Calculus BMTC131
Vigyan Academy
11 modules
HINGLISH
Access for 200 days
"Master the Art of Calculus with BMTC131 - Dive deep into the world of limits, derivatives, and integrals to excel in mathematics and beyond!"
Overview
"Calculus BMTC131" is a comprehensive course that delves into the fundamental principles of calculus, a branch of mathematics that focuses on rates of change and accumulation of quantities. This course covers topics such as limits, derivatives, integrals, and their applications in various fields including physics, economics, and engineering. Students enrolled in "Calculus BMTC131" will learn how to calculate slopes of curves, find maximum and minimum values of functions, and analyze the behavior of functions using derivatives. They will also explore techniques for finding areas under curves, volumes of solids of revolution, and solving differential equations using integrals. Throughout the course, emphasis will be placed on developing problem-solving skills, critical thinking, and mathematical reasoning. Students will engage in practice problems, assignments, and exams to reinforce their understanding of calculus concepts and their ability to apply them in real-world scenarios. By the end of "Calculus BMTC131", students will have a solid foundation in calculus and be prepared to tackle more advanced coursework in mathematics, science, and engineering. Whether you're a student looking to fulfill a requirement or someone interested in expanding your mathematical knowledge, this course will equip you with the tools to succeed in your academic and professional pursuits.
Modules
Sets and Operations on Them
14 attachments • 8 hrs
L1.1 INTRODUCTION TO SETS
L1.2 DESCRIPTION OF SETS
L1.3 CLASSIFICATION OF SET
L1.4 SUBSETS
L1.4 VENN DIAGRAM
L1.5 VENN DIAGRAMS
L1.6 COMPLEMENTATION
L1.7 INTERSECTION PT1
L1.8 INTERSECTION OF SETS PT2
L1.9 UNION OF SETS PT1
L1.10 UNION OF SETS PT2
L1.11 CARTESIAN PRODUCT
L1.12 LAWS ON OPERATIONS
L1.13 DE MORGAN'S LAW
Functions
5 attachments • 4 hrs
L2.1 RELATION
L2.2 FUNCTIONS
L2.3 SOME IMPORTANT FUNCTIONS
L2.4 COMPOSITION OF FUNCTIONS
L2.5 INVERSE OF FUNCTIONS
2D Coordinate Systems
5 attachments • 3 hrs
L3.1 CARTESIAN COORDINATE SYSTEM
L3.2 EQUATIONS OF LINE 1
L3.3 EQUATIONS OF LINE 2
L3.4 GRAPH OF FUNCTIONS
L3.5 POLAR COORDINATE SYSTEM
Complex Numbers
4 attachments • 2 hrs
L4.1 INTRO TO COMPLEX NUMBERS
L4.2 REPRESENTATION OF COM[LEX NUMEBRS
L4.3 ALGEBRA OF COMPLEX NUMBERS
L4.4 PRODUCT OF COMPLEX NUMBERS
Polynomial Equations and Their Solutions
6 attachments • 3 hrs
L5.1 QUADRATIC EQUATIONS 1
L5.2 QUADRATIC EQUATIONS 2
L5.3 POLYNOMIAL EQUATIONS 1
L5.4 POLYNOMIAL EQUATIONS 2
L5.5 POLYNOMIAL EQUATIONS 3
L5.6 POLYNOMIAL EQUATIONS 4
Real numbers
9 attachments
L6.1 PROPERTIES OF REAL NUMBERS
L6.2 SUPREMUM AND INFIMUM
L6.3 SUPREMUM AND INFIMUM 2
L6.4 ABSOLUTE VALUE 1
L6.5 ABSOLUTE VALUE 3
L6.6 INTERVALS
L6.7 FUNCTIONS
L6.8 DOMAIN AND RANGE OF FUNCTIONS
L6.9 INVERSE OF F,EVEN AND ODD FUNCTIONS
Limit
9 attachments • 4 hrs
L7.1 INTRODUCTION TO LIMITS
L7.2 INTRODUCTION LHL AND RHL
L7.3 EPSILON DELTA DEFINITION OF LIMIT(V.IMP)
L7.4 limit at infinity
L7.5 SOME THEOREMS
L7.6 PREVIOUS YEAR SOLUTIONS LIMIT 1
L7.7 LIMIT OF TRIGNOMETRIC FUNCTIONS
L7.8 LIMIT OF EXPONENTIAL FUNCTIONS
L7.9 LIMIT OF LOGARITHMIC FUNCTION
Continuity
6 attachments
L8.1 INTRODUCTION TO CONTINUITY
L8.2 PROBLEMS OF CONTINUITY
L8.3 CONTINUITY ON INTERVAL
L8.4 CONTINUITY OF TRIG FUNCTIONS
L8.5 ALGEBRA OF CONTINOUS FUNCTION
L8.6 INTERMIDIATE VALUE THEOREM
An Introduction to differentiation
10 attachments
L9.1 INTRODUCTION TO DIFFERENTIATION
L9.2 DIFFERENTIATION BY FIRST PRINCIPLE
L9.3 DIFFERENTIATION BY FIRST PRINCIPLE 2
L9.4 CONTINUITY AND DIFFERENTIABLITY
L9.5 LEFT AND RIGHT HAND DERIVATIVE
L9.6 ALGEBRA OF DERIVATIVES
L9.7 Chain Rule and problems of Q.R
L9.8 DERIVATIVE OF TRIGNOMETRIC FUNCTIONS
L9.9 DERIVATIVE OF INVERSE FUNCTION
L9.10 DERIVATIVE OF INVERSE TRIGNOMETRIC FUNCTIONS
Some more derivatives
4 attachments
L10.1 SOME MORE DERIVATIVES
L10.2 DERIVATIVE OF EXPONENTIAL FUNCTION
L10.3 DERIVATIVE OF HYPERBOLIC FUNCTION
L10.4 METHOD OF LOG FUNCTION
Higher order derivatives
5 attachments
L11.1 SECOND ORDER DERIVATIVES
L11.2 nth derivative of functions
L11.3
L11.4 POLYNOMIAL APPROXIMATION
L11.5 maclaurins polynomial
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About the creator
Vigyan Academy
Achieve Your Academic Goals with Vigyan Academy! At Vigyan Academy, we offer expertly designed courses and assignments for BScG/BAG Mathematics and Physics students. Our teaching approach is simple, conceptual, and designed to build your confidence through extensive practice.
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