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Calculus Fundamentals

Track :

Mathematics

Lessons no : 67

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What will you learn in this course?
  • Master limits, derivatives, and integrals to solve real-world mathematical problems effectively
  • Apply calculus concepts to analyze functions and model physical phenomena accurately
  • Utilize differentiation techniques to optimize and find maximum or minimum values in practical scenarios
  • Implement integration methods to calculate areas, volumes, and accumulated quantities precisely
  • Interpret the fundamental theorem of calculus to connect differentiation and integration seamlessly
  • Solve problems involving rates of change and motion using calculus principles
  • Develop skills to approach advanced topics like differential equations and multivariable calculus confidently
  • Use calculus tools to analyze and predict trends in scientific, engineering, and economic data
  • Enhance problem-solving abilities through applying calculus to real-life situations and experiments
  • Strengthen mathematical reasoning and critical thinking with calculus-based analysis
  • Leverage calculus concepts to improve understanding of physics, engineering, and data science applications
  • Build a solid foundation for further studies in mathematics, physics, and engineering disciplines
  • Apply calculus techniques to solve complex problems in various scientific and technological fields
  • Gain confidence in using calculus as a practical tool for academic and professional success

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Lessons | 67
Lesson 00 Calculus vs Pre Calculus | Course Outline | Recommended Books
00:06:24

Lesson 00 Calculus vs Pre Calculus | Course Outline | Recommended Books
Lesson 01 What is Calculus and its Types | Slope and Intercept of Straight Line
00:12:07

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
00:16:57

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
00:16:51

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 |
00:08:59

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
00:19:18

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
00:05:59

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
00:13:59

Lesson 07 Properties of Limits | Rules of Limits | Limits of a Rational Function
Lesson 08 Indeterminate Form of Limit | Indeterminate Forms with Solved Examples
00:09:57

Lesson 08 Indeterminate Form of Limit | Indeterminate Forms with Solved Examples
Lesson 09 Squeeze Theorem | Two Special Trigonometric Limits
00:09:42

Lesson 09 Squeeze Theorem | Two Special Trigonometric Limits
Lesson 10 Continuity of Function in OPEN CLOSE Interval| Vertical Horizontal Diagonal Asymptote
00:22:22

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
00:13:19

Lesson 11 The Intermediate Value Theorem | Applications of the Intermediate Value Theorem
Lesson 12 Infinite Limits | Limits to Infinity | Properties of Infinite Limits
00:21:40

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
00:19:06

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
00:15:11

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
00:14:15

Lesson 15 Differentiate and Continuity | How to Find the Vertical Tangent Line
Lesson 16 Part I Basic Differentiation Rules and Rates of Change
00:19:16

Lesson 16 Part I Basic Differentiation Rules and Rates of Change
Lesson 17 Part II Basic Differentiation Rules and Rates of Change
00:18:15

Lesson 17 Part II Basic Differentiation Rules and Rates of Change
Lesson 18 Product and Quotient Rules and Higher Order Derivatives
00:26:07

Lesson 18 Product and Quotient Rules and Higher Order Derivatives
Lesson 19 Chain Rule for Derivatives | Differentiation using The Chain Rule
00:26:13

Lesson 19 Chain Rule for Derivatives | Differentiation using The Chain Rule
Lesson 20 Implicit and Explicit Functions in Calculus for Differentiation
00:17:09

Lesson 20 Implicit and Explicit Functions in Calculus for Differentiation
Lesson 21 What is Related Rates in Calculus | How to Solve Related Rates Problems
00:28:14

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
00:16:04

Lesson 22 Extrema of an Interval | Minima Maxima Relative and Absolute Values
Lesson 23 Rolle s Theorem and Mean Value Theorem
00:20:20

Lesson 23 Rolle s Theorem and Mean Value Theorem
Lesson 24 Increasing and Decreasing Functions and the First Derivative
00:19:20

Lesson 24 Increasing and Decreasing Functions and the First Derivative
Lesson 25 Concavity and Second Derivative Test
00:28:15

Lesson 25 Concavity and Second Derivative Test
Lesson 26 Limits at Infinity
00:18:31

Lesson 26 Limits at Infinity
Lesson 27 A Summary of Curve Sketching | Analyzing the Graph of a Function
00:10:54

Lesson 27 A Summary of Curve Sketching | Analyzing the Graph of a Function
Lesson 28 Optimization Problems | Applied Minimum and Maximum Problems
00:17:34

Lesson 28 Optimization Problems | Applied Minimum and Maximum Problems
Lesson 29 Newton s Method | Newton s Method For Approximating The Zeros Of A Function
00:16:43

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
00:21:19

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
00:27:42

Lesson 31 Differentials |How to Calculate Differentials in Calculus | Error Handling using Calculus
Lesson 32 Integral Calculus | What is Integration OR Anti derivative
00:17:26

Lesson 32 Integral Calculus | What is Integration OR Anti derivative
Lesson 33 Antiderivatives and Indefinite Integration | Basic Integration Rules
00:19:14

Lesson 33 Antiderivatives and Indefinite Integration | Basic Integration Rules
Lesson 34 Area with Summation Notation | The Exhaustion Method | Upper and Lower Sum Integration
00:26:23

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
00:18:25

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
00:22:05

Lesson 36 Part II The Second Fundamental Theorem of Calculus | Net Change Theorem
Lesson 37 Riemann Sums and Definite Integrals | What is Definite Integrals
00:26:10

Lesson 37 Riemann Sums and Definite Integrals | What is Definite Integrals
Lesson 38 Integration by Substitution | Change of Variables for Definite Integrals
00:36:59

Lesson 38 Integration by Substitution | Change of Variables for Definite Integrals
Lesson 39 Numerical Integration | Trapezoidal Rule AND Simpson s Rule with Error Analysis
00:23:43

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