Calculus
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Notes
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Videos & Interactives
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Questions
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Differential Calculus
Limits and Continuity (Notes)
Average and Instantaneous Rates of Change (Notes)
Average and Instantaneous Rates of Change (Notes)
Differentiation and the Derivative (Notes)
Graphs of Derivative and Anti-Derivative Functions (Notes)
Derivatives of Functions (Notes)
Derivatives of Combinations of Functions (Notes)
Differentiation Rules (Notes)
Derivatives of Inverse Circular Functions (Notes)
Tangents and Normals using Derivatives (Notes)
Intervals that are Stationary or Strictly Changing (Notes)
Maximum Rate of Change (Notes)
Maxima and Minima Problems (Notes)
Second Derivatives (Notes)
Related Rates of Change (Notes)
Implicit Differentiation (Notes)
Implicit Second Derivative (Notes)
Integral Calculus
Anti-Differentiation (Notes)
Deriving the Anti-Derivatives of Functions (Notes)
Area Approximation (Notes)
Approximation Applications (Notes)
The Definite Integral (Notes)
Anti-Differentiation by Recognition (Notes)
Integration and the Fundamental Theorem of Calculus (Notes)
Properties of Anti-Derivatives and Integration (Notes)
Finding a Function from a Rate of Change (Notes)
Anti-Differentiation and Integration (Notes)
Integration that Results in Logarithms (Notes)
Integration that Results in Inverse Circular Functions (Notes)
Anti-Differentiation and Integration using Substitutions (Notes)
Integration using Trigonometric Identities (Notes)
Integration using Partial Fractions of Rational Functions (Notes)
Graphs of Anti-Derivative Functions (Notes)
Numeric and Symbolic Integration (Notes)
Cumulative Effects of Growth (Notes)
Arc Lengths of Curves (Notes)
Area Under a Curve (Notes)
Average Value (Notes)
Areas of Regions Bounded by Curves (Notes)
Area of a Circle using Integration (Notes)
Volumes of Solids of Revolution (Notes)
Volumes of Cones and Spheres (Notes)
Volumes of Solids of Revolution - Method of Shells (Notes)
Differential Equations
Formulation of Differential Equations (Notes)
Example Applications of Differential Equations (Notes)
Verifying Solutions to Differential Equations (Notes)
Direction (Slope) Field (Notes)
Solution to Differential Equations (Notes)
Euler's Method of Approximation (Notes)
Kinematics
Kinematics - Straight Line Motion (Notes)
Kinematics and Anti-Derivatives (Notes)
Kinematics - Displacement and Velocity (Notes)
Kinematics - Acceleration (Notes)
Constant Acceleration (Notes)
Velocity-Time Graphs (Notes)
Vector Calculus
Position Vectors as a Function of Time (Notes)
Cartesian Equations and Paths of a Parametric Functions (Notes)
Differentiation of Vector Functions (Notes)
Velocity and Acceleration Vectors as Functions of Time (Notes)
Maximum and Minimum Distance and Speed (Notes)
Integration of Vector Functions (Notes)
Arc Length of a Parametric Path (Notes)
Projectile Motion (Notes)
Circular Motion (Notes)
Limits and Continuity (Notes)
Average and Instantaneous Rates of Change (Notes)
Average and Instantaneous Rates of Change (Notes)
Differentiation and the Derivative (Notes)
Graphs of Derivative and Anti-Derivative Functions (Notes)
Derivatives of Functions (Notes)
- Power Rule by First Principles (Notes)
- Exponentials and Logarithms by First Principles (Notes)
- Circular Functions by First Principles (Notes)
- Visual Derivatives of Functions (Notes)
Derivatives of Combinations of Functions (Notes)
- Derivatives of Combinations by First Principles (Notes)
- Derivatives using Product, Quotient, and Chain Rules (Notes)
- Visual Derivatives of Combinations (Notes)
Differentiation Rules (Notes)
Derivatives of Inverse Circular Functions (Notes)
