Calculus, Multivariable Calculus & Linear Algebra - VISTAS
Course Instructor
Promath
To enroll in this course, please contact the Admin
/CourseBundles(46865)/3264578-Vels_m1_Civil.png)
Course Overview
Schedule of Classes
Course Curriculum
5 Subjects
Unit - I: Calculus I (VelsM1CIVIL)
4 Exercises • 105 Learning Materials
1.1 Radius of curvature in cartesian coordinates
1.1.1 Introduction.pdf
PDF
1.1.2 Radius of curvature
PDF
1.1.3 Cartesian formula for radius of curvature
PDF
1.1.4 Solved Problems
PDF
1.1.5 Solved problem 1
Video
6:8
1.1.6 Solved problem 2
Video
10:11
1.1.7 Solved problem 3
Video
4:42
1.1.8 Solved problem 4 and 5
PDF
1.1.9 Solved problem 6
PDF
1.1.10 Solved problem 7
PDF
1.1.11 Solved problem 8
PDF
1.1.12 Solved problem 9
PDF
1.1.13 Solved problem 10
PDF
1.1.14 Solved problem 11
PDF
1.1.15 Solved problem 12
PDF
1.1.16 Solved problem 13
PDF
1.17 Solved problem 14
PDF
1.18 Exercises
PDF
1.2 Radius of curvature in parametric co-ordinates
1.2.1 Introduction
PDF
1.2.2 Solved Problem 1
Video
9:42
1.2.3 Solved Problem 2
Video
8:20
1.2.4 Solved Problem 3
PDF
1.2.5 Solved Problem 4
PDF
1.2.6 Solved Problem 5
PDF
1.2.7 Solved Problem 6
PDF
1.2.8 Exercises
PDF
1.3 Radius of curvature in polar co-ordinates
1.3.1 Introduction
PDF
1.3.2 Solved Problem 1
Video
7:12
1.3.3 Solved Problem 2
Video
5:57
1.3.4 Solved Problem 3
Video
7:25
1.3.5 Solved Problem 4
PDF
1.3.6 Solved Problem 5
PDF
1.3.7 Solved Problem 6
PDF
1.3.8 Exercises
PDF
1.4 Circle of curvature
1.4.1 Introduction
PDF
1.4.2 Chord of curvature through the origin
PDF
1.4.3 Solved Problem 1
Video
5:10
1.4.4 Solved Problem 2
Video
5:28
1.4.5 Solved Problem 3
Video
8:27
1.4.6 Solved Problem 4
Video
4:28
1.4.7 Solved Problem 5
PDF
1.4.8 Solved Problem 6
PDF
1.4.9 Exercises
PDF
1.5 Evolute
1.5.1 Introduction
PDF
1.5.2 Solved Problem 1
Video
9:20
1.5.3 Solved Problem 2
Video
9:20
1.5.4 Solved Problem 3
PDF
1.5.5 Solved Problem 4
PDF
1.5.6 Solved Problem 5
PDF
1.5.7 Exercises
PDF
1.6 Envelopes
1.6.1 Introduction
PDF
1.6.2 Method-I
PDF
1.6.3 Method-II
PDF
1.6.4 Method-III
PDF
1.6.5 Solved Problem 1
Video
5:6
1.6.6 Solved Problem 2
Video
3:13
1.6.7 Solved Problem 3
Video
5:47
1.6.8 Solved Problem 4
Video
6:27
1.6.9 Solved Problem 5
PDF
1.6.10 Solved Problem 6
PDF
1.6.11 Solved Problem 7
PDF
1.6.12 Solved Problem 8
PDF
1.6.13 Solved Problem 9
PDF
1.6.14 Solved Problem 10
PDF
1.6.15 Solved Problem 11
PDF
1.6.16 Solved Problem 12
PDF
1.6.17 Solved Problem 13
PDF
1.6.18 Solved Problem 14
PDF
1.6.19 Solved Problem 15
PDF
1.6.20 Solved Problem 16
PDF
1.6.21 Exercises
PDF
1.7 Definite Integral
1.7.1 Introduction
Video
6:11
