CoursesGhar Com - Fundamentals of Mathematics

1. 1. Introduction/1. Introduction.mp47.52MB
2. 10. SET OPERATIONS - Venn Diagrams - Problems Solutions/1. Verify the Union & Integral of Difference sets with the help of Venn Diagrams.mp468.11MB
3. 11. NUMBER SYSTEM - Real Numbers - Addition Laws/1. Closure Law of Addition. Give an example and Verify it mathematically.mp418.41MB
4. 11. NUMBER SYSTEM - Real Numbers - Addition Laws/2. Commutative Law of Addition. Give an example and Verify it mathematically.mp410.48MB
5. 11. NUMBER SYSTEM - Real Numbers - Addition Laws/3. Associative Law of Addition. Give an example and Verify it mathematically.mp414.47MB
6. 11. NUMBER SYSTEM - Real Numbers - Addition Laws/4. Additive Identity Law of Addition. Give an example and Verify it mathematically.mp418.86MB
7. 11. NUMBER SYSTEM - Real Numbers - Addition Laws/5. Additive Inverse Law of Addition. Give an example and Verify it mathematically.mp418.73MB
8. 12. NUMBER SYSTEM - Real Numbers - Multiplication Laws/1. Closure Law of Multiplication. Give an example and Verify it mathematically.mp416.94MB
9. 12. NUMBER SYSTEM - Real Numbers - Multiplication Laws/2. Commutative Law of Multiplication. Give an example and Verify it mathematically.mp413.92MB
10. 12. NUMBER SYSTEM - Real Numbers - Multiplication Laws/3. Associative Law of Multiplication. Give an example and Verify it mathematically.mp415.61MB
11. 12. NUMBER SYSTEM - Real Numbers - Multiplication Laws/4. Multiplicative Identity Law. Give an example and Verify it mathematically.mp427.5MB
12. 12. NUMBER SYSTEM - Real Numbers - Multiplication Laws/5. Multiplicative Inverse Law. Give an example and Verify it mathematically.mp444.76MB
13. 12. NUMBER SYSTEM - Real Numbers - Multiplication Laws/6. Multiplication - Addition Laws. Give an example and prove it mathematically.mp436.22MB
14. 13. NUMBER SYSTEM - Real Numbers - Properties of Inequality/1. Trichotomy Property. Prove it mathematically.mp46.9MB
15. 13. NUMBER SYSTEM - Real Numbers - Properties of Inequality/2. Trichotomy Product Property. Prove it mathematically.mp422.51MB
16. 13. NUMBER SYSTEM - Real Numbers - Properties of Inequality/3. Transitive Property. Prove it mathematically with the help of an example.mp419.77MB
17. 13. NUMBER SYSTEM - Real Numbers - Properties of Inequality/4. Additive Property. Prove it mathematically with the help of an example.mp420.19MB
18. 13. NUMBER SYSTEM - Real Numbers - Properties of Inequality/5. Multiplicative Property. Prove it mathematically with the help of an example.mp454.15MB
19. 14. NUMBER SYSTEM - Real Numbers - Properties of Equality/1. Reflexive Property of inequality. Give an example and prove it mathematically.mp410.92MB
20. 14. NUMBER SYSTEM - Real Numbers - Properties of Equality/2. Symmetric Property of inequality. Prove it mathematically and give an example.mp425.95MB
21. 14. NUMBER SYSTEM - Real Numbers - Properties of Equality/3. Transitive Property of inequality. Prove it mathematically and give an example.mp414.24MB
22. 14. NUMBER SYSTEM - Real Numbers - Properties of Equality/4. Additive Property of inequality. Prove it mathematically and give an example.mp420.92MB
23. 14. NUMBER SYSTEM - Real Numbers - Properties of Equality/5. Multiplicative Property of inequality. Prove it mathematically with an example.mp432.05MB
24. 14. NUMBER SYSTEM - Real Numbers - Properties of Equality/6. Cancellation Property w.r.t Addition. Prove it mathematically with an example.mp440.41MB
25. 14. NUMBER SYSTEM - Real Numbers - Properties of Equality/7. Cancellation Property w.r.t Multiplication. Prove it mathematically.mp431.25MB
26. 15. NUMBER SYSTEM - Complex Numbers - Introduction to Complex Numbers/1. What is complex numbers Demonstrate how it looks like mathematically.mp415.06MB
