Math for Machine Learning : Calculus 1
Understand the fundamental principles of calculus.
Apply differentiation and integration techniques to solve problems.
Analyze and interpret mathematical models using calculus.
Develop critical thinking and problem-solving skills in various real-world contexts.
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77 Lessons
This course provides an introduction to the principles of calculus, covering topics such as limits, derivatives, and integrals. You will learn to apply calculus techniques to solve mathematical problems and analyze real-world phenomena. Emphasis is placed on developing a deep understanding of calculus concepts and their applications in various fields such as science, engineering, economics, and more.
Course Content
Introduction
Intro
Module 1 - Corequisite
Rational Expressions
Difference Quotient
Lines_ Graphs and Equations
Rational Functions and Graphs
Right Angle Trigonometry
Sine and Cosine of Special Angles
Unit Circle Definition of Sine and Cosine
Properties of Trig Functions
Graphs of Sine and Cosine
Module 2 - Corequisite
Graphs of Sinusoidal Functions
Graphs of Tan, Sec, Cot, Csc
Solving Basic Trig Equations
Trig Identities
Pythagorean Identities
Angle Sum and Difference Formulas
Double Angle Formulas
Composition of Functions
Solving Rational Equations
Module 3 - Corequisite
Logarithms_ Introduction
Log Functions and Their Graphs
Combining Logs and Exponents
Log Rules
Inverse Functions
Inverse Trig Functions
Solving Right Triangles
Polynomial and Rational Inequalities
Summation Notation
Module 4 Math for Machine Learning : Calculus 1
Module 5 Math for Machine Learning : Calculus 1
Computing Derivatives from the Definition
Interpreting Derivatives
Derivatives as Functions and Graphs of Derivatives
Proof that Differentiable Functions are Continuous
Power Rule and Other Rules for Derivatives
Higher Order Derivatives and Notation
Derivative of e^x
Proof of the Power Rule and Other Derivative Rules
Product Rule and Quotient Rule
Proof of Product Rule and Quotient Rule
Module 6 Math for Machine Learning : Calculus 1
Proof of Trigonometric Limits and Derivatives
Derivatives and Rates of Change (Rectilinear Motion)
Marginal Cost
The Chain Rule
More Chain Rule Examples and Justification
Justification of the Chain Rule
Implicit Differentiation
Derivatives of Exponential Functions
Derivatives of Log Functions
Logarithmic Differentiation
Module 7 Math for Machine Learning : Calculus 1
Related Rates - Distances
Related Rates - Volume and Flow
Related Rates - Angle and Rotation
Maximums and Minimums
Mean Value Theorem
Proof of Mean Value Theorem
Derivatives and the Shape of the Graph
First Derivative Test and Second Derivative Test
Derivatives and the shape of the graph - example
Extreme Value Examples
Module 8 Math for Machine Learning : Calculus 1
Linear Approximation
The Differential
L'Hospital's Rule
L'Hospital's Rule on Other Indeterminate Forms
Newtons Method
Antiderivatives
Finding Antiderivatives Using Initial Conditions
Any Two Antiderivatives Differ by a Constant
Summation Notation
Module 9 Math for Machine Learning : Calculus 1
Approximating Area
The Fundamental Theorem of Calculus, Part 1
The Fundamental Theorem of Calculus, Part 2
Proof of the Fundamental Theorem of Calculus
The Substitution Method
Why U-Substitution Works
Average Value of a Function
Proof of the Mean Value Theorem for Integrals
Recitation 2 a solution and some hints
Limit as x goes to infinity recitation problem
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