Fundamentals of Mathematics - VISTAS
Course Instructor
Promath
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Course Overview
Schedule of Classes
Course Curriculum
5 Subjects
Unit - I: Matrices (VelsM1Biotech)
68 Learning Materials
1.1 Matrix Introduction
1.1.1 Introduction
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1.1.2 Key Concepts
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1.1.3 Types of matrices
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1.1.4 Types of matrices
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1.1.5 Application of matrices
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1.1.6 Solved Problem 1
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8:4
1.1.7 Solved Problem 2
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2:11
1.1.8 Solved Problem 3
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4:39
1.1.9 Solved Problem 4
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3:8
1.1.10 Solved Problem 5
Video
5:13
1.2 Real matrices: Symmetric, skew – symmetric, orthogonal
1.2.1 Types of Real Matrices
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1.2.2 Orthogonal Matrix
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1.2.3 Solved Problem 1
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3:12
1.2.4 Solved Problem 2
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2:50
1.2.5 Solved Problem 3
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3:58
1.2.6 Solved Problem 4
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1.2.7 Solved Problem 5
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1.2.8 Solved Problem 6
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1.2.9 Solved Problem 7
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1.2.10 Solved Problem 8
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1.2.11 Solved Problem 9
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1.2.12 Solved Problem 10
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1.2.13 Exercises
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1.3 Complex matrices: Hermitian, Skew - Hermitian, Unitary Matrices
1.3.1 Complex matrices
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1.3.2 Solved Problem 1
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5:27
1.3.3 Solved Problem 2
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3:34
1.3.4 Solved Problem 3
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1.3.5 Solved Problem 4
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1.3.6 Solved Problem 5
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1.3.7 Solved Problem 6
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1.3.8 Solved Problem 7
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1.3.9 Solved Problem 8
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1.3.10 Solved Problem 9
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1.3.11 Solved Problem 10
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1.3.12 Solved Problem 11
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1.3.13 Exercises
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1.4 Rank of a matrix (Echelon form)
1.4.1 Introduction
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1.4.2 Rank of Matrix
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1.4.3 Elementary transformations
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1.4.4 Echelon form or Triangular form of a matrix
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1.4.5 Solved Problem 1
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6:38
1.4.6 Solved Problem 2
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5:35
1.4.7 Solved Problem 3
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1.4.8 Solved Problem 4
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1.4.9 Solved Problem 5
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1.4.10 Solved Problem 6
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1.4.11 Solved Problem 7
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1.4.12 Solved Problem 8
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1.4.13 Exercises
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1.5 Consistency of Non-Homogenous Linear Equations
1.5.1 Introduction
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1.5.2 Working Procedure
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1.5.3 Solved Problem 1
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10:19
1.5.4 Solved Problem 2
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7:32
1.5.5 Solved Problem 3
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7:20
1.5.6 Solved Problem 4
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1.5.7 Solved Problem 5
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1.5.8 Solved Problem 6
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1.5.9 Solved Problem 7
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1.5.10 Solved Problem 8
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1.5.11 Solved Problem 9
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1.5.12 Exercises
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1.6 Consistency of Homogenous Linear Equations
1.6.1 Introduction
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1.6.2 Working Rule for finding the solutions of the equation AX=0
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1.6.3 Solved Problem 1
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7:13
1.6.4 Solved Problem 2
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8:48
1.6.5 Solved Problem 3
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1.6.6 Solved Problem 4
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1.6.7 Exercises
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Unit - II: Differential Calculus (VelsM1Biotech)
8 Exercises • 69 Learning Materials
2.1 Function of two or more variable
2.1.1 Introduction
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2.1.2 Limit
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2.1.3 Continuity
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2.1.4 Solved Problem 1
Video
3:25
2.1.4 Quiz
Exercise
2.1.5 Solved Problem 2
Video
6:14
2.1.5 Quiz
Exercise
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 Solved Problem 6
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2.1.10 Solved Problem 7
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2.1.11 Exercise
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2.2 Derivatives
2.2.1 Introduction.pdf
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2.2.2 Solved Problem 1.mp4
Video
4:29
2.2.3 Solved Problem 2.mp4
Video
2:37
2.2.4 Solved Problem 3.pdf
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2.2.5 Solved Problem 4.pdf
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2.2.6 Solved Problem 5.pdf
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2.2.7 Exercises.pdf
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2.3 Total Derivative
2.3.1 Introduction
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2.3.2 Solved Problem 1
Video
000
2.3.2 Quiz
Exercise
2.3.3 Solved Problem 2
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000
2.3.3 Quiz
Exercise
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 Partial Differentiation of Implicit Functions
2.4.1 Introduction
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2.4.2 Implicit function of three variables
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2.4.3 Solved Problem 1
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000
2.4.3 Quiz
Exercise
2.4.4 Solved Problem 2
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2.4.5 Solved Problem 3
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2.4.6 Solved Problem 4