27. 15. NUMBER SYSTEM - Complex Numbers - Introduction to Complex Numbers/2. Conjugate Property of a complex number. Show the conjugate of a number.mp411.12MB
28. 15. NUMBER SYSTEM - Complex Numbers - Introduction to Complex Numbers/3. Modulus of a complex number. How to calculate the modulus of a complex number.mp414.18MB
29. 15. NUMBER SYSTEM - Complex Numbers - Introduction to Complex Numbers/4. Derivation of a complex number. How to derive a complex form mathematically.mp4104.34MB
30. 16. NUMBER SYSTEM - Properties of Complex Numbers - Addition Laws/1. Closure Law of Addition for a complex number. Verify it mathematically.mp419.12MB
31. 16. NUMBER SYSTEM - Properties of Complex Numbers - Addition Laws/2. Commutative Law of Addition for a complex number and Verify it mathematically.mp48.09MB
32. 16. NUMBER SYSTEM - Properties of Complex Numbers - Addition Laws/3. Associative Law of Addition for a complex number and Verify it mathematically.mp49.19MB
33. 16. NUMBER SYSTEM - Properties of Complex Numbers - Addition Laws/4. Additive Identity Law for a complex number and Verify it mathematically.mp412.83MB
34. 16. NUMBER SYSTEM - Properties of Complex Numbers - Addition Laws/5. Additive Inverse Law for a complex number. Verify it mathematically.mp416.39MB
35. 17. NUMBER SYSTEM - Properties of Complex Numbers - Multiplication Laws/1. Closure Law of Multiplication of a complex number.mp48.86MB
36. 17. NUMBER SYSTEM - Properties of Complex Numbers - Multiplication Laws/2. Commutative Law of Multiplication of a complex number.mp45.63MB
37. 17. NUMBER SYSTEM - Properties of Complex Numbers - Multiplication Laws/3. Associative Law of Multiplication of a complex number.mp48.47MB
38. 17. NUMBER SYSTEM - Properties of Complex Numbers - Multiplication Laws/4. Multiplicative Identity Law of a complex number.mp415.27MB
39. 17. NUMBER SYSTEM - Properties of Complex Numbers - Multiplication Laws/5. Multiplicative Inverse Law of a complex number.mp419.76MB
40. 17. NUMBER SYSTEM - Properties of Complex Numbers - Multiplication Laws/6. Addition-Multiplication Law of a complex number.mp49.81MB
41. 18. NUMBER SYSTEM - Complex Numbers - Verification of Laws of Addition/1. Verify the Closure Law of Addition of complex no. Prove it by giving an example.mp434.84MB
42. 18. NUMBER SYSTEM - Complex Numbers - Verification of Laws of Addition/2. Verify Commutative Law of Addition of complex no. Prove it by giving an example.mp437.04MB
43. 18. NUMBER SYSTEM - Complex Numbers - Verification of Laws of Addition/3. Verify Associative Law of Addition of complex no. Prove it by giving an example.mp475.99MB
44. 18. NUMBER SYSTEM - Complex Numbers - Verification of Laws of Addition/4. Verify Additive Identity Law of complex no. Prove it by giving an example.mp421.26MB
45. 18. NUMBER SYSTEM - Complex Numbers - Verification of Laws of Addition/5. Verify the Additive Inverse Law of a complex number. Prove it mathematically.mp411.61MB
46. 19. NUMBER SYSTEM - Complex Numbers - Verification of Laws of Multiplication/1. Verify Closure Law of Multiplication of complex no. Give an example to prove it.mp471.05MB
47. 19. NUMBER SYSTEM - Complex Numbers - Verification of Laws of Multiplication/2. Verify Commutative Law of Multiplication of complex no. Give an example to prove.mp465.94MB
48. 19. NUMBER SYSTEM - Complex Numbers - Verification of Laws of Multiplication/3. Verify Associative Law of Multiplication of complex no. Give an example to prove.mp4170.96MB
49. 2. SETS - Names of Sets/1. What is set Introduction to a set.mp433.14MB
50. 2. SETS - Names of Sets/10. Odd Integers.mp411.16MB
51. 2. SETS - Names of Sets/11. Prime Numbers.mp423.8MB
52. 2. SETS - Names of Sets/12. Rational Numbers.mp444.88MB
53. 2. SETS - Names of Sets/13. Irrational Numbers.mp428.55MB