1.7.2 The area problem
PDF
1.7.3 The Definite Integral
PDF
1.7.4 Standard formulae
PDF
1.7.5 Applications
PDF
1.7.6 Solved Problem 1
Video
2:43
1.7.6 Quiz
Exercise
1.7.7 Solved Problem 2
Video
2:47
1.7.7 Quiz
Exercise
1.7.8 Solved Problem 3
Video
3:20
1.7.8 Quiz
Exercise
1.7.9 Solved problem 4
PDF
1.7.10 Solved problem 5
PDF
1.7.11 Solved problem 6
PDF
1.7.12 Solved problem 7
PDF
1.7.13 Solved problem 8
PDF
1.7.14 Solved problem 9
PDF
1.7.15 Exercises
Exercise
1.8 Improper Integrals
1.8.1 Improper Integrals
PDF
1.8.2 I. Definition of an Improper Integral of Type I
PDF
1.8.3 II. Definition of an Improper Integral of Type II
PDF
1.8.4 Examples of Infinite limits of Integration
PDF
1.8.5 Solved Problem 1
Video
2:00
1.8.6 Solved Problem 2
Video
3:7
1.8.7 Solved Problem 3
Video
3:18
1.8.8 Solved Problem 4
Video
3:4
1.8.9 Solved Problem 5
Video
3:19
1.8.10 Solved problem 6
PDF
1.8.11 Solved problem 7
PDF
1.8.12 Solved problem 8
PDF
1.8.13 Solved problem 9
PDF
1.8.14 Solved problem 10
PDF
1.8.15 Solved problem 11
PDF
1.8.16 Solved problem 12
PDF
1.8.17 III. A comparison test for improper integrals
PDF
1.8.18 Solved problem 13
PDF
1.8.19 Solved problem 14
PDF
1.8.20 Exercises
PDF
Unit - II: Calculus II (VelsM1CIVIL)
56 Learning Materials
2.1 Rolle’s Mean value Theorem
2.1.1 Introduction
PDF
2.1.2 Solved Problem 1
Video
4:52
2.1.3 Solved Problem 2
Video
6:14
2.1.4 Solved Problem 3
PDF
2.1.5 Solved Problem 4
PDF
2.1.6 Solved Problem 5
PDF
2.1.7 Solved Problem 6
PDF
2.1.8 Exercises
PDF
2.2 Taylor's and Maclaurin's theorems
2.2.1 Introduction
PDF
2.2.2 Maclaurin's series expansion of some elementary functions
PDF
2.2.3 Solved Problem 1
Video
8:53
2.2.4 Solved Problem 2
Video
10:13
2.2.5 Solved Problem 3
PDF
2.2.6 Solved Problem 4
PDF
2.2.7 Solved Problem 5
PDF
2.2.8 Solved Problem 6
PDF
2.2.9 Solved Problem 7
PDF
2.2.10 Solved Problem 8
PDF
2.2.11 Solved Problem 9
PDF
2.2.12 Solved Problem 10
PDF
2.2.13 Solved Problem 11
PDF
2.2.14 Solved Problem 12
PDF
2.2.15 Solved Problem 13
PDF
2.2.16 Exercises
PDF
2.3 Indeterminate forms
2.3.1 Introduction
PDF
2.3.2 Indeterminate forms of the type
PDF
2.3.3 Solved Problem 1
Video
12:14
2.3.4 Solved Problem 2
Video
11:42
2.3.5 Solved Problem 3
PDF
2.3.6 Solved Problem 4
PDF
2.3.7 Solved Problem 5
PDF
2.3.8 Solved Problem 6
PDF
2.3.9 Solved Problem 7
PDF
2.3.10 Solved Problem 8
PDF
2.3.11 Solved Problem 9
PDF
2.3.12 Solved Problem 10
PDF
2.3.13 Solved Problem 11
PDF
2.3.14 Solved Problem 12
PDF
2.3.15 Solved Problem 13
PDF
2.3.16 Solved Problem 14
PDF
2.3.17 Solved Problem 15
PDF
2.3.18 Solved Problem 16
PDF
2.3.19 Solved Problem 17
PDF
2.3.20 Solved Problem 18
