Scientia School of Natural Sciences

Implicit Differentiation Intro

How to Differentiate Implicitly

Finding the Derivative 1

Finding the Derivative 2

Finding the Derivative 3

The Equation of a Tangent

Implicit Differentiation And Stationary Points

Implicit Differentiation And Stationary Points (Algebra)

Parametric Differentiation and Finding the Gradient

Parametric Differentiation and The Equation of a Normal

Parametric Differentiation and Stationary Points

Parametric Differentiation and Equation of a Normal 2

Parametric Differentiation and Nature of Stationary Points

Trigonometric Differentiation sec(x)

Trigonometric Differentiation cot(x)

Trigonometric Differentiation csc(x)

Trigonometric Differentiation and the Chain Rule

Trigonometric Differentiation and the Quotient Rule

Trigonometric Differentiation and the Second Derivative

Inverse Trigonometric Differentiation sin^-1(x)

Inverse Trigonometric Differentiation cos^-1(x)

Inverse Trigonometric Differentiation tan^-1(x)

Inverse Trigonometric Differentiation General Differentiation Results

Exponential Differentiation Linear Function

Exponential Differentiation Trig Function

Exponential Differentiation Product Rule

Exponential Differentiation Quotient Rule

Exponential Differentiation Chain Rule

Exponential Differentiation and Implicit Differentiation

Exponential Differentiation Second Derivative

Exponential Differentiation Parametric Equations

Introduction to Logarithmic Differentiation

Logarithmic Differentiation and Differentiation Rules

Derivatives and Properties of Logarithms

Derivative of a^x

Alternative to the Quotient Rule

Introduction to First Partial Derivatives

First Partial Derivatives and Del Notation

First Partial Derivatives 1

First Partial Derivatives 2

First Partial Derivatives and the Gradient

Introduction to Second Partial Derivatives

Second Partial Derivatives and Del Notation

Integration Requiring Logarithms

Integration of an Exponential Function

Integration of a Function and its Derivative

Integration of Exponential Functions 1

Integration of Exponential Functions 3

Integration of Inverse Trigonometric Functions 1

Integration of Inverse Trigonometric Functions 2

Integration of Inverse Trigonometric Functions 3

Integration of Exponential Functions 2

Integrating Even Powers of sine and cosine

Integrating Even Powers of Cosine

Integrating Odd Powers of Sine

Integrating Odd Powers of Cosine

Integrating Combinations of Odd and Even Powers of Sine and Cosine

Integrating Even Powers of tan

Introduction to Integration by Parts

Introduction to LIATE

Integral of ln(x)

Integral of sin^(-1)x

Repeated Integration by Parts

Integration by Parts Requiring an Equation

Integration by Parts with Limits 1

Integration by Parts with Limits 2

Deriving and Using Reduction Formula

Deriving a Reduction Formula Involving Trig Part i

Deriving a Reduction Formula Involving Trig Part ii

Deriving a Reduction Formula Involving an Exponential Function

Deriving a Reduction Formula Involving the Product Rule

Deriving a Reduction Formula Involving the Product Rule (Alternate Method)

Deriving a Reduction Formula Involving a Substitution Part (a)

Deriving a Reduction Formula Involving a Substitution Part (b)

Deriving a Reduction Formula Involving a Substitution Part (c)

Deriving a Reduction Formula Involving a Substitution Part (d)

Introduction to Partial Fractions

Decomposing into Partial Fractions (Linear Factors)

