Differential Calculus

Categories: Mathematics
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About Course

Welcome to the World of Calculus Mastery!

 

Are you ready to embark on a journey that will not only transform the way you perceive mathematics but also empower you with tools that unlock a realm of possibilities? Join us in in this course, where you’ll dive headfirst into the fascinating world of Differential Calculus.

 

Why Do You Need This Course For?

 

In this course, we go beyond textbooks and traditional teaching methods. We’re not just about limits, derivatives, and equations. We’re about unleashing your potential to understand the fundamental building blocks of change and motion. Imagine being able to decipher the language of curves, understand the heartbeat of functions, and unveil the secrets hidden in mathematical landscapes.

 

What Will You Learn?

 

Module 1: Limits – Breaking Boundaries

 

Discover the art of approaching mathematical infinity, dancing with trigonometric functions, and mastering the mystical Squeeze Theorem. Limits are not just mathematical hurdles; they’re gateways to understanding continuity, the heartbeat of functions, and the essence of calculus itself.

 

Module 2: Derivatives – Crafting Curves

 

Derivatives aren’t just about finding slopes; they’re about unraveling the story behind every curve. From tangents that touch the soul of functions to the Chain Rule that weaves the fabric of complex expressions, you’ll gain the power to see and shape the mathematical world around you.

 

Module 3: Advanced Derivation Techniques – Artistry in Calculus

 

Enter the realm of mathematical artistry! Implicit differentiation becomes your brush, logarithmic techniques your palette. The Inverse Function Theorem is your guide through the landscapes of inverse functions. You’ll elevate your skills to higher dimensions, exploring the poetry of higher order derivatives and the precision of linear approximation.

 

Module 4: Applications to Derivatives – Real-World Mastery

 

It’s time to apply your newfound calculus superpowers! Become the detective of mathematical mysteries using the Mean Value Theorem. Find peaks and valleys, navigate through inflection points, and conquer optimization problems. L’Hôpital’s Rule and the Newton-Raphson method are your secret weapons for tackling even the most elusive mathematical challenges.

 

Why is this Course Essential?

 

Beyond acing exams, mastering Differential Calculus opens doors to a multitude of fields. Whether you’re venturing into physics, engineering, economics, or data science, the ability to understand change on a fundamental level is your passport to success. This course is your key to unlocking advanced subjects, paving the way for your academic and professional journey.

 

What Awaits You After This Course?

 

Complete this course, and you’re not just gaining knowledge; you’re acquiring a skill set that’s the backbone of scientific exploration and innovation. From conquering multivariable calculus to delving into the mysteries of differential equations, you’ll be ready to take on the challenges of advanced mathematical landscapes.

 

So, are you ready to unleash your potential? Join us and redefine your relationship with mathematics. Let’s embark on this adventure together!

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What Will You Learn?

  • Understand the foundational concept of limits and their significance in calculus.
  • Grasp the concept of continuity and its implications.
  • Establish the fundamental concept of derivatives and their significance.
  • Apply derivative rules to well-known functions.
  • Compute tangent lines and understand their connection to derivatives.
  • Explore various derivation techniques, including the powerful Chain Rule.
  • Analyze critical points and monotony as applications of derivatives.
  • Locate and analyze minima and maxima using derivatives.
  • Understand inflection points and concavity through the second derivative.
  • Apply the L'Hôpital's Rule and the Newton-Raphson method for evaluating limits and finding roots.

Course Content

Limits & Continuity
In the Limits module, students will embark on a journey to understand the foundational concept of limits, exploring lateral limits, the Law of Limits, and strategies for resolving indeterminate forms. The module delves into the world of trigonometric limits, the Squeeze Theorem, and the significance of continuity. As students progress, they will master the Intermediate Value Theorem, analyze limits as variables approach infinity, and grasp the concept of asymptotic behavior and asymptotes, setting the stage for a comprehensive understanding of mathematical boundaries.

  • The Concept of Limits
    02:39
  • Lateral Limits
    03:55
  • The Laws of Limits
    04:52
  • First Quiz
  • Indetermination Form
    03:02
  • Trigonometric Limits
    04:38
  • Squeeze Theorem
    03:30
  • Second Quiz
  • Continuity (Part I)
    03:53
  • Continuity (Part II)
    03:08
  • Intermediate Value Theorem
    02:17
  • Third Quiz
  • Limits to Infinity (Part I)
    07:18
  • Limits to Infinity (Part II)
    03:05
  • Fourth Quiz
  • Oblique Asymptotes
    01:49

Introduction to Derivatives
The Derivatives module is an exploration of the artistry behind crafting curves. Students will establish a solid understanding of fundamental derivative concepts and apply rules to well-known functions. The module unfolds the intricacies of computing tangent lines and explores various derivation techniques, including the powerful Chain Rule. This module is designed to empower learners to not just find slopes but to unravel the stories embedded in curves, providing them with a toolkit for understanding and manipulating mathematical functions.

Advanced Derivation Techniques
In the Advanced Derivation Techniques module, students ascend to the realm of mathematical artistry. Implicit differentiation becomes a brush for handling implicit functions, logarithmic techniques add color to complex problems, and the Inverse Function Theorem acts as a guide through the landscapes of inverse functions. Learners extend their skills to higher orders, exploring the poetry of higher derivatives and the precision of linear approximation. This module transforms calculus from a set of rules to an art form, preparing students to tackle more sophisticated mathematical challenges.

Applications to Derivatives
The Applications to Derivatives module brings calculus into the real world, equipping students with the skills for practical problem-solving. From applying the Mean Value Theorem to understand the relationship between derivatives and average rates of change, to analyzing critical points and monotony, and solving optimization problems, this module bridges the gap between theory and application. Students will also explore inflection points, concavity through the second derivative, and apply advanced techniques like Hôpital's Rule and the Newton-Raphson method, ensuring they are adept at navigating real-world challenges across various disciplines.

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