Tangents and Normals using Derivatives (Notes)
Intervals that are Stationary or Strictly Changing (Notes)
Maximum Rate of Change (Notes)
Maxima and Minima Problems (Notes)
Second Derivatives (Notes)
Related Rates of Change (Notes)
Implicit Differentiation (Notes)
Implicit Second Derivative (Notes)
Integral Calculus
Anti-Differentiation (Notes)
Deriving the Anti-Derivatives of Functions (Notes)
Area Approximation (Notes)
Approximation Applications (Notes)
The Definite Integral (Notes)
Anti-Differentiation by Recognition (Notes)
Integration and the Fundamental Theorem of Calculus (Notes)
Properties of Anti-Derivatives and Integration (Notes)
Finding a Function from a Rate of Change (Notes)
Anti-Differentiation and Integration (Notes)
Integration that Results in Logarithms (Notes)
Integration that Results in Inverse Circular Functions (Notes)
Anti-Differentiation and Integration using Substitutions (Notes)
Integration using Trigonometric Identities (Notes)
Integration using Partial Fractions of Rational Functions (Notes)
Graphs of Anti-Derivative Functions (Notes)
Numeric and Symbolic Integration (Notes)
Cumulative Effects of Growth (Notes)
Arc Lengths of Curves (Notes)
Area Under a Curve (Notes)
Average Value (Notes)
Areas of Regions Bounded by Curves (Notes)
Area of a Circle using Integration (Notes)
Volumes of Solids of Revolution (Notes)
Volumes of Cones and Spheres (Notes)
Volumes of Solids of Revolution - Method of Shells (Notes)
Differential Equations
Formulation of Differential Equations (Notes)
Example Applications of Differential Equations (Notes)
Verifying Solutions to Differential Equations (Notes)
Direction (Slope) Field (Notes)
Solution to Differential Equations (Notes)
Euler's Method of Approximation (Notes)
Kinematics
Kinematics - Straight Line Motion (Notes)
Kinematics and Anti-Derivatives (Notes)
Kinematics - Displacement and Velocity (Notes)
Kinematics - Acceleration (Notes)
Constant Acceleration (Notes)
Velocity-Time Graphs (Notes)
Vector Calculus
Position Vectors as a Function of Time (Notes)
Cartesian Equations and Paths of a Parametric Functions (Notes)
Differentiation of Vector Functions (Notes)
Velocity and Acceleration Vectors as Functions of Time (Notes)
Maximum and Minimum Distance and Speed (Notes)
Integration of Vector Functions (Notes)
Arc Length of a Parametric Path (Notes)
Projectile Motion (Notes)
Circular Motion (Notes)
Partial Derivatives: Graphical Illustrator (GeoGebra Interactive)
Quadric Surfaces (GeoGebra Interactive)
Cylinders and Quadratic Surfaces Part 1 of 2 (patrickJMT Video)
Cylinders and Quadratic Surfaces, Part 2 of 2 (patrickJMT Video)
How I wish logistic growth was taught to me in Calc 2 (Zach Star)
Oxford Calculus
Taylor Series
Taylor Series (Maths Learning Centre UofA Video)
This is Why You're Learning Taylor Series (Zach Star Video)
Maclaurin Series or Taylor Series at 0 (GeoGebra Interactive)
Essence of Calculus
Overview of Differential Equations
Quadric Surfaces (GeoGebra Interactive)
Cylinders and Quadratic Surfaces Part 1 of 2 (patrickJMT Video)
Cylinders and Quadratic Surfaces, Part 2 of 2 (patrickJMT Video)
How I wish logistic growth was taught to me in Calc 2 (Zach Star)
Oxford Calculus
- Partial Differentiation Explained with Examples (Tom Rocks Maths Video)
- Finding Critical Points for Functions of Two Variables (Tom Rocks Maths Video)
- Classifying 2D Critical Points using the Discriminant (Tom Rocks Maths Video)
- Plotting 3D Graphs and Divergence Calculation (Tom Rocks Maths Video)
- Integrating Factors Explained (Tom Rocks Maths Video)
- Solving Simple PDEs (Tom Rocks Maths Video)
- Jacobians Explained (Tom Rocks Maths Video)
- Feynman's Integral Trick with Math With Bad Drawings (Tom Rocks Maths Video)
- Differential Equations (Tom Rocks Maths Video)