Integrating Using Partial Fractions

Partial Fractions and Linear Factors

An Unfactorisable Quadratic Factor 1

An Unfactorisable Quadratic Factor 2

A Repeated Factor

Improper Fraction 1

Improper Fraction 2

Derivation of the Trapezium Rule

Using the Trapezium Rule

Introduction To Complex Numbers

Simplifying the Square Root of Negative Numbers

Combining Complex Numbers

Multiplying Complex Numbers

Division Of Complex Numbers

Square Root Of A Complex Number

Solving Quadratic Equations With Real Coefficients

Solving Quadratic Equations With Complex Coefficients

Roots of Equations 1

Roots of Equations 2

Introduction To The Argand Diagram

Sum and Difference on an Argand Diagram

The Modulus of A Complex Number

The Argument Of A Complex Number

The Argument Of A Complex Number 2

Writing Complex Numbers in Modulus Argument Form

Modulus Argument Form Multiplication Proof

Modulus Argument Form Division Proof

Use of Multiplication And Division Proof

Demoivre's Theorem Introduction

Demoivre's Theorem - Mathematical Induction

De Moivre's Trig Identity

De Moivre's Trig Identity 2

De Moivre's Trig Identity 3

De Moivre's Theorem To Determine Values of Complex Numbers 2

De Moivre's Theorem To Determine Values of Complex Numbers 1

Multiples Of Sine And Cosine Derivation

Multiples Of Sine And Cosine 1

Multiples Of Sine And Cosine 2

Exponential Form of a Complex Number

Locus On The Argand Diagram - Circle 2

Locus On The Argand Diagram - Circle 3

Locus On The Argand Diagram - Half - Line 1

Locus On The Argand Diagram - Inequality

Locus On The Argand Diagram - Inequality 2

Locus On The Argand Diagram - Vector Equation of a Line

Locus On The Argand Diagram - Largest Value

Locus On The Argand Diagram - Intersection

Introduction To Sequences

Writing The Terms of A Sequence

Determining The nth Term of a Sequence

Introduction to Convergent Sequences

Divergent Sequence

Convergence of a Sequence 1

Convergence of a Sequence 2

Convergence of a Sequence 3

Convergence of a Sequence 3 Alternate Method

Convergence of a Sequence 4

Recurrence Relations 1

Recurrence Relations 2

Mathematical Induction 1

Mathematical Induction 2

01- Introduction to the Method of Differences 1

02 - Method of Differences and Partial Fractions 2(i)

03 - Method Of Differences and the Sum to Infinity 2(ii)

04 - Method Of Differences and a Partial Sum 2(iii)

Introduction to Arithmetic Progressions

Finding the Common Difference

Proving an Arithmetic Progression

Proof Involving the Sum of an Arithmetic Progression

Sum of an Arithmetic Progression 1

Finding an Unknown Term

Sum of an Arithmetic Progression 2

Sum of an Arithmetic Progression 3

Introduction to Geometric Progressions

Proving a Geometric Progression

Finding an Unknown Term

A Real World Problem

Proof Involving the Sum of a Geometric Progression

Using the Sum Formula for a Geometric Progression

Introduction to the Sum to Infinity

Sum to Infinity Problem

Problem Involving Logarithms

Convergence of a Geometric Progression

Maclaurin's Series Derivation

cos(x)

tan(x)

An exponential function

Maclaurin's Series and Binomial Expansion

ln(x)

Taylor's Series Derivation

ln(x)

A Rational Function

sin(x)

Introduction to Pascal's Triangle

How to Use Pascal's Triangle

Introduction to Factorials

Introduction to Factorials 1

Introduction to Factorials 2

Factorials and Rational Expressions

Factorials and Method of Differences

nCr An Alternative to Pascal's Triangle

nCr and Factorials

Introduction to Binomial Expansion

How to Determine a Specific Term

The Product of 2 Expansions

Term Independent of x

Term Independent of x (Alternate Method)

A Rational Power

Expansion Requiring Division

Partial Fractions Part i

Partial Fractions Part ii

Partial Fractions Part iii

Approximations

Approximations from Expansion Requiring Division

Intermediate Value Theorem

Iterative Formula

Linear Interpolation

Bisection Method

Newton Raphson Derivation

Newton Raphson

Newton Raphson (Calculator)

LESSON 1 - Matrix Multiplication 1

LESSON 2 - How to Calculate the Determinant of a Matrix

LESSON 3 - Determinant of a Non-Singular Matrix

LESSON 4 - Determinant of a Singular Matrix

LESSON 5 - Determinant by Factoring 1

LESSON 6 - Determinant By Factoring 2

LESSON 7 - Inverse of a Matrix - Cofactor Method

System of Equations 1

System of Equations 2

Inverse By Row Reduction

Row Reduction and System of Equations 1

Row Reduction and System of Equations 2

Row Reduction and System of Equations 3

Separable Differential Equations 1

Separable Differential Equations 2

Separable Differential Equations 3

Integrating Factor 1

Integrating Factor 3

First Order Homogeneous

Second Order Homogeneous 1 (real, Distinct)

Second Order Homogeneous 2 (repeated Root)

Second Order Homogeneous (complex Roots)

Integrating Factor 2

Second Order Non-Homogeneous (linear)

Second Order Non- Homogeneous (quadratic)

Second Order Non-Homogeneous (trig)

Second Order Non-Homogeneous Part i

Second Order Non-Homogeneous Part ii

Second Order Non-Homogeneous

Second Order Homogeneous

Differential Equations With A Substitution 1

Differential Equations With A Substitution 2

Differential Equations With A Substitution 3

MATHEMATICAL MODELLING 1

MATHEMATICAL MODELLING 2

Probability

Sample Space

Tree Diagrams

Mutually Exclusive Events

Non Mutually Exclusive Events

Independent Events

Conditional Probability

Introduction to Permutations

Permutations r out of n objects

Permutations with Repeated Objects

Permutations with Conditions

Permutations with Conditions 2

Permutations with Conditions 3

Permutations with Conditions 4

Permutations with Conditions 5

Permutations with Conditions 6

Permutations with Conditions 7

Combinations 1

Combinations 2

Combinations 3

Combinations 4