PDF
2.3.21 Solved Problem 19
PDF
2.3.22 Solved Problem 20
PDF
2.3.23 Solved Problem 21
PDF
2.3.24 Solved Problem 22
PDF
2.3.25 Solved Problem 23
PDF
2.3.26 Solved Problem 24
PDF
2.3.27 Solved Problem 25
PDF
2.3.28 Solved Problem 26
PDF
2.3.29 Solved Problem 27
PDF
2.3.30 Solved Problem 28
PDF
2.3.31 Solved Problem 29
PDF
2.3.32 Exercises
PDF
Unit - III: Sequences and series (VelsM1CIVIL)
41 Learning Materials
3.1 Sequences
3.1.1 Introduction.pdf
PDF
3.1.2 Operation on Sequence
PDF
3.1.3 Convergence, Divergence and Oscillation of a Sequence
PDF
3.1.4 Solved Problem 1
Video
3:48
3.1.5 Solved Problem 2
Video
4:30
3.1.6 Solved Problem 3
PDF
3.1.7 Solved Problem 4
PDF
3.1.8 Solved Problem 5
PDF
3.1.9 Exercises
PDF
3.2 Infinite series
3.2.1 Introduction
PDF
3.2.2 Properties of series
PDF
3.2.3 Necessary condition for convergence of a series
PDF
3.2.4 Series with positive terms
PDF
3.2.5 Solved Problem 1
Video
3:23
3.2.6 Solved Problem 2
Video
4:25
3.2.7 Solved Problem 3
Video
1:47
3.2.8 Solved Problem 4
PDF
3.2.9 Exercises
PDF
3.3 Comparison test
3.3.1 Introduction
PDF
3.3.2 Solved Problem 1
Video
5:9
3.3.3 Solved Problem 2
Video
5:3
3.3.4 Solved Problem 3
PDF
3.3.5 Solved Problem 4
PDF
3.3.6 Solved Problem 5
PDF
3.3.7 Solved Problem 6
PDF
3.3.8 Solved Problem 7
PDF
3.3.9 Solved Problem 8
PDF
3.3.10 Exercises
PDF
3.4 Integral test
3.4.1 Introduction
PDF
3.4.2 Solved Problem 1
Video
4:5
3.4.3 Solved Problem 2
Video
4:48
3.4.4 Solved Problem 3
Video
4:26
3.4.5 Solved Problem 4
PDF
3.4.6 Solved Problem 5
PDF
3.4.7 Exercises
PDF
3.5 Logarithmic test
3.5.1 Introduction
PDF
3.5.2 Solved Problem 1
Video
9:7
3.5.3 Solved Problem 2
Video
6:19
3.5.4 Solved Problem 3
Video
10:52
3.5.5 Solved Problem 4
PDF
3.5.6 Exercises
PDF
Unit - IV: Multivariable Calculus (VelsM1CIVIL)
42 Exercises • 97 Learning Materials
4.1 Function of two or more variable
4.1.1 Introduction
PDF
4.1.2 Limit
PDF
4.1.3 Continuity
PDF
4.1.4 Solved Problem 1
Video
3:25
4.1.4 Quiz
Exercise
4.1.5 Solved Problem 2
Video
6:14
4.1.5 Quiz
Exercise
4.1.6 Solved Problem 3
PDF
4.1.7 Solved Problem 4
PDF
4.1.8 Solved Problem 5
PDF
4.1.9 Solved Problem 6
PDF
4.1.10 Solved Problem 7
PDF
4.1.11 Exercise
PDF
4.2 Partial Differentiation
4.2.1 Introduction
PDF
4.2.2 Solved Problem 1
Video
000
4.2.2 Quiz
Exercise
4.2.3 Solved Problem 2
Video
000
4.2.3 Quiz
Exercise
4.2.4 Solved Problem 3
Video
000
4.2.4 Quiz
Exercise
4.2.5 Solved Problem 4
PDF
4.2.6 Solved Problem 5
PDF
4.2.7 Solved Problem 6
PDF
4.2.8 Solved Problem 7
PDF
4.2.9 Solved Problem 8
PDF
4.2.10 Solved Problem 9
PDF
4.2.11 Exercises
PDF
4.3 Maxima and minima of functions of two variables
