Course Materials
Lessons
Limits at Infinity
- Video - Understanding Limits at Infinity (6:20)
- Video - Calculating Limits at Infinity (7:51)
- Topic - Limits at Infinity
- Topic - Limits at Infinity involving Linear Fractions
- Topic - Limits at Infinity involving Quadratic Fractions
- Topic - Limits at Infinity involving Fractions Higher Degree Numerators
First Principles
- Video - Definition of First Principles (4:20)
- Video - Differentiation of x^2 from First Principles (2:12)
- Video - Differentiation of 3x^2 from First Principles (2:48)
- Video - Differentiation of Quadratic Polynomials from First Principles (4:27)
- Video - Differentiation of (x+1)^2 from First Principles (3:55)
- Video - Differentiation of x^3 from First Principles (2:05)
- Video - Differentiation of Square Root of x from First Principles (3:04)
- Topic - First Principles: Linear Expressions
- Topic - First Principles: Quadratic Expressions
- Topic - First Principles: Cubic Expressions
- Topic - First Principles: Surd Expressions
- Topic - First Principles: Rational Expressions
First Principles at a Given x-Value
- Topic - First Principles at Given x Values: Linear Expressions
- Topic - First Principles at Given x Values: Quadratic Expressions
- Topic - First Principles at Given x Values: Cubic Expressions
- Topic - First Principles at Given x Values: Surd Expressions
- Topic - First Principles at Given x Values: Rational Expressions
Basic Differentiation Rules
- Video - Differentiation of Constant Terms (2:14)
- Video - Differentiation of Linear Functions (3:16)
- Video - Methods of Differentiation (5:01)
- Video - Differentiation of Negative Exponents (5:12)
- Video - Differentiation of Non-Monic Negative Exponents (8:13)
- Video - Simplifying Expressions before Differentiation (6:37)
- Video - Principle of Differentiation of Surds (5:02)
- Video - Principle of Differentiation of Surds: Square Roots (4:58)
- Video - Principle of Differentiation of Surds: Quad Roots (2:24)
- Video - Principle of Differentiation of Surds involving Fractions (6:35)
- Video - Differentiation of Polynomial Functions (3:48)
- Video - Differentiation of Functions in Terms of Specific Letters (2:43)
- Video - Differentiation of Functions in Terms of Specific Letters involving Additions (4:37)
- Video - Differentiation of Functions in Terms of Specific Letters involving Multiplications (6:20)
- Video - Equations involving Differentiation (1:51)
Chain Rule
- Video - Fundamental of Chain Rule (7:58)
- Video - Chain Rule involving Rational Functions (5:24)
- Video - Chain Rule involving Irrational Functions (6:06)
- Video - Derivative Value using Chain Rule involving Irrational Functions (1:46)
- Topic - Chain Rule: Power of Linear Expressions
- Topic - Chain Rule: Power of Quadratic Expressions
- Topic - Chain Rule: Surds 1/2 Power
- Topic - Chain Rule: Surds 3/2 Power
- Topic - Chain Rule: Surds 1/3 Power
- Topic - Chain Rule: Linear Rational Expressions
- Topic - Chain Rule: Quadratic Rational Expressions
- Topic - Chain Rule: Rational Expressions of Surds
- Topic - Chain Rule: Cubic Rational Expressions
Product Rule
- Video - Fundamental of Product Rule (7:49)
- Video - Product Rule and Chain Rule 1 (3:32)
- Video - Product Rule and Chain Rule 2 (4:12)
- Video - Derivative Value using Product Rule and Chain Rule (3:26)
- Topic - Product Rule: Linear Products
- Topic - Product Rule: Non-Monic Linear Products
- Topic - Product Rule: Quadratic Products
- Topic - Product Rule: Complete Square & Linear Products
- Topic - Product Rule: Complete Cubic and Quadratic Products
Quotient Rule
- Video - Fundamental of Quotient Rule (2:53)
- Video - Differentiations using Quotient Rule (7:53)
- Video - Finding Pronumerals involving Quotient Rule (2:42)
- Video - Derivative Value using Quotient Rule (1:37)
- Topic - Quotient Rule: Basic Rule
- Topic - Quotient Rule: Non-Monic Denominators
- Topic - Quotient Rule: Quadratic Numerators
- Topic - Quotient Rule: Quadratic Numerators and Denominators
