Monash College Unit Guide

ENGINEERING MATHEMATICS A (MCD1220)

Purpose

The intention of this unit is to provide a foundation of essential mathematical skills to prepare students for engineering studies. The aim of this unit is to develop knowledge in complex numbers and vectors. This unit provides an extension into circular functions and differential calculus including antiderivatives and differential equations. It investigates applications particularly for use in other engineering subjects, such as kinematics.

Prerequisites

MCD1230 Introductory Engineering Mathematics or mathematical methods unit 3 & 4 equivalent

Learning Outcomes

On completion of this unit, students should be able to:

1. Explore and use Pythagorean identities of circular functions.
2. Perform calculations utilizing the complementary and supplementary angle identities, addition formulae, double-angle formulae.
3. Explain the meaning of inverse and reciprocal trigonometric functions.
4. Apply the combinations of sine and cosine functions, converting to a single sine or cosine: or
5. Understand the concept of complex numbers and construct the Argand Diagram.
6. Perform operations with complex numbers in Cartesian, polar and exponential form. Understand the Euler formula.
7. Apply De Moivre's theorem for computation powers and roots of complex numbers.
8. Find loci and subsets of the complex plane.
9. Understand the concept of vectors in Cartesian form, position vector, vector algebra, magnitude of vector, unit vector, angles between vectors and direction cosines.
10. Find scalar and vector resolute, scalar product of vectors, application of scalar product.
11. Use one side two side limits to discuses left and right continuity.
12. Apply limits, continuity and differentiation to solve mathematical problems
13. Identify and analyse the nature of critical point using derivative tests.
14. Apply the differentiation and antidifferentiation to solve the problems in Kinematics
15. Extend the concept of derivatives by inverse circular functions.
16. Apply the method of logarithmic differentiation and implicit differentiation.
17. Perform antidifferentiation calculations using inverse trigonometric functions, integration by substitution, integration by parts and integration by partial fractions.
18. Use definite integration to find volumes of revolution, centre of mass, mean value and root mean square.
19. Perform computation with vector calculus, such as displacement, velocity and acceleration.
20. Understand the concept of exponential growth, differential equation and initial value problem.
21. Solve differential equations with separable variable and explore various differential equations in engineering applications.

Assessment

Assessment task 1 (class or on-line test(s)): 20%

Assessment task 2 (one of the following - class or on-line test(s), extended task, research, negotiated assignment, student design): 20 %

Test consists of the combination of multiple choice, short answer and analytical questions.

Examination: 60% closed book exam in duration of 3 hours plus 10 minutes reading time

Exam consists of the combination of multiple choice, short answer and analytical questions with percentage component 30 + 50 + 20.

A programmable scientific or graphics calculator is allowed for all assessments

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