4.3.1 Introduction
PDF
4.3.2 Solved Problem 1
Video
9:7
4.3.2 Quiz
Exercise
4.3.3 Solved Problem 2
Video
17:17
4.3.3 Quiz
Exercise
4.3.4 Solved Problem 3
Video
12:24
4.3.4 Quiz
Exercise
4.3.5 Solved Problem 4
PDF
4.3.6 Solved Problem 5
PDF
4.3.7 Solved Problem 6
PDF
4.3.8 Solved Problem 7
PDF
4.3.9 Solved Problem 8
PDF
4.3.10 Solved Problem 9
PDF
4.3.11 Solved Problem 10
PDF
4.3.12 Solved Problem 11
PDF
4.3.13 Exercises
PDF
4.4 Lagrange's method of undetermined multipliers
4.4.1 Introduction
PDF
4.4.2 Solved Problem 1
Video
9:50
4.4.2 Quiz
Exercise
4.4.3 Solved Problem 2
Video
10:25
4.4.3 Quiz
Exercise
4.4.4 Solved Problem 3
Video
7:55
4.4.4 Quiz
Exercise
4.4.5 Solved Problem 4
PDF
4.4.6 Solved Problem 5
PDF
4.4.7 Exercises
PDF
4.5 Double Integrals
4.5.1 Introduction
PDF
4.5.2 Applications of Multiple Integral in Engineering
PDF
4.5.3 Evaluation of Double Integration in Cartesian Coordinates
PDF
4.5.4 Evaluation of Double Integration in Polar Coordinates
PDF
4.5.5 Properties of Double integrals
PDF
4.5.6 Problem based on Cartesian Form
Video
2:46
4.5.6 Quiz
Exercise
4.5.7 Solved problem 2
Video
5:13
4.5.7 Quiz
Exercise
4.5.8 Solved problem 3
Video
2:30
4.5.8 Quiz
Exercise
4.5.9 Solved problem 4
PDF
4.5.10 Solved problem 5
PDF
4.5.11 Problem based on Region Given
Video
5:36
4.5.11 Quiz
Exercise
4.5.12 Solved problem 7
PDF
4.5.13 Solved problem 8
PDF
4.5.14 Solved problem 9
PDF
4.5.15 Problem based on Polar Form
Video
2:49
4.5.15 Quiz
Exercise
4.5.16 Solved problem 11
Video
3:49
4.5.16 Quiz
Exercise
4.5.17 Solved problem 12
PDF
4.5.18 Exercises
Exercise
4.6 Triple Integrals
4.6.1 Triple integrals
PDF
4.6.2 Problem based on Cartesian Form
Video
4:41
4.6.2 Quiz
Exercise
4.6.3 Solved problem 2
Video
3:40
4.6.3 Quiz
Exercise
4.6.4 Solved problem 3
PDF
4.6.5 Solved problem 4
PDF
4.6.6 Solved problem 5
PDF
4.6.7 Problem based on Region Given
Video
4:40
4.6.7 Quiz
Exercise
4.6.8 Solved problem 7
PDF
4.6.9 Solved Problem 8
Video
4:19
4.6.9 Quiz
Exercise
4.6.10 Exercises
Exercise
4.7 Greens Theorem
4.7.1 Introduction
PDF
4.7.2 Solved Problem 1
Video
6:50
4.7.2 Quiz
Exercise
4.7.3 Solved Problem 2
Video
12:6
4.7.3 Quiz
Exercise
4.7.4 Solved Problem 3
Video
8:55
4.7.4 Quiz
Exercise
4.7.5 Solved Problem 4
Video
9:41
4.7.5 Quiz
Exercise
4.7.6 Solved Problem 5
Video
7:50
4.7.6 Quiz
Exercise
4.7.7 Solved Problem 6
PDF
4.7.8 Solved Problem 7
PDF
4.7.9 Solved Problem 8
PDF
4.7.10 Exercises
PDF
4.8 Gauss Divergence Theorem
4.8.1 Introduction
PDF
4.8.2 Solved Problem 1
Video
15:7
4.8.2 Quiz
Exercise
4.8.3 Solved Problem 2
Video
5:24
4.8.3 Quiz
Exercise
4.8.4 Solved Problem 3