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2.4.7 Solved Problem 5
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2.4.8 Solved Problem 6
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2.4.9 Solved Problem 7
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2.4.10 Exercises
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2.5 Radius of curvature in cartesian coordinates
2.5.1 Introduction.pdf
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2.5.2 Radius of curvature
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2.5.3 Cartesian formula for radius of curvature
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2.5.4 Solved Problem problems
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2.5.5 Solved problem 1
Video
6:8
2.5.6 Solved problem 2
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10:10
2.5.7 Solved problem 3
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4:42
2.5.8 Solved problem 4 and 5
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2.5.9 Solved problem 6
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2.5.10 Solved problem 7
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2.5.11 Solved problem 8
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2.5.12 Solved problem 9
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2.5.13 Solved problem 10
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2.5.14 Solved problem 11
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2.5.15 Solved problem 12
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2.5.16 Solved problem 13
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2.5.17 Solved problem 14
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2.5.18 Exercises
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2.6 Maxima and minima of functions of two variables
2.6.1 Introduction
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2.6.2 Solved Problem 1
Video
9:6
2.6.2 Quiz
Exercise
2.6.3 Solved Problem 2
Video
17:16
2.6.3 Quiz
Exercise
2.6.4 Solved Problem 3
Video
12:23
2.6.4 Quiz
Exercise
2.6.5 Solved Problem 4
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2.6.6 Solved Problem 5
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2.6.7 Solved Problem 6
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2.6.8 Solved Problem 7
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2.6.9 Solved Problem 8
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2.6.10 Solved Problem 9
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2.6.11 Solved Problem 10
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2.6.12 Solved Problem 11
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2.6.13 Exercises
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Unit - III: Integral Calculus (VelsM1Biotech)
14 Exercises • 66 Learning Materials
3.1 Definite Integral
3.1.1 Introduction
Video
6:11
3.1.2 The area problem
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3.1.3 The Definite Integral
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3.1.4 Standard formulae
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3.1.5 Applications
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3.1.6 Solved Problem 1
Video
2:43
3.1.6 Quiz
Exercise
3.1.7 Solved Problem 2
Video
2:47
3.1.7 Quiz
Exercise
3.1.8 Solved Problem 3
Video
3:20
3.1.8 Quiz
Exercise
3.1.9 Solved problem 4
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3.1.10 Solved problem 5
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3.1.11 Solved problem 6
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3.1.12 Solved problem 7
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3.1.13 Solved problem 8
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3.1.14 Solved problem 9
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3.1.15 Exercises
Exercise
3.2 Properties of Definite Integral
3.2.1 Properties of Definite Integral
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3.2.2 Applications
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3.2.3 Solved Problem 1
Video
4:10
3.2.3 Quiz
Exercise
3.2.4 Solved Problem 2
Video
4:12
3.2.4 Quiz
Exercise
3.2.5 Solved Problem 3
Video
3:49
3.2.5 Quiz
Exercise
3.2.6 Solved Problem 4
Video
3:22
3.2.6 Quiz
Exercise
3.2.7 Solved problem 5
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3.2.8 Solved problem 6
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3.2.9 Solved problem 7
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3.2.10 Solved problem 8
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3.2.11 Solved problem 9
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3.2.12 Solved problem 10
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3.2.13 Exercises
Exercise
3.3 Integration by Parts
3.3.1 Integration by parts
Video
5:27
3.3.2 Bernoullis formula for Integration by parts
Video
6:40
3.3.3 Why we need Integration by Parts
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3.3.4 Applications
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3.3.5 Solved Problem 1
Video
3:33
3.3.5 Quiz
Exercise
3.3.6 Solved Problem 2
Video
3:33
3.3.6 Quiz
Exercise
3.3.7 Solved Problem 3
Video
5:45
3.3.7 Quiz
Exercise
3.3.8 Solved Problem 4
Video
6:45
3.3.8 Quiz
Exercise
3.3.9 Type I - Problems on Integration by Parts - Solved Problem 1
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3.3.10 Solved Problem 2
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3.3.11 Solved Problem 3
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3.3.12 Solved Problem 4
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3.3.13 Solved Problem 5
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3.3.14 Solved Problem 6
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3.3.15 Solved Problem 7
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3.3.16 Solved Problem 8
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3.3.17 Type II - Problems on Bernoulli's Formula - Solved Problem 9
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3.3.18 Solved Problem 10
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3.3.19 Reduction Formula
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3.3.20 Type III - Problems on Reduction Formula - Solved Problem 11
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3.3.21 Solved Problem 12
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3.3.22 Exercises
Exercise
3.4 Integration of rational functions by partial fraction
3.4.1 Integration of Rational functions by partial fraction
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3.4.2 Applications
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3.4.3 Solved Problem 1
Video
5:27
3.4.4 Solved Problem 2
Video
3:52
3.4.5 Solved Problem 3
Video
5:15
3.4.6 Solved Problem 4
Video
9:5
3.4.7 Solved Problem 5
Video
4:34
3.4.8 Type 1 Solved problem 6
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3.4.9 Solved problem 7
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3.4.10 Type 2 Solved problem 8
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3.4.11 Solved problem 9
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3.4.12 Type 3 Solved problem 10
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3.4.13 Solved problem 11
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3.4.14 Type 4 Solved problem 12
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3.4.15 Solved problem 13
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3.4.16 Solved problem 14
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3.4.17 Solved problem 15
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3.4.18 Solved problem 16
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3.4.19 Exercises
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Unit - IV: Linear Ordinary Differential Equations (VelsM1Biotech)