Higher Derivatives
- Video - Fundamental of Higher Derivatives (5:34)
- Video - Higher Derivatives involving Chain Rule (4:59)
- Video - Higher Derivatives involving Surds (5:27)
- Video - Higher Derivatives involving Quotient Rule (2:40)
- Video - Higher Derivatives involving Product Rule (6:16)
- Topic - Higher Derivatives of Quadratic Polynomials
- Topic - Higher Derivatives of Cubic Polynomials
- Topic - Higher Derivatives using Chain Rule
Kinematics using Differentiation
- Video - Velocity and Speed using Exponential Functions (1:10)
- Video - Motion At Rest in Exponential Functions (1:38)
- Video - Motion Never At Rest (1:40)
- Video - Displacement-time Graphs (8:46)
- Video - Displacement-Velocity Graphs: Lines (7:12)
- Video - Displacement-Velocity Graphs: Curves (6:09)
- Video - Velocity-Time Graphs: Straight Lines 1 (5:15)
- Video - Velocity-Time Graphs: Piecewise Graphs 1 (4:24)
- Video - Velocity-Time Graphs: Curves (7:18)
- Video - Acceleration-Time Graphs: Concave Downwards (8:27)
- Video - Acceleration-Time Graphs: Concave Upwards (6:43)
Differentiation and Displacement, Velocity and Acceleration
- Video - Velocity and Speed (3:04)
- Video - Kinematics given Velocity (9:49)
- Video - Kinematics given Displacement (10:51)
- Topic - Working with Displacement
- Topic - Moving Forward or Backward
- Topic - Obtaining Velocity from Displacement
- Topic - Obtaining Acceleration from Velocity
- Topic - Obtaining Acceleration from Displacement
- Topic - Obtaining Displacement from Velocity
- Topic - Obtaining Displacement from Acceleration
- Topic - Understanding Velocity and Speed
- Topic - Total Distance Travelled of Linear Displacement
- Topic - Total Distance Travelled of Quadratic Displacement
- Topic - Total Distance Travelled of Cubic Displacement
Rates of Change
- Video - Basic Rates of Change in Polynomial Functions (4:08)
- Video - Rates of Change of Population (9:29)
- Video - Rates of Change of Volumes in terms of Quantity (6:32)
- Video - Rates of Change of Volumes in terms of Ratio (4:47)
- Video - Related Rate of Change involving Surface Area and Volume (6:29)
- Video - Related of Rates of Change involving Radius and Volume (3:22)
- Video - Related of Rates of Change involving Pythagoras Theorem (4:14)
- Video - Eliminating Height Pronumerals in Rates of Change (5:14)
- Video - Eliminating Radius Pronumerals in Rates of Change (6:15)
- Video - Rate of Change Involving Angles (7:01)
Optimisation
- Video - Maxima and Minima of Quadratic Functions (4:16)
- Video - Maxima and Minima of Cubic Functions 1 (8:47)
- Video - Maxima and Minima of Cubic Functions 2 (4:02)
- Video - Maxima and Minima in 2D Applications (4:23)
- Video - Maxima and Minima in 3D Applications 1 (6:09)
- Video - Maxima and Minima in 3D Applications 2 (3:53)
- Video - Absolute Maximum and Minimum (8:59)
- Video - Minimum Speed of the Motion (1:43)
- Video - Maximum Velocity Given Displacement (1:35)
Basic Integration Rules
- Video - Principles of Antidifferentiation (7:29)
- Video - Antidifferentiation and Differentiation (6:10)
- Video - Antidifferentiation of Polynomial Functions (3:51)
- Video - Integration of Fractions (7:09)
- Video - Integration for Surds (7:34)
- Video - Basic Integration Rules (7:18)
- Video - Integration of Multi Term Expressions (2:25)
- Video - Integration of Rational Exponents (9:38)
- Video - Simplifying before Integration (9:37)
- Video - Expanding before Integration (7:27)
- Video - Binomial Expansion before Integration (6:34)
Integration of Power Functions
- Video - Principle of Integration of Power Function (2:49)
- Video - Integration of Power Functions (1:56)
- Video - Integration of Power Functions involving Fractions (2:23)
- Video - Integration of Power Functions Surds (1:06)
- Video - Integration of Power Functions (5:32)
- Video - Integration of Reciprocal Functions (1:35)
- Video - Integration of Irrational Functions (4:32)
- Video - Integration of Reciprocal Irrational Functions (4:41)
