TRANSMATH SYLLABUS

There are sixteen Transmath modules covering nine topics. A list of sub-
sections within each module is given here as a brief indication of the 
syllabus covered.

Algebra
	Elementary Algebra (5 exercises)
		1.	Pre-requisites (Negative Numbers, Order of Operations, 
			HCF and LCM, Fractions, Powers & Indices)
		2.	Symbols and Numbers
		3.	Like Terms (Ex.1 & Ex.2)
		4.	Multiplying Expressions (Ex.3)
		5.	Factorising Expressions (Ex.4)
		6.	Algebraic Fractions (Ex.5*)
		7.	Summary

Calculus
	Introduction to Differentiation (5 exercises)
		1.	The Tangent Problem
		2.	Rates of Change (Ex.1)
		3.	Combined Rates of Change (Ex.2)
		4.	Gradient of Curves
		5.	Derivatives of Polynomials (Ex.3)
		6.	Negative and Fractional Powers (Ex.4)
		7.	Trig, Exp and Log Functions (Ex.5*)
		8.	Summary

	Techniques of Differentiation (5 exercises)
		1.	Max. and Min. (Ex.1*)
		2.	Compound Functions (Product Rule (Ex.2*), 
			Quotient Rule (Ex.3*), Chain Rule (Ex.4*))
		3.	Implicit Differentiation (Ex.5*)
		4.	Summary

	Indefinite Integration (4 exercises)
		1.	Introduction
		2.	Standard Integrals (Ex.1*)
		3.	Fractional and Negative Powers (Ex.2)
		4.	Change of Variable (Ex.3*)
		5.	Integration by Parts (Ex.4*)
		6.	Other Tricks (adding on zero, multiplying by one)
		7.	Summary

	Techniques of Integration (5 exercises)
		1.	Introduction
		2.	Trigonometric Integrals (Ex.1*)
		3.	Trigonometric Substitution (Ex.2*)
		4.	Partial Fractions (Ex.4*) (incl. Completing the Square 
			and Polynomial Long Division (Ex.3*))
		5.	Reduction Formulas (Ex.5)
		6.	Summary

	Definite Integration (2 exercises)
		1.	Introduction
		2.	Limits of an Integral (Ex.1*)
		3.	Area under a Curve (including Area under Speed-Time 
			graph)
		4.	Volumes of Revolution (Ex.2*)
		5.	Summary

	Ordinary Differential Equations (5 exercises)
		1.	Introduction
		2.	1st Order Separable Equations (Ex.1*)
		3.	1st Order Linear Equations (Integrating Factor) (Ex.2*)
		4.	Applications (Population Dynamics, Motion of a Rocket)
		5.	2nd Order Linear Equations (Complementary Function 
			(Ex.3*), Particular Integral (Ex.4*), 
			General Solution, Particular Solution (Ex.5*))
		6.	Summary

Complex Numbers
	Introduction to Complex Numbers (4 exercises)
		1.	Introduction
		2.	Imaginary Numbers (Ex.1)
		3.	The Argand Diagram
		4.	Modulus and Argument Form (Ex.2)
		5.	De Moivre's Theorem (Ex.3*)
		6.	nth Roots of a Complex Number (Ex.4*)
		7.	Summary

Functions
	Introduction to Functions (3 exercises)
		1.	Introduction
		2.	Definitions
		3.	Algebraic Functions (Ex.1)
		4.	Function of a Function (Ex.2*)
		5.	Inverse Functions (Ex.3)
		6.	Summary

Matrices
	Introduction to Matrices (4 exercises)
		1.	Introduction
		2.	Applications
		3.	Definitions (Transpose and Symmetry (Ex.1))
		4.	Matrix Algebra (Addition (Ex.2), Multiplicative 
			Condition (Ex.3), Multiplication (Ex.4))
		5.	Summary

	Transformations (1 exercise)
		1.	Introduction
		2.	Transformations in the Plane
		3.	Rotation and Reflection
		4.	Stretching and Shearing
		5.	Combinations of Transformations
		6.	Inverse Transformations
		7.	Investigation* and Exercises (Ex.1)
		8.	Summary

	Advanced Matrices (4 exercises)
		1.	Introduction
		2.	Determinants (Ex.1)
		3.	Inverse of a Matrix (Ex.2)
		4.	Systems of Linear Equations (Ex.3*)
		5.	Eigenvalues and Eigenvectors (Ex.4*)
		6.	Summary


Numerical Methods
	Introduction to Numerical Methods (3 exercises)
		1.	Introduction
		2.	Definitions
		3.	Root Finding (Bisection Method, Newton-Raphson 
			Method (Ex.1))
		4.	Numerical Integration (Trapezoidal Rule, Simpson's 
			Rule (Ex.2))
		5.	Solution of First Order ODEs (Euler's Method (Ex3.))
		6.	Summary

Trigonometry
	Introduction to Trigonometry (5 exercises)
		1.	Introduction
		2.	The Triangle (Ex.1)
		3.	Pythagoras' Theorem (Ex.2)
		4.	Trigonometric Ratios (Ex.3)
		5.	Trigonometric Identities (Ex.4*)
		6.	Sine and Cosine Rules (Ex.5)
		7.	Trigonometric Functions
		8.	Summary

Sequences and Series
	Introduction to Sequences and Series (3 exercises)
		1.	Introduction
		2.	Sequences (Algebraic, geometric, harmonic, 
			quadratic, (Ex.1))
		3.	Partial Sums (Ex.2)
		4.	Infinite Geometric Series (Ex.3)
		5.	Summary

Vectors
	Introduction to Vectors (6 exercises)
		1.	Introduction
		2.	Vector Algebra (Ex.1)
		3.	Vectors in terms of i, j and k (Ex.2)
		4.	Equation of a Straight Line (Ex.3)
		5.	Scalar Product (Ex.4)
		6.	Equation of a Plane (Ex.5)
		7.	Vector Product (Ex.6)
		8.	Summary

Total number of exercises = 64 

* Exercises and other sections marked with an asterisk require Mathematica.