22 Exercises • 67 Learning Materials
4.1 Linear Differential Equations of Higher Order
4.1.1 What is Ordinary Differential Equations?
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4.1.2 What are the applications of higher order ODEs in Engineering?
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4.1.3 Linear differential equations of higher order
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4.1.4 Operator D
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4.1.5 To find the General solution of f(D)y = 0
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4.1.6 Solved Problem 1
Video
5:39
4.1.6 Quiz
Exercise
4.1.7 Solved Problem 2
Video
3:32
4.1.7 Quiz
Exercise
4.1.8 Solved Problem 3
Video
3:53
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 Solved problem 6
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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 Solved problem 10
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4.1.16 Solved problem 11
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4.1.17 Solved problem 12
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4.1.18 Exercises
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4.2 General solution of f(D)y = e^ax
4.2.1 Particular Integral of f(D)y = e^ax
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4.2.2 Solved Problem 1
Video
4:56
4.2.2 Quiz
Exercise
4.2.3 Solved Problem 2
Video
3:34
4.2.3 Quiz
Exercise
4.2.4 Solved Problem 3
Video
4:47
4.2.4 Quiz
Exercise
4.2.5 Solved Problem 4
Video
6:17
4.2.5 Quiz
Exercise
4.2.6 Solved Problem 5
Video
6:33
4.2.6 Quiz
Exercise
4.2.7 Solved problem 6
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4.2.8 Solved problem 7
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4.2.9 Solved problem 8
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4.2.10 Solved problem 9
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4.2.11 Solved problem 10
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4.2.12 Exercises
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4.3 General solution of f(D)y = cos ax or sin ax
4.3.1 Particular Integral of f(D) = cosax or sinax
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4.3.2 Working rule
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4.3.3 Solved Problem 1
Video
6:26
4.3.3 Quiz
Exercise
4.3.4 Solved Problem 2
Video
5:22
4.3.4 Quiz
Exercise
4.3.5 Solved Problem 3
Video
6:24
4.3.5 Quiz
Exercise
4.3.6 Solved Problem 4
Video
6:47
4.3.6 Quiz
Exercise
4.3.7 Solved Problem 5
Video
5:6
4.3.7 Quiz
Exercise
4.3.8 Solved Problem 6
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4.3.9 Solved Problem 7
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4.3.10 Solved Problem 8
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4.3.11 Exercises
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4.4 General solution of f(D)y = x^m
4.4.1 Particular Integral of f(D)y = xm
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4.4.2 Solved Problem 1
Video
5:42
4.4.2 Quiz
Exercise
4.4.3 Solved Problem 2
Video
6:7
4.4.3 Quiz
Exercise
4.4.4 Solved Problem 3
Video
8:25
4.4.4 Quiz
Exercise
4.4.5 Solved problem 4
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4.4.6 Solved problem 5
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4.4.7 Solved problem 6
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4.4.8 Solved problem 7
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4.4.9 Solved Problem 8
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4.4.10 Exercises
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4.5 General solution of f(D)y = e^ax . f(x)
4.5.1 Particular Integral of f(D)y = e^ax f(x)
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4.5.2 Solved Problem 1
Video
7:16
4.5.2 Quiz
Exercise
4.5.3 Solved Problem 2
Video
9:52
4.5.3 Quiz
Exercise
4.5.4 Solved Problem 3
Video
10:19
4.5.4 Quiz
Exercise
4.5.5 Solved Problem 4
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4.5.6 Solved Problem 5
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4.5.7 Exercise
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4.6 General solution of f(D)y = x^m . f(x)
4.6.1 Particular integral = xm sinax or xm cosax
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4.6.2 Solved Problem 1
Video
8:20
4.6.2 Quiz
Exercise
4.6.3 Solved Problem 2
Video
8:00
4.6.3 Quiz
Exercise
4.6.4 Solved Problem 3
Video
7:56
4.6.4 Quiz
Exercise
4.6.5 Solved Problem 4
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4.6.6 Solved Problem 5
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4.6.7 Solved Problem 6
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4.6.8 Solved Problem 7
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4.6.9 Exercises
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Unit - V: Vector Algebra (Upcoming) (VelsM1Biotech)
Course Instructor
Promath
787 Courses • 165783 Students
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