Introduction to Advanced Higher Mathematics
Introducing Advanced Higher Mathematics
Formulae
Algebra
Partial Fractions
Partial Fractions: Quiz
Factorials and Binomial Coefficients
Factorials and Binomial Coefficients: Quiz
The Binomial Theorem
Differentiation
Standard Derivatives and Rules for Differentiation
Standard Derivatives and Rules for Differentiation: Quiz
Further Differentiation
Further Differentiation: Quiz
Functions
Properties of Functions
Properties of Functions: Quiz
Critical Points
Related Graphs
Graphs of Trigonometric Functions
Integration
Basic Integration and Integration by Substitution
Basic Integration and Integration by Substitution: Quiz
Further Integration
Integration by Parts
Equations
Systems of Linear Equations and Gaussian Elimination
Special Cases
Matrices
Terms and Basic Matrix Operations
Matrix Multiplication and the Transpose of a Matrix
Matrix Multiplication: Quiz
Special Matrices
Linear Equations in Matrix Form and Geometric Transformations
Complex Numbers
Polynomial Equations
Argand Diagram and Geometric Figures
Polar Form and de Moivre’s Theorem
Sequences and Series
Arithmetic Sequences
Geometric Sequences
Maclaurin Series
Associated Series
Sequences and Series: Quiz
Maclaurin Series: Quiz
Vectors
Basic Skills Information
Equations of Lines
Equations of Planes
Intersections of Planes
Intersections of Lines and Planes
Angles Between Lines and Planes
Differential Equations
First-order Equations
Second-order Equations
Number Theory and Proof
Numbers, Notation and Direct Proof
Proof by Contradiction and by Contrapositive
Further Proof
Proof by Induction
Euclidean Algorithm