🎉

Calculus

Calculus for machine learning

91 Lessons

Start Learning

Core Stage 1

Prerequisites

Algebra

🎉

Numbers & Basic Operations

Preview

Active Quest

Polynomials and Factoring

Preview

Exponents and Radicals

Logarithms and Exponential Functions

Solving Equations and Inequalities

Functions and Their Properties

Graphing Functions

Transformations of Functions

Inverse Functions

Trigonometry

Angles and the Unit Circle

Trigonometric Functions and Their Graphs

Trigonometric Identities and Equations

Inverse Trigonometric Functions

Law of Sines & Law of Cosines

Polar Coordinates and Graphing

Pre-Calculus

Limits and Intuitive Understanding

Continuity and Discontinuity

Sequences and Series Basics

Parametric Equations

Conic Sections and Their Graphs

Core Stage 2

Calculus 1

Limits & Continuity

Introduction to Limits (Concept & Intuition)

Evaluating Limits Algebraically

One-Sided Limits

Limits at Infinity & Asymptotes

Epsilon-Delta Definition of Limits

Continuity and Discontinuous Functions

Derivatives & Differentiation

Definition of the Derivative (Limit Definition)

Basic Differentiation Rules (Power, Sum, Difference)

Product and Quotient Rules

Chain Rule

Implicit Differentiation

Higher-Order Derivatives

Derivatives of Trigonometric Functions

Derivatives of Exponential and Logarithmic Functions

Derivatives of Inverse Functions

Applications of Derivatives

Tangent and Normal Lines

Critical Points & Finding Extrema

Increasing & Decreasing Functions (First Derivative Test)

Concavity & Inflection Points

Mean Value Theorem

Related Rates

Optimization Problems

Core Stage 3

Calculus 2

Definite & Indefinite Integrals

Introduction to Integration

Basic Integration Rules

u-Substitution Method

Integration by Parts

Trigonometric Integrals

Trigonometric Substitution

Integration by Partial Fractions

Applications of Integration

Area Under a Curve

Area Between Two Curves

Volumes: Disk Method

Volumes: Washer Method

Shell Method

Arc Length & Surface Area

Work: Variable Force

Center of Mass & Centroids

Fluid Pressure and Force

Improper Integrals

Infinite Limits of Integration

Convergence and Divergence

Core Stage 4

Calculus 3

Functions of Several Variables

Introduction to Multivariable Functions

Partial Derivatives

Higher-Order Partial Derivatives

Gradient and Directional Derivatives

Divergence and Curl

Chain Rule in Multivariable Calculus

Multiple Integrals

Double Integrals over Rectangles

Double Integrals: General Regions

Triple Integrals

Change of Variables

Vector Calculus

Vector Fields and Their Properties

Line Integrals

Green’s Theorem

Surface Integrals and Stokes’ Theorem

Divergence Theorem

Core Stage 5

Optimization & Deep Learning Calculus

Gradients, Jacobians & Hessians

Scalar Fields & The Gradient Vector

The Jacobian Matrix: Derivative of Vector Functions

The Hessian Matrix: Curvature and Second Derivatives

Analyzing Optimization Surfaces (Saddle Points vs Local Minima)

Vectorized Chain Rule & Backpropagation

Multivariate Chain Rule Review

Computational Graphs & Flow of Information

The Vectorized Chain Rule: Matrix Form

Implementing Backpropagation: Recursive Derivatives

Constrained Optimization (Lagrange)

