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

Given its prominence to neural networks and quantum computing, now is a good time to learn Linear Algebra.

MIT A 2020 Vision of Linear Algebra, Spring 2020Instructor: Gilbert StrangView the complete course: https://ocw.mit.edu/2020-visionYouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61iQEFiWLE21EJCxwmWvvek

Professor Strang describes independent vectors and the column space of a matrix as a good starting point for learning linear algebra. His outline develops the five shorthand descriptions of key chapters of linear algebra.

Learn Algebra in this full college course. Algebraic concepts are often used in programming.

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

Chapters:

• (0:00:00) Exponent Rules
• (0:10:14) Simplifying using Exponent Rules
• (0:31:46) Factoring
• (0:45:08) Factoring – Additional Examples
• (0:55:37) Rational Expressions
• (1:15:22) Rational Equations
• (1:37:01) Absolute Value Equations
• (1:42:23) Interval Notation
• (1:49:35) Absolute Value Inequalities
• (1:56:55) Compound Linear Inequalities
• (2:05:59) Polynomial and Rational Inequalities
• (2:16:20) Distance Formula
• (2:20:59) Midpoint Formula
• (2:23:30) Circles: Graphs and Equations
• (2:33:06) Lines: Graphs and Equations
• (2:41:35) Parallel and Perpendicular Lines
• (2:49:05) Functions
• (3:00:53) Toolkit Functions
• (3:08:00) Transformations of Functions
• (3:20:29) Introduction to Quadratic Functions
• (3:33:02) Standard Form and Vertex Form for Quadratic Functions
• (3:37:18) Justification of the Vertex Formula
• (3:41:11) Polynomials
• (3:49:06) Exponential Functions
• (3:56:53) Exponential Function Applications
• (4:08:38) Exponential Functions Interpretations
• (4:18:17) Compound Interest
• (4:29:33) Logarithms: Introduction
• (4:38:15) Log Functions and Their Graphs
• (4:48:59) Combining Logs and Exponents
• (4:53:38) Log Rules
• (5:02:10) Solving Exponential Equations Using Logs
• (5:10:20) Solving Log Equations
• (5:19:27) Doubling Time and Half Life
• (5:35:34) Systems of Linear Equations
• (5:47:36) Distance, Rate, and Time Problems
• (5:53:20) Mixture Problems
• (5:59:48) Rational Functions and Graphs
• (6:13:13) Combining Functions
• (6:17:10) Composition of Functions
• (6:29:32) Inverse Functions

Readers of Frank’s World know at least two things about me: I love data and I love learning. In 30 months, earned 41 certifications in Data Science, Data Engineering, and AI. All of this wouldn’t have been possible without the innovation of online learning.

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In this video, ForrestKnight shares his curated list of free courses from reputable universities like MIT, Stanford, and Princeton that satisfy the same requirements as an undergraduate Computer Science degree, minus general education. Everything is open source online and free.

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In the years since, Microsoft has added more professional programs, from Cybersecurity to DevOps. Naturally, I took and completed the tracks for AI and Big Data. You can hear Andy Leonard and I talk about our experiences with the program and how they differ from traditional MCP programs in this episode of Data Driven. Or click on the play button below.

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In this episode of Data Driven, Andy and I answer two questions sent in by listeners.

Press the play button below to listen here or visit the show page at DataDriven.tv