Calculus Fundamentals

Mathematics

2023-11-16

Lessons List

Lesson 00 Calculus vs Pre Calculus | Course Outline | Recommended Books

Lesson 01 What is Calculus and its Types | Slope and Intercept of Straight Line

Lesson 02 What is Function Tangent Secant Chord Diameter and Radius | Limits in Calculus

Lesson 03 What is Limits in Calculus | How to Understand and Solve Limits in Calculus

Lesson 04 Limits that Fail to Exist | Three limits that Fail to Exist | What is Infinite Limits |

Lesson 05 Intervals OPEN and CLOSE|Formal definition of Limits| Epsilon Delta Definition of a Limit

Lesson 06 How Limits Used in Machine Learning Deep Learning and Data Science | Limits in Real Life

Lesson 07 Properties of Limits | Rules of Limits | Limits of a Rational Function

Lesson 08 Indeterminate Form of Limit | Indeterminate Forms with Solved Examples

Lesson 09 Squeeze Theorem | Two Special Trigonometric Limits

Lesson 10 Continuity of Function in OPEN CLOSE Interval| Vertical Horizontal Diagonal Asymptote

Lesson 11 The Intermediate Value Theorem | Applications of the Intermediate Value Theorem

Lesson 12 Infinite Limits | Limits to Infinity | Properties of Infinite Limits

Lesson 13 The Derivative and Tangent Line Problem | Function Tangent Secant Chord and Diameter

Lesson 14 How to Find the Tangent Slope of Straight and Curve Line | The Derivative of a Function

Lesson 15 Differentiate and Continuity | How to Find the Vertical Tangent Line

Lesson 16 Part I Basic Differentiation Rules and Rates of Change

Lesson 17 Part II Basic Differentiation Rules and Rates of Change

Lesson 18 Product and Quotient Rules and Higher Order Derivatives

Lesson 19 Chain Rule for Derivatives | Differentiation using The Chain Rule

Lesson 20 Implicit and Explicit Functions in Calculus for Differentiation

Lesson 21 What is Related Rates in Calculus | How to Solve Related Rates Problems

Lesson 22 Extrema of an Interval | Minima Maxima Relative and Absolute Values

Lesson 23 Rolle s Theorem and Mean Value Theorem

Lesson 24 Increasing and Decreasing Functions and the First Derivative

Lesson 25 Concavity and Second Derivative Test

Lesson 26 Limits at Infinity

Lesson 27 A Summary of Curve Sketching | Analyzing the Graph of a Function

Lesson 28 Optimization Problems | Applied Minimum and Maximum Problems

Lesson 29 Newton s Method | Newton s Method For Approximating The Zeros Of A Function

Lesson 30 Higher Order Derivatives Applications | How to Sketch the Graph of the Derivative

Lesson 31 Differentials |How to Calculate Differentials in Calculus | Error Handling using Calculus

Lesson 32 Integral Calculus | What is Integration OR Anti derivative

Lesson 33 Antiderivatives and Indefinite Integration | Basic Integration Rules

Lesson 34 Area with Summation Notation | The Exhaustion Method | Upper and Lower Sum Integration

Lesson 35 Part I The Fundamental Theorem of Calculus | The Mean Value Theorem for Integrals

Lesson 36 Part II The Second Fundamental Theorem of Calculus | Net Change Theorem

Lesson 37 Riemann Sums and Definite Integrals | What is Definite Integrals

Lesson 38 Integration by Substitution | Change of Variables for Definite Integrals

Lesson 39 Numerical Integration | Trapezoidal Rule AND Simpson s Rule with Error Analysis

Lesson 40 Logarithmic and Exponential Functions in Calculus

Lesson 41 Real Life Application of Logarithms and Exponential Its Implementation

Lesson 42 The Natural Logarithmic Function Differentiation

Lesson 43 The Natural Logarithmic Function Integration

Lesson 44 Inverse Functions | How to Find the Inverse of a Function

Lesson 45 Exponential Functions Differentiation and Integration

Lesson 46 EXPONENTIAL and LOGARITHMIC Function to BASE a

Lesson 47 Part II EXPONENTIAL and LOGARITHMIC Function to BASE a

Lesson 48 Inverse Trigonometric Functions Differentiation | BASIC DIFFERENTIATION RULES

Lesson 49 Integration of Inverse Trigonometric Functions

Lesson 50 Hyperbolic Functions and its Inverse | Derivative of Hyperbolic Functions

Lesson 51 What is Differential Equation with basic Examples

Lesson 52 Slope Fields and Euler s Method with Examples

Lesson 53 Differential Equation Growth and Decay

Lesson 54 Separation of Variables and the Logistic Equation | Applications Logistic Growth Equation

Lesson 55 First Order Linear Differential Equations its Applications | What is Bernoulli Equation

Lesson 56 Part II Applications of First Order Linear Differential Equations

Lesson 57 Related Rates and Differential Equations in Calculus with Examples

Lesson 58 Differentiation VS Derivative VS Differential with Examples

Lesson 59 Differential Equations Types with Examples

Lesson 60 Area of a Region between Two Curves

Lesson 61 THE DISK METHOD | THE SHELL METHOD | Comparison of Disk and Shell Methods

Lesson 62 Arc Length and Surfaces of Revolution

Lesson 63 Work Done | Moments Centers of Mass and Centroids | Fluid Pressure and Fluid Force

Lesson 64 Basic Integration Rules | Indeterminate Form and L Hospital Rule

Lesson 65 Integration by Parts | Tabular Method of Integration

Lesson 66 Trigonometric Integrals in Calculus

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Alfredo Delgado

Wonderfull 2025-01-22

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Calculus course in hindi, in this course Explore the essential principles and concepts of calculus, laying the groundwork for advanced mathematical and deep learning applications

