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freeCodeCamp.org

Learn Calculus 1 in this full college course.

This course was created by Dr. Linda Green, a lecturer at the University of North Carolina at Chapel Hill. Check out her YouTube channel: https://www.youtube.com/channel/UCkyLJh6hQS1TlhUZxOMjTFw

Lecture Notes

Course Contents:

  • (0:00:00) [Corequisite] Rational Expressions
  • (0:09:40) [Corequisite] Difference Quotient
  • (0:18:20) Graphs and Limits
  • (0:25:51) When Limits Fail to Exist
  • (0:31:28) Limit Laws
  • (0:37:07) The Squeeze Theorem
  • (0:42:55) Limits using Algebraic Tricks
  • (0:56:04) When the Limit of the Denominator is 0
  • (1:08:40) [Corequisite] Lines: Graphs and Equations
  • (1:17:09) [Corequisite] Rational Functions and Graphs
  • (1:30:35) Limits at Infinity and Graphs
  • (1:37:31) Limits at Infinity and Algebraic Tricks
  • (1:45:34) Continuity at a Point
  • (1:53:21) Continuity on Intervals
  • (1:59:43) Intermediate Value Theorem
  • (2:03:37) [Corequisite] Right Angle Trigonometry
  • (2:11:13) [Corequisite] Sine and Cosine of Special Angles
  • (2:19:16) [Corequisite] Unit Circle Definition of Sine and Cosine
  • (2:24:46) [Corequisite] Properties of Trig Functions
  • (2:35:25) [Corequisite] Graphs of Sine and Cosine
  • (2:41:57) [Corequisite] Graphs of Sinusoidal Functions
  • (2:52:10) [Corequisite] Graphs of Tan, Sec, Cot, Csc
  • (3:01:03) [Corequisite] Solving Basic Trig Equations
  • (3:08:14) Derivatives and Tangent Lines
  • (3:22:55) Computing Derivatives from the Definition
  • (3:34:02) Interpreting Derivatives
  • (3:42:33) Derivatives as Functions and Graphs of Derivatives
  • (3:56:25) Proof that Differentiable Functions are Continuous
  • (4:01:09) Power Rule and Other Rules for Derivatives
  • (4:07:42) [Corequisite] Trig Identities
  • (4:15:14) [Corequisite] Pythagorean Identities
  • (4:20:35) [Corequisite] Angle Sum and Difference Formulas
  • (4:28:31) [Corequisite] Double Angle Formulas
  • (4:36:01) Higher Order Derivatives and Notation
  • (4:39:22) Derivative of e^x
  • (4:46:52) Proof of the Power Rule and Other Derivative Rules
  • (4:56:31) Product Rule and Quotient Rule
  • (5:02:09) Proof of Product Rule and Quotient Rule
  • (5:10:40) Special Trigonometric Limits
  • (5:17:31) [Corequisite] Composition of Functions
  • (5:29:54) [Corequisite] Solving Rational Equations
  • (5:40:02) Derivatives of Trig Functions
  • (5:46:23) Proof of Trigonometric Limits and Derivatives
  • (5:54:38) Rectilinear Motion
  • (6:11:41) Marginal Cost
  • (6:16:51) [Corequisite] Logarithms: Introduction
  • (6:25:32) [Corequisite] Log Functions and Their Graphs
  • (6:36:17) [Corequisite] Combining Logs and Exponents
  • (6:40:55) [Corequisite] Log Rules
  • (6:49:27) The Chain Rule
  • (6:58:44) More Chain Rule Examples and Justification
  • (7:07:43) Justification of the Chain Rule
  • (7:10:00) Implicit Differentiation
  • (7:20:28) Derivatives of Exponential Functions
  • (7:25:38) Derivatives of Log Functions
  • (7:29:38) Logarithmic Differentiation
  • (7:37:08) [Corequisite] Inverse Functions
  • (7:51:22) Inverse Trig Functions
  • (8:00:56) Derivatives of Inverse Trigonometric Functions
  • (8:12:11) Related Rates – Distances
  • (8:17:55) Related Rates – Volume and Flow
  • (8:22:21) Related Rates – Angle and Rotation
  • (8:28:20) [Corequisite] Solving Right Triangles
  • (8:34:54) Maximums and Minimums
  • (8:46:18) First Derivative Test and Second Derivative Test
  • (8:51:37) Extreme Value Examples
  • (9:01:33) Mean Value Theorem
  • (9:09:09) Proof of Mean Value Theorem
  • (0:14:59) [Corequisite] Solving Right Triangles
  • (9:25:20) Derivatives and the Shape of the Graph
  • (9:33:31) Linear Approximation
  • (9:48:28) The Differential
  • (9:59:11) L’Hospital’s Rule
  • (10:06:27) L’Hospital’s Rule on Other Indeterminate Forms
  • (10:16:13) Newtons Method
  • (10:27:45) Antiderivatives
  • (10:33:24) Finding Antiderivatives Using Initial Conditions
  • (10:41:59) Any Two Antiderivatives Differ by a Constant
  • (10:45:19) Summation Notation
  • (10:49:12) Approximating Area
  • (11:04:22) The Fundamental Theorem of Calculus, Part 1
  • (11:15:02) The Fundamental Theorem of Calculus, Part 2
  • (11:22:17) Proof of the Fundamental Theorem of Calculus
  • (11:29:18) The Substitution Method
  • (11:38:07) Why U-Substitution Works
  • (11:40:23) Average Value of a Function
  • (11:47:57) Proof of the Mean Value Theorem for Integrals
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