solved Problem 6
Video
6:38
4.8.7 Quiz
Exercise
4.8.8 Solved Problem 7
Video
8:35
4.8.8 Quiz
Exercise
4.8.9 Exercises
PDF
Unit - V: Ordinary Differential Equations (VelsM1EEE)
14 Exercises • 101 Learning Materials
5.1 Exact Differential Equation
5.1.1 Introduction
PDF
5.1.2 Applications of First Order ODE in Engineering
PDF
5.1.3 Application of First Order ODE
Video
8:39
5.1.4 Exact Differential Equation
PDF
5.1.5 Application Exact differential Equation
PDF
5.1.6 Solved Problem 1
Video
2:41
5.1.6 Quiz
Exercise
5.1.7 Solved Problem 2
Video
3:5
5.1.7 Quiz
Exercise
5.1.8 Solved Problem 3
Video
2:35
5.1.8 Quiz
Exercise
5.1.9 Solved Problem 4
PDF
5.1.10 Solved Problem 5
PDF
5.1.11 Solved Problem 6
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5.1.12 Solved Problem 7
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5.1.13 Solved Problem 8
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5.1.14 Solved Problem 9
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5.1.15 Solved Problem 10
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5.1.16 Solved Problem 11
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5.1.17 Solved Problem 12
PDF
5.1.18 Solved Problem 13
PDF
5.1.19 Exercise
Exercise
5.2 Linear Differential Equation
5.2.1 Introduction
PDF
5.2.2 Application Linear differential equation
PDF
5.2.3 Solved Problem 1
Video
2:56
5.2.3 Quiz
Exercise
5.2.4 Solved Problem 2
Video
2:58
5.2.4 Quiz
Exercise
5.2.5 Solved Problem 3
Video
3:49
5.2.5 Quiz
Exercise
5.2.6 Solved Problem 4
PDF
5.2.7 Solved Problem 5
PDF
5.2.8 Solved Problem 6
PDF
5.2.9 Solved Problem 7
PDF
5.2.10 Solved Problem 8
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5.2.11 Solved Problem 9
PDF
5.2.12 Solved Problem 10
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5.2.13 Solved Problem 11
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5.2.14 Solved Problem 12
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5.2.15 Exercise
Exercise
5.3 Non-Linear Differential Equation
5.3.1 Introduction
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5.3.2 Application of Equation solvable for p
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5.3.3 Solved Problem 1
Video
5:12
5.3.4 Solved Problem 2
Video
4:58
5.3.5 Solved Problem 3
Video
6:12
5.3.6 Solved Problem 4
PDF
5.3.7 Solved Problem 5
PDF
5.3.8 Solved Problem 6
PDF
5.3.9 Solved Problem 7
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5.3.10 Exercises
PDF
5.4 Equation Solvable for Y
5.4.1 Introduction
PDF
5.4.2 Solved Problem 1
Video
5:12
5.4.3 Solved Problem 2
Video
3:9
5.4.4 Solved Problem 3
Video
5:12
5.4.5 Solved Problem 4
PDF
5.4.6 Solved Problem 5
PDF
5.4.7 Solved Problem 6
PDF
5.4.8 Exercises
PDF
5.5 Equation Solvable for X
5.5.1 Introduction
PDF
5.5.2 Solved Problem 1
Video
3:22
5.5.3 Solved Problem 2
Video
4:20
5.5.4 Solved Problem 3
Video
5:19
5.5.5 Solved Problem 4
PDF
5.5.6 Solved Problem 5
PDF
5.5.7 Solved Problem 6
PDF
5.5.8 Solved Problem 7
PDF
5.5.9 Exercises
PDF
5.6 Clairauts Equation
5.6.1 Introduction
PDF
5.6.2 Solved Problem 1
Video
3:11
5.6.3 Solved Problem 2
Video
4:27
5.6.4 Solved Problem 3
Video
3:28
5.6.5 Solved Problem 4
PDF
5.6.6 Solved Problem 5
PDF
5.6.7 Solved Problem 6
PDF
5.6.8 Solved Problem 7
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5.6.9 Solved Problem 8
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5.6.10 Solved Problem 9
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5.6.11 Solved Problem 10
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5.6.12 Solved Problem 11
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5.6.13 Exercises
PDF
5.7 Linear Differential Equations of Higher Order
5.7.1 What is Ordinary Differential Equations?
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5.7.2 What are the applications of higher order ODEs in Engineering?
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5.7.3 Linear differential equations of higher order
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5.7.4 Operator D
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5.7.5 To find the General solution of f(D)y = 0
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5.7.6 Solved Problem 1
Video
5:39
5.7.6 Quiz
Exercise
5.7.7 Solved Problem 2
Video
3:32
5.7.7 Quiz
Exercise
5.7.8 Solved Problem 3
Video
3:53
5.7.8 Quiz
Exercise
5.7.9 Solved Problem 4
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5.7.10 Solved Problem 5
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5.7.11 Solved problem 6
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5.7.12 Solved problem 7
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5.7.13 Solved problem 8
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5.7.14 Solved problem 9
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5.7.15 Solved problem 10
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5.7.16 Solved problem 11
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5.7.17 Solved problem 12
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5.7.18 Exercise
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5.8 Method of variation of parameters
5.8.1 Introduction
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5.8.2 Method of variation of parameters
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5.8.3 Solved Problem 1
Video
6:48
5.8.3 Quiz
Exercise
5.8.4 Solved Problem 2
Video
7:42
5.8.4 Quiz
Exercise
5.8.5 Solved Problem 3
Video
10:13
5.8.5 Quiz
Exercise
5.8.6 Solved problem 4
PDF
5.8.7 Solved problem 5
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5.8.8 Solved problem 6
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5.8.9 Solved problem 7
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5.8.10 Solved problem 8
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5.8.11 Exercises
PDF
Course Instructor
Promath
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