- Separation of Variables Integration Technique Explained with Examples (Tom Rocks Maths Video)
- Solving Homogeneous First Order Differential Equations (Tom Rocks Maths Video)
- M.I.T. Integration Bee Question (Tom Rocks Maths Video)
- Taylor's Theorem Explained with Examples and Derivation (Tom Rocks Maths Video)
- Heat Equation Derivation (Tom Rocks Maths Video)
- Separable Solutions to PDEs (Tom Rocks Maths Video)
- How to Solve the Heat Equation (Tom Rocks Maths Video)
- Fourier Series Derivation (Tom Rocks Maths Video)
- Gradient (Grad) and Divergence (Div) Explained (Tom Rocks Maths Video)
Taylor Series
Taylor Series (Maths Learning Centre UofA Video)
This is Why You're Learning Taylor Series (Zach Star Video)
Maclaurin Series or Taylor Series at 0 (GeoGebra Interactive)
Essence of Calculus
- Chapter 1 (3Brown1Blue Video)
- The Paradox of the Derivative (3Brown1Blue Video)
- Derivative Formulas through Geometry (3Brown1Blue Video)
- Visualising the Chain Rule and Product Rule (3Brown1Blue Video)
- What's so special about Euler's number e? Derivatives of Exponentials (3Brown1Blue Video)
- Implicit differentiation, what's going on here? (3Brown1Blue Video)
- Limits, L'Hopital's Rule, and Epsilon Delta Definitions (3Brown1Blue Video)
- Integration and the Fundamental Theorem of Calculus (3Brown1Blue Video)
- What does area have to do with slope? (3Brown1Blue Video)
- Higher Order Derivatives (3Brown1Blue Video)
- Taylor Series (3Brown1Blue Video)
- What They Won't Teach You In Calculus (3Brown1Blue Video)
Overview of Differential Equations
- Chapter 1 (3Brown1Blue Video)
- But what is a partial differential equation? (3Brown1Blue Video)
- Solving the Heat Equation (3Brown1Blue Video)
- But what is a Fourier series? From Heat Flow to Circle Drawings (3Brown1Blue Video)
- Understanding e to the i pi in 3.13 Minutes (3Brown1Blue Video)
First Order Differential Equations
Introduction to the Integrating Factor (Tayub Majeed TM Maths Questions)
The Integrating Factor (Tayub Majeed TM Maths Questions)
Modelling with the Integrating Factor (Tayub Majeed TM Maths Questions)
Reducible First-Order Differential Equations (Tayub Majeed TM Maths Questions)
Second Order Differential Equations
1. Sketching Combinations of Trigonometric and Exponential Functions (Tayub Majeed TM Maths Questions)
2. Introduction to 2nd-Order DEs (Tayub Majeed TM Maths Questions)
3. 2nd-Order Linear, Homogeneous DEs (Tayub Majeed TM Maths Questions)
4. 2nd-Order Linear, Non-Homogeneous DEs (Tayub Majeed TM Maths Questions)
5. Special Cases of 2nd-Order Linear, Non-Homogeneous DEs (Tayub Majeed TM Maths Questions)
6. Modeling with 2nd-Order Linear DEs (Tayub Majeed TM Maths Questions)
7. Coupled 1st-Order DEs (Tayub Majeed TM Maths Questions)
8. Reducible Second-Order Differential Equations (Tayub Majeed TM Maths Questions)
Introduction to the Integrating Factor (Tayub Majeed TM Maths Questions)
The Integrating Factor (Tayub Majeed TM Maths Questions)
Modelling with the Integrating Factor (Tayub Majeed TM Maths Questions)
Reducible First-Order Differential Equations (Tayub Majeed TM Maths Questions)
Second Order Differential Equations
1. Sketching Combinations of Trigonometric and Exponential Functions (Tayub Majeed TM Maths Questions)
2. Introduction to 2nd-Order DEs (Tayub Majeed TM Maths Questions)
3. 2nd-Order Linear, Homogeneous DEs (Tayub Majeed TM Maths Questions)
4. 2nd-Order Linear, Non-Homogeneous DEs (Tayub Majeed TM Maths Questions)
5. Special Cases of 2nd-Order Linear, Non-Homogeneous DEs (Tayub Majeed TM Maths Questions)
6. Modeling with 2nd-Order Linear DEs (Tayub Majeed TM Maths Questions)
7. Coupled 1st-Order DEs (Tayub Majeed TM Maths Questions)
8. Reducible Second-Order Differential Equations (Tayub Majeed TM Maths Questions)