Optimization with Constraints: The Geometric View

The Method of Lagrange Multipliers

KKT Conditions for Inequality Constraints

Application: Support Vector Machines (SVMs) and Max-Margin

Automated Differentiation

Manual vs. Numeric vs. Automatic Differentiation

Dual Numbers & Forward-Mode AD

Wengert Lists & Reverse-Mode AD

How Deep Learning Frameworks (PyTorch/TF) Calculate Gradients

Path to Professional Mastery

🎉

Calculus

Calculus for machine learning

91 Lessons

Start Learning

Core Stage 1

Prerequisites

Algebra

🎉

Numbers & Basic Operations

Preview

Active Quest

Polynomials and Factoring

Preview

Exponents and Radicals

Logarithms and Exponential Functions

Solving Equations and Inequalities

Functions and Their Properties

Graphing Functions

Transformations of Functions

Inverse Functions

Trigonometry

Angles and the Unit Circle

Trigonometric Functions and Their Graphs

Trigonometric Identities and Equations

Inverse Trigonometric Functions

Law of Sines & Law of Cosines

Polar Coordinates and Graphing

Pre-Calculus

Limits and Intuitive Understanding

Continuity and Discontinuity

Sequences and Series Basics

Parametric Equations

Conic Sections and Their Graphs

Core Stage 2

Calculus 1

Limits & Continuity

Introduction to Limits (Concept & Intuition)

Evaluating Limits Algebraically

One-Sided Limits

Limits at Infinity & Asymptotes

Epsilon-Delta Definition of Limits

Continuity and Discontinuous Functions

Derivatives & Differentiation

Definition of the Derivative (Limit Definition)

Basic Differentiation Rules (Power, Sum, Difference)

Product and Quotient Rules

Chain Rule

Implicit Differentiation

Higher-Order Derivatives

Derivatives of Trigonometric Functions

Derivatives of Exponential and Logarithmic Functions

Derivatives of Inverse Functions

Applications of Derivatives

Tangent and Normal Lines

Critical Points & Finding Extrema

Increasing & Decreasing Functions (First Derivative Test)

Concavity & Inflection Points

Mean Value Theorem

Related Rates

Optimization Problems

Core Stage 3

Calculus 2

Definite & Indefinite Integrals

Introduction to Integration

Basic Integration Rules

u-Substitution Method

Integration by Parts

Trigonometric Integrals

Trigonometric Substitution

Integration by Partial Fractions

Applications of Integration

Area Under a Curve

Area Between Two Curves

Volumes: Disk Method

Volumes: Washer Method

Shell Method

Arc Length & Surface Area

Work: Variable Force

Center of Mass & Centroids

Fluid Pressure and Force

Improper Integrals

Infinite Limits of Integration

Convergence and Divergence

Core Stage 4

Calculus 3

Functions of Several Variables

Introduction to Multivariable Functions

Partial Derivatives

Higher-Order Partial Derivatives

Gradient and Directional Derivatives

Divergence and Curl

Chain Rule in Multivariable Calculus

Multiple Integrals

Double Integrals over Rectangles

Double Integrals: General Regions

Triple Integrals

Change of Variables

Vector Calculus

Vector Fields and Their Properties

Line Integrals

Green’s Theorem

Surface Integrals and Stokes’ Theorem

Divergence Theorem

Core Stage 5

Optimization & Deep Learning Calculus

Gradients, Jacobians & Hessians

Scalar Fields & The Gradient Vector

The Jacobian Matrix: Derivative of Vector Functions

The Hessian Matrix: Curvature and Second Derivatives

Analyzing Optimization Surfaces (Saddle Points vs Local Minima)

Vectorized Chain Rule & Backpropagation

Multivariate Chain Rule Review

Computational Graphs & Flow of Information

The Vectorized Chain Rule: Matrix Form

Implementing Backpropagation: Recursive Derivatives

Constrained Optimization (Lagrange)

Optimization with Constraints: The Geometric View

The Method of Lagrange Multipliers

KKT Conditions for Inequality Constraints

Application: Support Vector Machines (SVMs) and Max-Margin

Automated Differentiation

Manual vs. Numeric vs. Automatic Differentiation

Dual Numbers & Forward-Mode AD

Wengert Lists & Reverse-Mode AD

How Deep Learning Frameworks (PyTorch/TF) Calculate Gradients

Path to Professional Mastery