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Course Materials
Lessons
Limits at Constants
- Video - Understanding Limits at Constant Values (6:28)
- Topic - Limits at Constant Values
- Topic - Limits at Constant Values involving Common Factors
- Topic - Limits at Constant Values involving Differences of Squares
- Topic - Limits at Constant Values involving Factorise
- Topic - Limits at Constant Values involving Quadratic Factorise
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)
- 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 a Given x Value: Quadratic Expressions
- Topic - First Principles at a Given x Value: 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 (3:20)
- 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 (1:59)
- Video - Differentiation of Polynomial Functions (13:28)
- 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)
- 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)
- Topic - Product Rule: Linear Products
- Topic - Product Rule: Non-Monic Linear Products
- Topic - Product Rule: Quadratic Products
- Topic - Product Rule: Complete Square and Linear Products
- Topic - Product Rule: Complete Cubic and Quadratic Products
- Topic - Product Rule: Complete Square and Linear Products
- Topic - Product Rule: Complete Cubic and Quadratic Products
Quotient Rule
- Video - Fundamental of Quotient Rule (2:53)
- Topic - Quotient Rule: Basic Rule
- Topic - Quotient Rule: Non-Monic Denominators
- Topic - Quotient Rule: Quadratic Numerators
- Topic - Quotient Rule: Quadratic Numerators and Denominators
- Topic - Quotient Rule: Basic Rule
- Topic - Quotient Rule: Non-Monic Denominators
- Topic - Quotient Rule: Quadratic Numerators
- Topic - Quotient Rule: Quadratic Numerators and Denominators
Derivatives of Exponential Functions
- Video - Fundamental of Derivative of Exponential Functions (1:30)
- Video - Derivative of Exponential Functions using Chain Rule (4:43)
- Video - Derivative of Exponential Functions using Quotient Rule (5:42)
- Video - Derivative of Exponential Functions using Product Rule (3:05)
- Video - Second Derivative of Exponential Functions (6:10)
- Video - Finding Equations of Tangent of Exponential Functions (3:04)
- Video - Stationary Point using Derivative of Exponential Functions (9:56)
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 (1:34)
- Video - Stationary Points using Derivative of Logarithmic Functions (5:32)
Derivatives of Trigonometric Functions
- Video - Differentiation of Sine Function : Chain Rule (13:03)
- Video - Differentiation of Sine Function : Product Rule (13:13)
- Video - Differentiation of Sine Function : Quotient Rule (6:38)
- Video - Differentiation of Cosine Function : Chain Rule (16:09)
- Video - Differentiation of Cosine Function : Product Rule (9:09)
- Video - Differentiation of Cosine Function : Quotient Rule (6:30)
- Video - Differentiation of Tangent Function (13:07)
- Video - Differentiation of Degrees (11:09)
- Video - Applications of Differentiation (6:01)
Tangents
- Video - Gradient of Tangents (4:46)
- Video - Application of Gradient of Tangents (7:49)
- Video - Equation of Tangents (6:15)
- Video - Angle and Gradient of Tangents (3:39)
- Video - Gradient of Parallel and perpendicular Tangents (8:38)
- Video - Horizontal Tangents (2:39)
- Video - Tangents and Corresponding y-intercepts (2:07)
- Video - Tangents and Corresponding x-intercepts (4:33)
Normals
- Video - Equation of Normals (7:13)
- Video - Equation of Normals at Hyperbola (5:42)
- Video - Applications of Tangents and Normals of Cubic Polynomials (4:29)
- Video - Equation of Normals involving Surd Functions (3:33)
- Video - Normal of Parabola Cuts Parabola Again (4:52)
- Video - Equation of Tangents and Normals at Hyperbola (7:18)
Turning Points
- Video - Coordinates of Turning Points (7:30)
- Video - Identifying the Nature of Turning Points using Tables (5:25)
- Video - Identifying Stationary Points (8:17)
- Video - Understanding Nature of Stationary Points (5:31)
- Video - No Stationary Points (1:50)
- Video - Condition of being Stationary Points (2:45)
- Video - Identifying the Nature of Stationary Points (6:48)
- Video - Stationary Points by their Shapes (7:34)
- Video - Turning Points of Hyperbola (3:42)
- Video - Turning Points of Rational Functions (1:17)
Points of Inflection and Concavity
- Video - Concavity of Graphs (5:02)
- Video - Points of Inflection (4:47)
- Video - Points of Inflection and Concavities (5:48)
- Video - No Points of Inflection (3:31)
- Video - Sketching Graphs using Points of Inflection (11:03)
- Video - Horizontal Points of Inflection (6:57)
- Video - Nature of Turning Points of Hyperbola (1:59)
- Video - Nature of Turning Points of Rational Functions (3:03)
Kinematics
- Video - Speed and Velocity 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 (20:27)
- Video - Velocity-Time Graphs: Piecewise Graphs (17:12)
- Video - Velocity-Time Graphs: Curves (8:26)
- Video - Acceleration-Time Graphs: Concave Downwards (8:27)
- Video - Acceleration-Time Graphs: Concave Upwards (6:43)
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 Rates 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 (8:47)
- Video - Maxima and Minima in 2D Applications (4:23)
- Video - Maxima and Minima in 3D Applications (6:09)
- Video - Absolute Maximum and Minimum (8:59)
- Video - Minimum Speed of the Motion (1:43)
- Video - Maximum Velocity Given Displacement (1:35)
Application of Derivatives of Trigonometric Functions
- Video - Simple Harmonic Motion: Velocity and Acceleration (9:30)
- Video - Simple Harmonic Motion: Displacement, Velocity and Acceleration with Time (12:20)
- Video - Rate of Change Involving Angles (7:01)
- Video - Speed and Velocity using Trigonometric Functions (0:59)
