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MATH187 - Mathematics 1: Algebra and Differential Calculus
Intention
This subject provides the first stage of Mathematics for all Mathematics students--and other interested students who have a solid Mathematics background.
The aim of this subject is to develop ideas, concepts and skills in Mathematics, especially applied skills, for application in later subjects.
It is anticipated that students commencing their studies with MATH187 will continue on with MATH188 in Spring Session.
Clientele
Students eligible to take MATH187 are those who satisfy the following:
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NSW HSC Mathematics (2 Unit) Band 4 or higher, or
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NSW HSC Mathematics Extension 1 Band 2 or higher, or
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NSW HSC Mathematics Extension 2, Band 2 or higher;
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or equivalent
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Students not eligible to take MATH187 are those who satisfy the following:
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NSW HSC General Mathematics, or
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NSW HSC Mathematics (2 Unit) Bands 2 or 3, or
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or equivalent
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Formal Prerequisites
Either a mark of at least 80 in MATH151 OR in NSW HSC Examination: Mathematics Band 4 or Mathematics Extension 1.
Assumed knowledge
It is assumed that students have completed NSW HSC Mathematics Extension 1. If any of the skills learnt during school years are "rusty", we recommend some bridging work before attempting MATH187. The content of this disc will provide you with a healthy start.
Content
Students in MATH187 are taught the following.
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Complex Numbers
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Introduction to complex number; arithmetic of complex numbers; DeMoivre's Theorem.
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Polar Coordinates
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Introduction to polar coordinates, including plotting points, converting to Cartesian and sketching polar graphs.
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Functions
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Continuity of functions; the Intermediate Value Theorem, Rolle's Theorem, the Mean Value Theorem and applications of these theorems.
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Differentiation
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Revision of functions; introduction to differentiation rules and techniques; revision of limits; L'Hopital's rule; finding limits of various indeterminate forms.
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Linear Algebra
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Introduction to matrices; solving systems of equations using matrix methods, determinants and applications.
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Vector Geometry
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Introduction to vectors in three dimensions and their applications to elementary geometry.
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After successful completion of this subject the student should be able to:
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(i)
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demonstrate a basic knowledge of the principles and techniques in Differential Calculus;
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(ii)
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demonstrate a basic knowledge of the principles and techniques in Linear Algebra;
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(iii)
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apply principles and techniques from Linear Algebra in the context of three-dimensional Vector Geometry;
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(iv)
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demonstrate problem solving skills and the ability to analyse the final results;
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(v)
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apply general mathematical principles and think logically and analytically through problems.
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