54. 2. SETS - Names of Sets/14. Real Numbers.mp412MB
55. 2. SETS - Names of Sets/2. Natural Numbers.mp48.8MB
56. 2. SETS - Names of Sets/3. Whole Numbers.mp49.46MB
57. 2. SETS - Names of Sets/4. Integers.mp416.74MB
58. 2. SETS - Names of Sets/5. Positive Integers.mp410.58MB
59. 2. SETS - Names of Sets/6. Negative Integers.mp45.01MB
60. 2. SETS - Names of Sets/7. Even Numbers.mp418.96MB
61. 2. SETS - Names of Sets/8. Odd Numbers.mp49.06MB
62. 2. SETS - Names of Sets/9. Even Integers.mp48.36MB
63. 20. NUMBER SYSTEM - Complex Numbers - Problem Solution/1. Problem 1 Solve the given complex expressions to their simplified forms.mp474.04MB
64. 20. NUMBER SYSTEM - Complex Numbers - Problem Solution/2. Transform the given expressions into complex forms.mp437.7MB
65. 20. NUMBER SYSTEM - Complex Numbers - Problem Solution/3. Problem 3 Show that the sum or product of any two conjugate numbers is real.mp441.96MB
66. 20. NUMBER SYSTEM - Complex Numbers - Problem Solution/4. Problem 4 Write the complex multiplicative inverse for the given expressions.mp465.34MB
67. 20. NUMBER SYSTEM - Complex Numbers - Problem Solution/5. Problem 5 Factorize the given expressions into complex forms.mp450.46MB
68. 20. NUMBER SYSTEM - Complex Numbers - Problem Solution/6. Problem 6 Write the expression as a single complex form by separating the terms.mp4128.4MB
69. 21. BINARY OPERATION OF SETS - Addition Properties/1. What is binary operation Explain it mathematically by giving the examples.mp468.97MB
70. 21. BINARY OPERATION OF SETS - Addition Properties/2. Closure Addition Property of binary operation. To which sets it can applicable.mp445.49MB
71. 21. BINARY OPERATION OF SETS - Addition Properties/3. Commutative Addition of binary operation. To which sets it can be applicable.mp451.62MB
72. 21. BINARY OPERATION OF SETS - Addition Properties/4. Associative Addition of binary operation. To which sets it can be applicable.mp421.66MB
73. 21. BINARY OPERATION OF SETS - Addition Properties/5. Additive Identity of binary operation. To which sets it can be applicable.mp464.82MB
74. 21. BINARY OPERATION OF SETS - Addition Properties/6. Additive Inverse of binary operation. To which sets it can be applicable.mp474.57MB
75. 22. BINARY OPERATION OF SETS - Multiplication Properties/1. Closure Multiplication of binary operation. To which sets it can be applicable.mp432.09MB
76. 22. BINARY OPERATION OF SETS - Multiplication Properties/2. Commutative Multiplication of binary operation.To which sets it can applicable.mp426.48MB
77. 22. BINARY OPERATION OF SETS - Multiplication Properties/3. Associative Multiplication of binary operation. To which sets it is applicable.mp419.08MB
78. 22. BINARY OPERATION OF SETS - Multiplication Properties/4. Multiplicative Identity of binary operation. To which sets it can be applicable.mp446.83MB
79. 22. BINARY OPERATION OF SETS - Multiplication Properties/5. Multiplicative Inverse of binary operation. To which sets it can be applicable.mp463.89MB
80. 23. COORDINATE SYSTEM - Cartesian System - X-Y Plane - Problem Solution/1. What is Cartesian coordinate systemsDraw Cartesian xy plane with all parameters.mp471.75MB
81. 23. COORDINATE SYSTEM - Cartesian System - X-Y Plane - Problem Solution/2. Ordered Pairs of X-Y Cartesian coordinate system.mp483.91MB
82. 23. COORDINATE SYSTEM - Cartesian System - X-Y Plane - Problem Solution/3. Addition of X-Y Cartesian ordered pairs.mp412.63MB
83. 23. COORDINATE SYSTEM - Cartesian System - X-Y Plane - Problem Solution/4. Product of X-Y Cartesian ordered pairs.mp453.55MB
84. 23. COORDINATE SYSTEM - Cartesian System - X-Y Plane - Problem Solution/5. Problem 1 Plot the given ordered pairs in X-Y Cartesian plane.mp433.63MB
85. 23. COORDINATE SYSTEM - Cartesian System - X-Y Plane - Problem Solution/6. Problem 2 Write the ordered pairs for the plotted points in X-Y Cartesian plane.mp443.54MB