Video
4:15
4.8.4 Quiz
Exercise
4.8.5 Solved Problem 4
Video
6:53
4.8.5 Quiz
Exercise
4.8.6 Solved Problem 5
Video
13:58
4.8.6 Quiz
Exercise
4.8.7 Solved Problem 6
Video
8:16
4.8.7 Quiz
Exercise
4.8.8 Solved Problem 7
Video
10:21
4.8.8 Quiz
Exercise
4.8.9 Solved Problem 8
PDF
4.8.10 Exercises
PDF
4.9 Stokes Theorem
4.9.1 Introduction
PDF
4.9.2 Solved Problem 1
Video
10:3
4.9.2 Quiz
Exercise
4.9.3 Solved Problem 2
Video
9:19
4.9.3 Quiz
Exercise
4.9.4 Solved Problem 3
Video
14:11
4.9.4 Quiz
Exercise
4.9.5 Solved Problem 4
Video
7:31
4.9.5 Quiz
Exercise
4.9.6 Solved Problem 5
Video
6:45
4.9.6 Quiz
Exercise
4.9.7 Solved Problem 6
Video
6:38
4.9.7 Quiz
Exercise
4.9.8 Solved Problem 7
Video
8:35
4.9.8 Quiz
Exercise
4.9.10 Exercises
PDF
Unit - V: Matrices (VelsM1CIVIL)
24 Exercises • 111 Learning Materials
5.1 Matrix Introduction
5.1.1 Introduction
PDF
5.1.2 Key Concepts
PDF
5.1.3 Types of matrices
PDF
5.1.4 Types of matrices
PDF
5.1.5 Application of matrices
PDF
5.1.6 Solved Problem 1
Video
8:4
5.1.7 Solved Problem 2
Video
2:11
5.1.8 Solved Problem 3
Video
4:39
5.1.9 Solved Problem 4
Video
3:8
5.1.10 Solved Problem 5
Video
5:13
5.2 Real matrices: Symmetric, skew – symmetric, orthogonal
5.2.1 Types of Real Matrices
PDF
5.2.2 Orthogonal Matrix
PDF
5.2.3 Solved Problem 1
Video
3:12
5.2.4 Solved Problem 2
Video
2:50
5.2.5 Solved Problem 3
Video
3:58
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
PDF
5.2.11 Solved Problem 9
PDF
5.2.12 Solved Problem 10
PDF
5.2.13 Exercises
PDF
5.3 Complex matrices: Hermitian, Skew - Hermitian, Unitary Matrices
5.3.1 Complex matrices
PDF
5.3.2 Solved Problem 1
Video
5:27
5.3.3 Solved Problem 2
Video
3:34
5.3.4 Solved Problem 3
PDF
5.3.5 Solved Problem 4
PDF
5.3.6 Solved Problem 5
PDF
5.3.7 Solved Problem 6
PDF
5.3.8 Solved Problem 7
PDF
5.3.9 Solved Problem 8
PDF
5.3.10 Solved Problem 9
PDF
5.3.11 Solved Problem 10
PDF
5.3.12 Solved Problem 11
PDF
5.3.13 Exercises
PDF
5.4 Rank of a matrix (Echelon form)
5.4.1 Introduction
PDF
5.4.2 Rank of Matrix
PDF
5.4.3 Elementary transformations
PDF
5.4.4 Echelon form or Triangular form of a matrix
PDF
5.4.5 Solved Problem 1
Video
6:38
5.4.6 Solved Problem 2
Video
5:35
5.4.7 Solved Problem 3
PDF
5.4.8 Solved Problem 4
PDF
5.4.9 Solved Problem 5
PDF
5.4.10 Solved Problem 6
PDF
5.4.11 Solved Problem 7
PDF
5.4.12 Solved Problem 8
PDF
5.4.13 Exercises
PDF
5.5 Characteristic equation
5.5.1 Eigen values and Eigen vectors
PDF
5.5.2 Applications Eigenvalues and Eigenvectors in Engineering
PDF
5.5.3 Characteristic equation
PDF
5.5.4 Solved problem 1
Video
2:15
5.5.4 Quiz
Exercise
5.5.5 Solved problem 2
Video