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Calculus Fundamentals

Mathematics

Lesson 00 Calculus vs Pre Calculus | Course Outline | Recommended Books

Lesson 01 What is Calculus and its Types | Slope and Intercept of Straight Line

Lesson 02 What is Function Tangent Secant Chord Diameter and Radius | Limits in Calculus

Lesson 03 What is Limits in Calculus | How to Understand and Solve Limits in Calculus

Lesson 04 Limits that Fail to Exist | Three limits that Fail to Exist | What is Infinite Limits |

Lesson 05 Intervals OPEN and CLOSE|Formal definition of Limits| Epsilon Delta Definition of a Limit

Lesson 06 How Limits Used in Machine Learning Deep Learning and Data Science | Limits in Real Life

Lesson 07 Properties of Limits | Rules of Limits | Limits of a Rational Function

Lesson 08 Indeterminate Form of Limit | Indeterminate Forms with Solved Examples

Lesson 09 Squeeze Theorem | Two Special Trigonometric Limits

Lesson 10 Continuity of Function in OPEN CLOSE Interval| Vertical Horizontal Diagonal Asymptote

Lesson 11 The Intermediate Value Theorem | Applications of the Intermediate Value Theorem

Lesson 12 Infinite Limits | Limits to Infinity | Properties of Infinite Limits

Lesson 13 The Derivative and Tangent Line Problem | Function Tangent Secant Chord and Diameter

Lesson 14 How to Find the Tangent Slope of Straight and Curve Line | The Derivative of a Function

Lesson 15 Differentiate and Continuity | How to Find the Vertical Tangent Line

Lesson 16 Part I Basic Differentiation Rules and Rates of Change

Lesson 17 Part II Basic Differentiation Rules and Rates of Change

Lesson 18 Product and Quotient Rules and Higher Order Derivatives

Lesson 19 Chain Rule for Derivatives | Differentiation using The Chain Rule

Lesson 20 Implicit and Explicit Functions in Calculus for Differentiation

Lesson 21 What is Related Rates in Calculus | How to Solve Related Rates Problems

Lesson 22 Extrema of an Interval | Minima Maxima Relative and Absolute Values

Lesson 23 Rolle s Theorem and Mean Value Theorem

Lesson 24 Increasing and Decreasing Functions and the First Derivative

Lesson 25 Concavity and Second Derivative Test

Lesson 26 Limits at Infinity

Lesson 27 A Summary of Curve Sketching | Analyzing the Graph of a Function

Lesson 28 Optimization Problems | Applied Minimum and Maximum Problems

Lesson 29 Newton s Method | Newton s Method For Approximating The Zeros Of A Function

Lesson 30 Higher Order Derivatives Applications | How to Sketch the Graph of the Derivative

Lesson 31 Differentials |How to Calculate Differentials in Calculus | Error Handling using Calculus

Lesson 32 Integral Calculus | What is Integration OR Anti derivative

Lesson 33 Antiderivatives and Indefinite Integration | Basic Integration Rules

Lesson 34 Area with Summation Notation | The Exhaustion Method | Upper and Lower Sum Integration

Lesson 35 Part I The Fundamental Theorem of Calculus | The Mean Value Theorem for Integrals

Lesson 36 Part II The Second Fundamental Theorem of Calculus | Net Change Theorem

Lesson 37 Riemann Sums and Definite Integrals | What is Definite Integrals

Lesson 38 Integration by Substitution | Change of Variables for Definite Integrals

Lesson 39 Numerical Integration | Trapezoidal Rule AND Simpson s Rule with Error Analysis

Lesson 40 Logarithmic and Exponential Functions in Calculus

Lesson 41 Real Life Application of Logarithms and Exponential Its Implementation

Lesson 42 The Natural Logarithmic Function Differentiation

Lesson 43 The Natural Logarithmic Function Integration

Lesson 44 Inverse Functions | How to Find the Inverse of a Function

Lesson 45 Exponential Functions Differentiation and Integration

Lesson 46 EXPONENTIAL and LOGARITHMIC Function to BASE a

Lesson 47 Part II EXPONENTIAL and LOGARITHMIC Function to BASE a

Lesson 48 Inverse Trigonometric Functions Differentiation | BASIC DIFFERENTIATION RULES

Lesson 49 Integration of Inverse Trigonometric Functions

Lesson 50 Hyperbolic Functions and its Inverse | Derivative of Hyperbolic Functions

Lesson 51 What is Differential Equation with basic Examples

Lesson 52 Slope Fields and Euler s Method with Examples

Lesson 53 Differential Equation Growth and Decay

Lesson 54 Separation of Variables and the Logistic Equation | Applications Logistic Growth Equation

Lesson 55 First Order Linear Differential Equations its Applications | What is Bernoulli Equation

Lesson 56 Part II Applications of First Order Linear Differential Equations

Lesson 57 Related Rates and Differential Equations in Calculus with Examples

Lesson 58 Differentiation VS Derivative VS Differential with Examples

Lesson 59 Differential Equations Types with Examples

Lesson 60 Area of a Region between Two Curves

Lesson 61 THE DISK METHOD | THE SHELL METHOD | Comparison of Disk and Shell Methods

Lesson 62 Arc Length and Surfaces of Revolution

Lesson 63 Work Done | Moments Centers of Mass and Centroids | Fluid Pressure and Fluid Force

Lesson 64 Basic Integration Rules | Indeterminate Form and L Hospital Rule

Lesson 65 Integration by Parts | Tabular Method of Integration

Lesson 66 Trigonometric Integrals in Calculus

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Calculus Fundamentals

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