Calculus 1 Fundamentals

Name: Calculus 1 Fundamentals
Rating: 4.0 (92 reviews)

Master the building blocks of Calculus : Limits & Derivatives

Created byTanmay Varshney

Last updated 7/2020

English

What you'll learn

Limits: Conceptual understanding of limits,various rules and theorems including the handy ones: The L’Hospital rule and the Sandwich theorem to deal with all kind of problems related to limits.
Derivatives: Finding derivatives of all functions,The First principle of derivative,the Product Rule,the Quotient rule along with the most important,The Chain rule.
A lot of practice problems and quizzes along with exposure to problems useful in competitive exams also.

Course content

4 sections • 21 lectures • 2h 48m total length

Introduction to Limits0:51
Explore the concept and existence of limits, the algebra of limits, and techniques for trigonometric limits. Apply L'Hôpital's rule and the sandwich theorem, and study limits at infinity.
Concept of Limits4:11
Explore the concept of limits with an example: the function f(x) = (4x+4)/(x+1) is undefined at x = -1, but f(x) approaches 4 as x approaches -1 from either side.
Existence of Limits8:17
Analyze the existence of limits by comparing left and right limits. At x approaches 1, left limit is 0 and right limit is 1, so the limit does not exist.
Examples8:53
This lecture explains evaluating limits by comparing left and right limits, noting when a limit does not exist. Example with x^2 + sin x shows the limit equals 1.
Algebra of Limits7:36
explore the algebra of limits by evaluating sums, differences, products, and quotients of functions using the limits of each part, when they exist and the denominator is nonzero.
The L'Hospital Rule15:38
Explore how to evaluate limits using L'Hôpital's rule, transforming 0/0 or infinity forms into derivatives to compare rates of change for numerator and denominator.
Quiz 1
The Sandwich Theorem6:01
explore the sandwich (squeeze) theorem: if f(x) ≥ g(x) ≥ h(x) near a and lim f = lim h = L, then lim g = L; lim x→0 x cos(1/x).
Limits of Trigonometric Functions8:03
Examine limits of trig functions: sin x / x → 1 and cos x → 1 as x → 0, using expansions to evaluate (1 - cos x)/x.
Limits at Inifinity15:36
Explore how to evaluate limits as x approaches positive or negative infinity by factoring out the highest power of x, simplifying indeterminate forms, and applying leading-term analysis to polynomials.
Miscellaneous Examples19:10
Explore how to evaluate limits through left and right approaches, solve piecewise and radical expressions using conjugates, and determine when the limit exists or does not exist, including a floor function example.
Quiz 2

Introduction to Derivatives0:42
Explore the notion of derivatives, learn the first principle, review derivatives of common functions used in calculus, and master the chain rule for differentiating composite functions.
Concept of Derivatives9:07
Learn the concept of derivatives as the instantaneous rate of change, introduced via the limit definition and a distance-time example, culminating in f'(3)=6 for f(x)=x^2+1.
First Principle of Derivatives9:07
Derive the first principle of derivatives from the limit definition f'(x)=lim_{h->0}[f(x+h)-f(x)]/h and apply it to f(x)=sin x to obtain f'(x)=cos x.
Algebra of Derivatives10:01
Explore the algebra of derivatives by applying addition, subtraction, product, and quotient rules to functions, with examples f(x)=x^2 and g(x)=1+x, showing how to differentiate sums, differences, products, and quotients.
Quiz 3
Derivatives of Common Function11:32
Explore derivatives of common functions, including power rules, constants, product and quotient rules, and trig and exponential rules. Apply these rules to differentiate sine, cosine, natural log, and exponential expressions.
The Chain Rule14:09
Apply the chain rule to differentiate composite functions by identifying inner and outer functions, then multiply the outer derivative by the inner derivative, with examples like sin^3 x and (1+x^2)^2.
Miscellaneous Examples19:09
Present various derivative examples using first principles, limits, and difference quotients, applying subtraction, division, and chain rules to sine, cosine, and exponential functions.
Quiz 4

Requirements

Basic knowledge of Functions.
Basics of Algebra.
Basics of Trigonometry would be a plus to have.
However,all of the above pre-requisites are optional and we will be providing adequate references related to the course for your convenience.

Description

Visit our website gyaanX and signup for the course and get a chance to win gift cards in our monthly lucky draw.

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Calculus is the study of change with its primary focus on:

1. Rate of Change (Differentiation Calculus)

2. Accumulation (Integral Calculus)

Calculus is used in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled and an optimal solution is desired.

It allows one to go from (non-constant) rates of change to the total change or vice versa, and many times in studying a problem we know one and are trying to find the other.

In this course, we will be covering the building blocks of Calculus : Limits and Derivatives(Differential Calculus) in an interactive manner with the help of 15+ video lectures, miscellaneous examples, quizzes and solutions.

Calculus Fundamentals: Section 1 - LIMITS

Concept of Limits: For making you familiar with the notion of the Limit.
Existence of Limits: Introduction to the Left Hand Limit and the Right Hand Limit.
Algebra of Limits: Addition, Subtraction, Multiplication and Division in Limits.
L’Hospital Rule: A handy tool to circumvent the common indeterminate forms when computing limits.
The Sandwich Theorem: To evaluate limits of functions that can't be computed at a given point.
Limits of Trigonometric Functions: To cover the important limit identities of trigonometric functions.
Limits at Infinity: To evaluate limits at points tending to positive and negative infinity.

Calculus Fundamentals: Section 2 - DERIVATIVES

Concept of Derivatives: Meaning of the term "Derivative" in Mathematics.
First Principle of Derivatives: The conventional way of computing derivatives.
Algebra of Derivatives: Addition, Subtraction, Multiplication and Division in Derivatives.
Derivatives of common functions: To set you free to calculate derivative of combination of any functions.
The Chain Rule: To calculate the derivatives of composite functions no matter how complex they are.

Calculus Fundamentals: Section 3 - FORMULAE & REFERENCES

For a quick glance over the formulae and notations used throughout the course.

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Enrol in this course, Learn the fundamentals and Master the calculus.

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Updated now with Practice Worksheets for Limits and Derivatives - The MORE you practice, the BETTER you become.

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Who this course is for:

Anyone who is a Beginner in Calculus.
Anyone who wants to brush up their Calculus fundamentals.
Anyone who is familiar with basic trigonometry and wants to take a step forward.
As a pre-requisite course for those who are planning to learn Advanced Calculus.
Anyone who enjoys learning Math concepts.

Calculus 1 Fundamentals

What you'll learn

Explore related topics

Course content

Limits10 lectures • 1hr 34min

Derivatives7 lectures • 1hr 14min

Practice Worksheets2 lectures0

Formulae & References2 lectures0

Requirements

Description

Who this course is for: