EMTH118-19S1 (C) Semester One 2019

# Engineering Mathematics 1A

15 points

Details:
 Start Date: Monday, 18 February 2019 End Date: Sunday, 23 June 2019
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Friday, 1 March 2019
• Without academic penalty (including no fee refund): Friday, 10 May 2019

## Description

A first course in the methods and applications of engineering mathematics. Topics include calculus, linear algebra, and modelling techniques. This Course is designed for engineering students who have done well in NCEA Mathematics with calculus.

A pass in EMTH118 allows entry into EMTH119 and also prepares students for EMTH171 and ENGR102.

Topics:
Linear equations and matrices; functions, limits and continuity; vector geometry; differentiation; applications of differentiation; integration; and applications of integration, including an introduction to first order differential equations.

## Learning Outcomes

• Students who have succeeded in this course will be able to:

Define the key concepts in:
• systems of linear equations
• matrix algebra
• functions and their inverses as the basis for mathematical models
• functions and their graphs
• vector geometry
• single-variable calculus

Describe and interpret:
• the connection between matrices and linear systems
• solutions of linear systems geometrically, and in the context of engineering and modelling problems
• the connection between differential and integral calculus
• solutions of first order differential equations in engineering contexts
• the description of lines and planes using vectors

Use techniques from the course (including the use of MATLAB where appropriate) to:
• solve systems of linear equations by Gaussian elimination
• evaluate limits of functions and solve continuity problems
• use vector geometry to solve angle, distance, and intersection problems
• find derivatives and use them in engineering and modelling applications
• find integrals and use them in engineering and modelling applications
• solve separable first order differential equations

Identify the appropriate method of solution for problems in linear algebra and calculus.

## Prerequisites

1) MATH101, or
2) NCEA 14 Credits (18 strongly recommended) at level 3 Mathematics (including the standards 'Apply differentiation methods in solving problems (91578)' and 'Apply integration methods in solving problems (91579)'), or
3) Cambridge: D at A level or an A at AS level in Mathematics, or
4) IB: 4 at HL or 5 at SL in Mathematics, or
5) approval of the Head of School based on alternative prior learning.

## Restrictions

MATH102, MATH108, MATH199

## Assessment

Assessment Due Date Percentage
Tutorial preparation and participation 10%
Online quizzes 10%
Tests (x2) 32%
Final Examination 48%

Note: To obtain a clear pass in this course and progress to EMTH118, you must both pass the course as a whole (≥50%) and obtain at least 40% in the final examination.

## Textbooks / Resources

Stewart, James: Calculus Early Transcendentals. 8th edition. ISBN: 9781305272378