MATHEMATICAL CONCEPTS

[Mathematical Concepts]

 Note: The majority of the Mathematical Concepts tutorials (listed below) include a number of practice questions at the end of the tutorial.

 
Specific Calculations    Determination of %YieldSolution Make-up & DilutionUnit ConversionsRearranging & Linearising Equations
 
Functions    Definition • Powers, Exponentials & Logarithms • Manipulation of Powers • Relationship between Logarithms and Exponentials • Manipulation of Logarithms • Trigonometric Functions • Trigonometric Identities • Use of Trigonometric Identities in Calculations
 
Calculus: Differentiation    Background • Rates of Change • Formal Derviation of the Magic Formula • Stationary Points • Function of a Function, Products & Quotients • Non-Polynomial Functions • Summary • Practice Exercises
 
Calculus: Integration    Introduction • Indefinite Integrals • Operation on Integrals • Definite Integrals • Integration of a Function of a Function • Practice Exercises
 
Matrices    Dimensions • Multiplication by a Constant, Addition & Subtraction • Multiplication of Matrices • Transpose • Determinant • Cofactor • Inverse • Using Matrices to Solve Simultaneous Equations • Practice Exercises
 
Vectors    Introduction • Notation • Cartesian Components • Adding/Subtracting Vectors • The Dot Product • The Cross Product • Practice Exercises
 
Complex Numbers    Imaginary Numbers • Complex Numbers • Addition/Subtraction • Multiplication • Complex Conjugates • Division using Complex Conjugates • The Argand Diagram • Polar Representation • The Exponential Form • Converting between Different Forms • Practice Exercises
 

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