ADVANCED SCHOOL MATHEMATICS

• ABOUT


• DOING PHYSICS WITH MATLAB


• VISUAL PHYSICS ONLINE

• Trigonometry and Geometry


• Differentiation

PROBABILITY THEORY

• Probability


• Binomial Theorem


• Permutations, Combinations and Probability

GRAPH THEORY

• Graphs and Linear Functions


• Ellipses and Circles


• Online Activity: Graphing Polynomial Functions


• Hyperbola, Exponential, Logarithmic, Power Functions


• Trigonometric Functions


• Slope of a curve, Maxima and Minima


• Sketching Functions


• Problem solving using graphs and inequality relationships


• Exercises: Problems and Solutions

COMPLEX NUMBERS

• Characteristics of Complex Numbers


• Arithmetical Operations with Complex Numbers


• Powers and Roots of Complex Numbers


• Curves and Regions


• Exercises: Problems and Solutions

CONICS

• Ellipse


• Hyperbola


• Rectangular Hyperbola


• Parabola


• Conics Sections


• Exercises: Problems and Solutions

INTEGRATION

• Indefinite Integrals


• Definite Integrals


• Methods of Integration: Substitutions


• Methods of Integration: Algebraic Manipulations


• Methods of Integration: Integration by Parts


• Exercises: Problems and Solutions

VOLUMES

• Area Under Curves


• Volumes based upon Cross Sections


• Disk Method


• Cylindrical Shell Method


• Exercises: Problems and Solutions

MECHANICS

• Kinematics


• Dynamics


• Advanced Mechanics


• Simple Harmonic Motion


• Resisted Motion in Horizontal Direction


• Horizontal Motion with Resistance: drag and viscous drag forces


• Resisted Motion in Vertical Direction


• Analytical and Numerical Analysis of Vertical Motion with Resistance: drag and viscous drag force, falling, drag coefficient


• Circular Motion


• Circular Motion and Complex Numbers


• Motion Around a Banked Curve


• Conical Pendulum


• Exercises: Problems and Solutions

POLYNOMIALS

• Introduction to Functions and Polynomials


• Long Division of Polynomials


• Roots of Polynomials


• Roots: Half-interval Method and Newton's Method


• Fundamental Theorem of Algebra, Complex Numbers and Multiple Roots


• Exercises: Problems and Solutions

LINKS

• NSW Education Standards Authority


• WOLFRAM ALPHA: Computational engine for checking your mathematics


• MATHTUTOR: Help yourself - an excellent online maths tutor


• Libre Texts