MONASH UNIVERSITY FOUNDATION YEAR

1. INTRODUCTION

A student taking this course must also be concurrently enrolled in (or previously studied) MUFY Mathematics Part A as many of the topics in MUFY Advanced Mathematics require an understanding of the concepts in MUFY Mathematics Part A.

2. COURSE OBJECTIVES

Advanced Mathematics is designed to prepare students who wish to take tertiary courses with a high mathematical content, or which use a considerable amount of mathematical reasoning. In Part A, students study matrices, complex numbers, vectors, trigonometric functions and differentiation techniques. In Part B the topics covered are integration techniques and applications of definite integrals, differential equations and kinematics.

3. COURSE CONTENT

Semester A: 1. Matrices & Linear Algebra

The concept of a matrix; matrix algebra, including addition, subtraction, and multiplication of matrices, and multiplication of a matrix by a scalar. The conditions necessary for the sum or product of matrices to exist.

The unit matrix, I; the meaning of the inverse, A-1, of a matrix A; the fact that AA-1 = A-1A = I.

Determinants; the determinant of a 2 x 2 matrix; the inverse of a 2 x 2 matrix. The use of matrices to solve systems of two equations in two unknowns.

Singular matrices; the fact that, if a matrix is singular, the equations it represents must be either dependent or inconsistent.

2. Complex Numbers

Algebraic form [pic] where [pic] and where x, y are real numbers. The terminology complex plane. The real part, and imaginary part, of z defined. Addition and subtraction defined algebraically. Multiplication based on the definition[pic].

The complex conjugate [pic] of [pic]. Property [pic]. Modulus of z. Division by complex numbers.

Polar form for non-zero z; arguments [pic] of z.