COMPLETE Calculus for Math Major & Minor | Semester 1 | Exam Prep + PYQs | Calcutta University

Complete Calculus for SEM 1 Math Major & Minor | Exam Prep + Full Syllabus + PYQs | Calcutta University | PALMATHS
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About This Video
In this video, we provide a complete guide to Calculus for Semester 1 as per the Calcutta University syllabus for Math Major & Minor students. This lecture covers everything you need to know-from basic concepts to advanced problem-solving techniques-along with solved Previous Year Questions (PYQs) and exam preparation tips.
*Topics* :
0:23 Hyperbolic Function
35:42 Successive differentiation and Leibnitz theorem
01:55:44 Indeterminate form
02:57:42 Reduction formula
04:39:54 Area, Arc length, Surface area and volume of a solid of revolution
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Syllabus Coverage
This video includes detailed explanations and solved examples for the following topics:
1. *Differentiability*
Differentiability of a function at a point and in an interval.
Meaning of the sign of the derivative.
2. *Differentiation Techniques*
Differentiating hyperbolic functions.
Higher-order derivatives and the Leibnitz rule.
Applications of Leibnitz rule to functions like:
𝑒^(𝑎𝑥+𝑏) sin x
𝑒^(𝑎𝑥+𝑏) cos x
(𝑎𝑥 + 𝑏)^𝑛 sin x
(𝑎𝑥 + 𝑏)^𝑛 cos x
3. *Indeterminate Forms and L’Hospital’s Rule*
Understanding indeterminate forms.
L’Hospital’s rule (statement and examples).
4. *Reduction Formulae*
Derivation and application of reduction formulae for:
∫ sinⁿ 𝑥 𝑑𝑥
∫ cosⁿ 𝑥 𝑑𝑥
∫ tanⁿ 𝑥 𝑑𝑥
∫ secⁿ 𝑥 𝑑𝑥
∫ (𝑙𝑜𝑔 𝑥)ⁿ 𝑑𝑥
∫ sinⁿ 𝑥 sinᵐ 𝑥 𝑑𝑥
∫ sinⁿ 𝑥 cosᵐ 𝑥 𝑑𝑥
5. *Parametric Equations and Applications*
Parametric equations and how to parametrize a curve.
Finding the arc length of a curve and parametric curves.
Calculating the area under a curve.
Determining the area and volume of surfaces of revolution.
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What You’ll Learn
Step-by-step solutions to problems from the syllabus.
Exam-focused tips to tackle tricky questions.
PYQs solved to help you understand the exam pattern.
Clear explanations of complex concepts.
Time-saving techniques for problem-solving.
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Who Is This For?
This lecture is specifically designed for Calcutta University students pursuing Math Major & Minor in Semester 1. However, it’s also beneficial for students from other universities like Vidyasagar University, West Bengal State University, University of Burdwan, and University of North Bengal who have Calculus as part of their curriculum.
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Why Watch This Video?
Complete Syllabus Coverage: Everything you need for Semester 1 Calculus.
Solved PYQs: Learn how to tackle previous year questions with ease.
Exam-Focused: Tips and tricks to maximize your scores.
Clear Explanations: Simplified concepts for better understanding.
Time-Saving: One-stop solution for all your Calculus needs.
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This Video Is Perfect For Students Looking For:
Calculus for Semester 1
Calcutta University Math Major & Minor Syllabus
Calculus PYQs and Exam Prep
Step-by-Step Problem Solving
Calculus Tips and Tricks
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#PALMATHS #Calculus #CalcuttaUniversity #MathMajor #MathMinor #Semester1

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