86. 24. COORDINATE SYSTEM - Cartesian System - Complex Plane/1. What is Cartesian complex coordinates Draw complex plane with all parameters.mp436.77MB
87. 24. COORDINATE SYSTEM - Cartesian System - Complex Plane/2. Ordered Pairs of Complex Cartesian coordinate system.mp443.94MB
88. 25. COORDINATE SYSTEM - Polar System - Polar Plane, Real Plane and Complex Plane/1. Show the Polar form and draw the polar coordinate system with all the parameters.mp421.02MB
89. 25. COORDINATE SYSTEM - Polar System - Polar Plane, Real Plane and Complex Plane/2. Show the Real form and draw the Real coordinate system with all the parameters.mp438.71MB
90. 25. COORDINATE SYSTEM - Polar System - Polar Plane, Real Plane and Complex Plane/3. Show Polar Complex form and draw its coordinate system with all the parameters.mp441.76MB
91. 25. COORDINATE SYSTEM - Polar System - Polar Plane, Real Plane and Complex Plane/4. How to make a Polar equations of the polar coordinate system.mp430.38MB
92. 25. COORDINATE SYSTEM - Polar System - Polar Plane, Real Plane and Complex Plane/5. Problem 1 Transform the Cartesian complex form into Polar form.mp425.36MB
93. 25. COORDINATE SYSTEM - Polar System - Polar Plane, Real Plane and Complex Plane/6. Problem 2 Transform the Cartesian Real form into Polar form.mp427.93MB
94. 26. GROUPS - Categories of Groups/1. Name the five categories of the groups.mp410.42MB
95. 26. GROUPS - Categories of Groups/2. Groupoid. Which group is said to be a groupoid. Explain it logically.mp430.05MB
96. 26. GROUPS - Categories of Groups/3. Monoid. Which group is said to be a Monoid Prove it mathematically & logically.mp435.84MB
97. 26. GROUPS - Categories of Groups/4. Semi-Group. Which group is said to be a Semi-Group Prove it.mp431.32MB
98. 26. GROUPS - Categories of Groups/5. Group. Which is the pure form of group Explain and prove it.mp452.52MB
99. 26. GROUPS - Categories of Groups/6. Abelian Group. Which group is said to be an Abelian Explain and prove it.mp449.99MB
100. 27. GROUPS - Problem Solution/1. Construct the Adjoining table by applying addition operation. Identify the group.mp4118.81MB
101. 27. GROUPS - Problem Solution/2. Construct Adjoining table of a set with even & odd elements. Identify the group.mp497.45MB
102. 3. SETS - Types of Sets/1. How many types of sets we have.mp45.49MB
103. 3. SETS - Types of Sets/10. Improper subset.mp415.67MB
104. 3. SETS - Types of Sets/11. Power set.mp463.49MB
105. 3. SETS - Types of Sets/12. Power set - Learn to derive all the subsets of a set with four elements.mp471.89MB
106. 3. SETS - Types of Sets/13. Power set - Learn to derive all the subsets of a set with five elements.mp4162.31MB
107. 3. SETS - Types of Sets/14. Universal set.mp438.14MB
108. 3. SETS - Types of Sets/2. Null OR Empty set.mp413.39MB
109. 3. SETS - Types of Sets/3. Singleton set.mp415.98MB
110. 3. SETS - Types of Sets/4. Finite set.mp419.62MB
111. 3. SETS - Types of Sets/5. Infinite set.mp411.63MB
112. 3. SETS - Types of Sets/6. Equal set.mp433.82MB
113. 3. SETS - Types of Sets/7. Equivalent set.mp435.35MB
114. 3. SETS - Types of Sets/8. Subset.mp426.35MB
115. 3. SETS - Types of Sets/9. Proper subset.mp456.63MB
116. 4. SETS - Forms of Sets/1. How many forms of sets we have.mp43.13MB
117. 4. SETS - Forms of Sets/2. Tabular form.mp415.78MB
118. 4. SETS - Forms of Sets/3. Descriptive form.mp411.76MB
119. 4. SETS - Forms of Sets/4. Set-builder form.mp453.32MB
120. 5. SETS - Some Problems' Solutions/1. Problem 1 Write all the given sets in set-builder forms.mp4179.46MB
121. 5. SETS - Some Problems' Solutions/2. Problem 2 Write all the given sets in Tabular forms.mp4116.04MB
122. 5. SETS - Some Problems' Solutions/3. Problem 3 Write all the given sets in Descriptive forms.mp4149.29MB