Indefinite Integration by Recognition
- Video - Reverse Chain Rule (7:06)
- Video - Integration by Recognition: Using Derivative of Exponential Functions (3:45)
- Video - Integration by Recognition using Derivative of Sine Function (3:32)
- Video - Integration by Recognition using Derivative of Cosine Function (4:20)
- Video - Integration by Recognition using Derivative of Tangent Function (4:16)
- Video - Integration by Recognition: Using Derivative of Logarithmic Functions (4:10)
- Video - Integration by Recognition using Product Rule (6:16)
- Video - Integration by Recognition using Long Division (7:22)
- Video - Integration of cosec x by Recognition involving Log TAN (4:18)
- Video - Integration of sec x by Recognition (4:52)
Integration by Substitution
- Video - Integration using Substitutions 1 (3:45)
- Video - Integration using Substitutions 2 (3:05)
- Video - Integration using Substitutions 3 (2:06)
- Video - Removal of Pronumerals 1 (4:39)
- Video - Removal of Pronumerals 2 (2:28)
- Video - Removal of Pronumerals 3 (2:43)
- Topic - Integration by Substitution: Basic
- Topic - Integration by Substitution: Surds
- Topic - Integration by Substitution: Rational Expressions
Particular Values
- Video - Finding Integral Constants (7:27)
- Video - Finding Integral Constants involving Point of Inflections (4:45)
- Video - Finding Integral Constants involving Second Derivatives (2:33)
- Topic - Finding Integral Constants from Linear Expressions
- Topic - Integral Constants by Non-Monic Expressions from Linearity
- Topic - Finding Integral Constants from Quadratics
- Topic - Integral Constants using Non-Monic Expressions from Quadratics
- Topic - Finding Two Integral Constants from Linear Expressions
Derivatives of Exponential Functions
- Video - Derivative of Exponential Functions (1:30)
- Video - Derivative of Exponential Functions using Chain Rule (6:29)
- Video - Derivative of Exponential Functions using Quotient Rule (7:20)
- Video - Derivative of Exponential Functions using Product Rule (6:12)
- Video - Second Derivative of Exponential Functions (6:10)
- Video - Equations of Tangent of Exponential Functions (4:46)
- Video - Stationary Point using Derivative of Exponential Functions (9:56)
- Video - Maximum Turning Point of Exponential Functions (7:18)
Definite Integral of Exponential Functions
- Video - Definite Integration of Exponential Functions (6:47)
- Video - Volume of Region bounded by Exponential Graphs (1:57)
- Topic - Definite Integral of Exponential Functions
- Topic - Definite Integral of Exponential Functions involving Reciprocals
- Topic - Definite Integral of Exponential Functions involving Expansions
- Topic - Definite Integral of Exponential Functions involving Surds
Derivatives of Logarithmic Functions
- Video - Fundamental of Derivative of Logarithmic Functions (2:41)
- Video - Derivative of Logarithmic Functions using Logarithm Law of Addition (4:06)
- Video - Derivative of Logarithmic Functions using Logarithm Law of Subtraction (1:47)
- Video - Derivative of Logarithmic Functions involving Indices (3:36)
- Video - Derivative of Mixed Logarithmic Functions (5:24)
- Video - Derivative of Non-Natural Logarithmic Functions (3:09)
- Video - Stationary Points using Derivative of Logarithmic Functions (5:32)
- Video - Derivative of Logarithmic Functions using Quotient Rule (4:40)
- Video - Tangents and Normals of Logarithmic Functions (2:15)
Integration of Rational Functions
- Video - Integration Rule of Rational Functions (5:13)
- Video - Integration Rule of Rational Functions involving Coefficients (6:59)
- Video - Integration Rule of Rational Functions after Simplification (6:16)
- Video - Integration of Rational Functions by Substitution (2:54)
- Video - Integrating Linear by Linear Resulting Natural Log Functions (3:11)
- Video - Integrating Quadratics by Linear Resulting Natural Log Functions (2:18)
- Video - Integrations of Cubic by Quadratic Resulting Natural Log Functions (2:31)
