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Calculus 1 Fundamentals: Limits & Derivatives

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Overview

Master the building blocks of Calculus:  Limits & Derivatives

Section 1 - LIMITS

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

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 the derivative of combination of any functions.
  • The Chain Rule: To calculate the derivatives of composite functions no matter how complex they are.

Syllabus

  • Calculus Fundamentals : Overview
  • Introduction to Limits
  • Concept of Limits
  • Existence of Limits
  • Examples
  • Algebra of Limits
  • The L'Hospital Rule
  • The Sandwich Theorem
  • Limits of trigonometric functions
  • Limits at Infinity
  • Miscellaneous Examples-Limits
  • Introduction to Derivatives
  • Concept of Derivatives
  • First principle of Derivative
  • Algebra of Derivatives
  • Derivative of common functions
  • The Chain rule
  • Miscellaneous examples-Derivatives

Taught by

Tanmay Varshney

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