4:9
5.5.5 Quiz
Exercise
5.5.6 Solved problem 3
PDF
5.5.7 Solved problem 4
PDF
5.5.8 Exercises
Exercise
5.6 Eigen values and Eigen vectors of a matrix
5.6.1 Introduction
PDF
5.6.2 Eigen vectors
PDF
5.6.3 Solved problem 1
Video
12:41
5.6.3 Quiz
Exercise
5.6.4 Solved problem 2
PDF
5.6.5 Solved problem 3
Video
11:48
5.6.5 Quiz
Exercise
5.6.6 Solved problem 4
PDF
5.6.7 Solved problem 5
PDF
5.6.8 Solved problem 6
Video
12:35
5.6.8 Quiz
Exercise
5.6.9 Solved problem 7
PDF
5.6.10 Solved problem 8
PDF
5.6.11 Solved problem 9
PDF
5.6.12 Solved problem 10
PDF
5.6.13 Solved problem 11
Video
11:57
5.6.13 Quiz
Exercise
5.6.14 Exercises
Exercise
5.7 Properties of Eigen values and Eigen vectors
5.7.1 Introduction
PDF
5.7.2 Properties of Eigen values
PDF
5.7.3 Solved Problem 1
Video
1:53
5.7.3 Quiz
Exercise
5.7.4 Solved problem 2
PDF
5.7.5 Solved problem 3
Video
1:58
5.7.5 Quiz
Exercise
5.7.6 Solved problem 4
PDF
5.7.7 Solved problem 5
PDF
5.7.8 Solved problem 6
Video
1:45
5.7.8 Quiz
Exercise
5.7.9 Solved problem 7
PDF
5.7.10 Solved problem 8
Video
2:45
5.7.10 Quiz
Exercise
5.7.11 Solved problem 9
PDF
5.7.12 Solved problem 10
PDF
5.7.13 Solved problem 11
Video
2:34
5.7.13 Quiz
Exercise
5.7.14 Solved problem 12
PDF
5.7.15 Solved problem 13
PDF
5.7.16 Solved problem 14
PDF
5.7.17 Properties of Eigen vectors
PDF
5.7.18 Exercises
Exercise
5.8 Cayley - Hamilton Theorem
5.8.1 Introduction
PDF
5.8.2 Solved problem 1
Video
10:15
5.8.2 Quiz
Exercise
5.8.3 Solved problem 2
Video
8:7
5.8.3 Quiz
Exercise
5.8.4 Solved problem 3
Video
7:26
5.8.4 Quiz
Exercise
5.8.5 Solved problem 4
PDF
5.8.6 Solved problem 5
PDF
5.8.7 Solved problem 6
PDF
5.8.8 Solved problem 7
PDF
5.8.9 Solved problem 8
PDF
5.8.10 Solved problem 9
PDF
5.8.11 Solved problem 10
PDF
5.8.12 Exercises
Exercise
5.9 Diagonalisation of matrix (Similarity Transformation)
5.9.1 Introduction
PDF
5.9.2 Applications of Diagonalization of a Matrix in Engineering
PDF
5.9.3 Solved problem 1
Video
18:33
5.9.3 Quiz
Exercise
5.9.4 Solved problem 2
Video
15:16
5.9.4 Quiz
Exercise
5.9.5 Solved problem 3
PDF
5.9.6 Solved problem 4
PDF
5.9.7 Solved problem 5
PDF
5.9.8 Exercises
PDF
5.10 Diagonalisation of matrix (Orthogonal Transformation)
5.10.1 Introduction
PDF
5.10.2 Solved problem 1
Video
16:34
5.10.2 Quiz
Exercise
5.10.3 Solved problem 2
Video
17:48
5.10.3 Quiz
Exercise
5.10.4 Solved problem 3
Video
21:48
5.10.4 Quiz
Exercise
5.10.5 Solved problem 4
PDF
5.10.6 Solved problem 5
PDF
5.10.7 Exercises
Exercise
Course Instructor
Promath
787 Courses • 165783 Students
By clicking on Continue, I accept the Terms & Conditions,
Privacy Policy & Refund Policy