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

- Calculus 1 Corequisite Notes: http://lindagreen.web.unc.edu/files/2020/08/courseNotes_math231L_2020Fall.pdf
- Calculus 1 Notes: http://lindagreen.web.unc.edu/files/2019/12/courseNotes_m231_2018_S.pdf

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