123. 5. SETS - Some Problems' Solutions/4. Problem 4 Identify the Finite and Infinite sets among all the give sets.mp4143.47MB
124. 5. SETS - Some Problems' Solutions/5. Problem 5 Identify the equal and equivalent sets out of the give sets.mp4134.08MB
125. 5. SETS - Some Problems' Solutions/6. Problem 6 Write the Proper and Improper subsets of the given sets.mp4219.91MB
126. 5. SETS - Some Problems' Solutions/7. Problem 7 Identify and write all the subsets for a power set of the given set.mp4185.9MB
127. 5. SETS - Some Problems' Solutions/8. Problem 8 Identify the True and False sets among the give sets.mp449.7MB
128. 6. SET OPERATIONS - Types of Set Operations/1. Union of sets. What is Union of sets and its notation. Explain it with example.mp425.35MB
129. 6. SET OPERATIONS - Types of Set Operations/2. Intersection of sets and its notation. Explain it with example.mp426.34MB
130. 6. SET OPERATIONS - Types of Set Operations/3. Disjoint of sets. Explanation of a disjoint set with the relevant example.mp421.49MB
131. 6. SET OPERATIONS - Types of Set Operations/4. Overlapping of sets. Explanation of an overlapping set with an example.mp430.26MB
132. 6. SET OPERATIONS - Types of Set Operations/5. Difference of sets. What are its notations Explained with the relevant example.mp448.76MB
133. 6. SET OPERATIONS - Types of Set Operations/6. Complement of sets. What are the notations Explained with the relevant example.mp432.87MB
134. 7. SET OPERATIONS - Properties of Set Operations/1. Property 1 Commutative of Union. Verify it mathematically that LHS = RHS.mp427.55MB
135. 7. SET OPERATIONS - Properties of Set Operations/2. Property 2 Commutative of Intersection. Verify it mathematically that LHS = RHS.mp425.33MB
136. 7. SET OPERATIONS - Properties of Set Operations/3. Property 3 Associative of Union. Verify it mathematically that LHS = RHS.mp440.68MB
137. 7. SET OPERATIONS - Properties of Set Operations/4. Property 4 Associative of Intersection. Verify it mathematically that LHS = RHS.mp438.15MB
138. 7. SET OPERATIONS - Properties of Set Operations/5. Property 5 Distributive of Union over Intersection. Verify it mathematically.mp458.09MB
139. 7. SET OPERATIONS - Properties of Set Operations/6. Property 6 Distributive of Intersection over Union. Verify it mathematically.mp438.76MB
140. 8. SET OPERATIONS - De Morgan's Laws/1. What are De Morgan's laws Show the two types of De Morgan's laws.mp410.95MB
141. 8. SET OPERATIONS - De Morgan's Laws/2. De Morgan's First law. Verify it mathematically and show that the LHS = RHS.mp462.89MB
142. 8. SET OPERATIONS - De Morgan's Laws/3. De Morgan's 2nd law. Verify it mathematically and show that the LHS = RHS.mp440.86MB
143. 8. SET OPERATIONS - De Morgan's Laws/4. Prove the De Morgan's First law with an example. Show that the LHS = RHS.mp488.38MB
144. 8. SET OPERATIONS - De Morgan's Laws/5. Prove the De Morgan's 2nd law with an example. Show that the LHS = RHS.mp473.03MB
145. 9. SET OPERATIONS - Venn Diagrams/1. What is Venn Diagram.mp48.65MB
146. 9. SET OPERATIONS - Venn Diagrams/2. Show the Venn Diagram for Union & Intersection of the subset of the sets[A⊂B].mp466.48MB
147. 9. SET OPERATIONS - Venn Diagrams/3. Show the Venn Diagram for Union & Intersection of the subset of the sets[B⊂A].mp423.25MB
148. 9. SET OPERATIONS - Venn Diagrams/4. Show the Venn Diagram for Union & Intersection of the Disjoint sets.mp431.74MB
149. 9. SET OPERATIONS - Venn Diagrams/5. Show the Venn Diagram for Union & Intersection of the Overlapping sets.mp435.43MB
150. 9. SET OPERATIONS - Venn Diagrams/6. Draw the Venn Diagrams for the Difference of the sets.mp443.24MB
151. 9. SET OPERATIONS - Venn Diagrams/7. Show the Venn Diagram for the Complement of the sets.mp424.49MB