- Video - Motion At Rest in Trigonometric Functions (2:57)
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 using Double Angle Formula
- Video - Definite Integral of Trigonometric Functions by Substituting Cosine (2:49)
- Video - Integrating Trigonometric Functions using Double Angle Formula (9:46)
- Video - Definite Integration of Trigonometric Functions using Double Angle Formula (3:47)
- Video - Integration of Sine using Double Angle Formula (9:02)
- Video - Integration of Cosine using Double Angle Formula (5:21)
- Video - Integration of Product of Sine and Cosine using Double Angle Formula (6:53)
Particular Values
- Video - Finding Integral Constants (7:27)
- Topic - Finding Integral Constants from Linear Expressions
- Topic - Finding Integral Constants using Non-Monic Expressions from Linear Expressions
- Topic - Finding Integral Constants from Quadratic Expressions
- Topic - Finding Integral Constants using Non-Monic Expressions from Quadratic Expressions
- Topic - Finding Two Integral Constants from Linear Expressions
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)
Sine and Cosine Integration by Substitution
- 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 - Integrating Trigonometric Functions using Substitutions (5:19)
- Video - Definite Integration of Trigonometric Functions using Substitutions (5:56)
- Video - Integration of Sine using Substitution (6:20)
- Video - Integration of Cosine using Substitution (4:30)
- Video - Definite Integral of Trigonometric Functions by Substituting Sine (3:09)
- Video - Definite Integral of Trigonometric Functions using Cosine Double Angle Formula (4:06)
- Video - Integration of Product of Sine and Cosine using Substitution (3:50)
- Video - Definite Integral of Trigonometric Functions using Reverse Chain Rule (7:20)
Definite Integral of Exponential Functions
- Video - Definite Integration of Exponential Functions (3:40)
- 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
Definite Integral of Rational Functions
- Video - Finding Area of Rational Functions by Differentiating Logarithmic Functions (3:12)
- Topic - Definite Integral of Rational Functions: Basic Form
- Topic - Definite Integral of Rational Functions: Monic Linear Denominator
- Topic - Definite Integral of Rational Functions: Non-Monic Linear Fractions
- Topic - Definite Integral of Rational Functions: Multi-Term Denominators
- Topic - Definite Integral of Rational Functions: Multi-Term Denominators and Non-Monic Numerators
- Topic - Definite Integral of Rational Functions: Non-Monic Factor Multi-Term Denominators
- Topic - Definite Integral of Rational Functions: Non-Monic Factor Multi-Term Fractions
- Topic - Definite Integral of Rational Functions: Non-Monic Multi-Term Denominators
- Topic - Definite Integral of Rational Functions: Non-Monic Multi-Term Fractions
- Topic - Definite Integral of Rational Functions: Monic Quadratic Denominators
- Topic - Definite Integral of Rational Functions: Non-Monic Quadratic Denominators
- Topic - Definite Integral of Rational Functions: Non-Monic Cubic Denominators
- Topic - Definite Integral of Rational Functions: Rational Expressions
- Topic - Definite Integral of Rational Functions: Non-Monic Rational Expressions
Definite Integration by Substitution
- Video - Definite Integrals using Substitutions (4:22)
- Video - Definite Integrals using Substitutions involving Surds (3:43)
- Video - Definite Integrals using Substitutions involving Fractions (3:47)
- Video - Definite Integral of Trigonometric Functions by Substituting Sine (3:09)
- Video - Definite Integral of Trigonometric Functions using Cosine Double Angle Formula (4:06)
- Video - Definite Integral of Trigonometric Functions by Substituting Cosine (2:49)
Area between Two Functions
- Video - Area between Two Functions (3:56)
- Video - Finding the Enclosed Area by Graphing Functions (6:24)
- Video - Signed Enclosed Area between Two Functions (4:39)
- Video - Combined Signed Enclosed Areas between Two Functions (6:46)
- Video - Finding the Area between Sine Curve and a Straight Line (10:44)
- Video - Finding the Area between Sine and Cosine Curves (7:15)
Kinematics using Integration
- Video - Rates of Change and Integration (6:09)
- Video - Finding Expressions using Integration from Rates of Change (4:48)
- Video - Expression of the Distance using Integration (2:23)
- Video - Working with Velocity in Trigonometric Functions (3:11)
- Video - Working with Acceleration in Natural Exponential Functions (5:15)
- Video - Maximum Speed using Acceleration (8:17)
- Video - Changes in Displacement and Velocity (2:58)
Volumes using Integration
- Video - Volumes Rotated about the x-axis (8:33)
- Video - Volumes Rotated about the y-axis (5:58)
- Video - Finding the Volume involving Trigonometric Functions (5:40)
- Topic - Volume of Revolution bounded by Straight Lines and the X-axis
- Topic - Volume of Revolution bounded by Semi-Circles and the X-axis
- Topic - Volume of Revolution bounded by Surd Graphs and the Y-axis
- Topic - Volume of Revolution bounded by Parabolas and the X-axis
- Topic - Volume of Revolution bounded by Parabolas and the Y-axis
- Topic - True/False of Expression of Volumes Rotating the X-axis
- Topic - True/False of Expression of Volumes Rotating the Y-axis
Volumes for Two Functions
- Video - Volumes Between Two Functions (5:13)
- Topic - Volume of Revolution between Horizontal Lines and Parabolas
- Topic - Volume of Revolution between Straight Lines and Parabolas
- Topic - Volume of Revolution between Straight Lines and Surd Graphs
- Topic - Volume of Revolution about the Y-axis between Parabolas and Surd Graphs
- Topic - Half Volume of Revolution between Parabolas and Surd Cubic Graphs
- Topic - Volume of Revolution between Parabolas
