Course Code:                 MATH 1202

Course Title:                  Applied Mathematics II

Level:                            I

Semester:                      2

No. of Credits:                3

Prerequisites:                 CAPE Advanced Level Proficiency in Pure Mathematics (Units 1

and 2), GCE A-Level Mathematics or equivalent.

 

Course Rationale  

 

 Introductory courses in Applied Mathematics have been in existence since 1991. The current 6-credit courses are being modified for three main reasons.  First, due to harmonization of courses across the three campuses, the credit rating for this course is being reduced from 6 to 3.  Second, many from the Department of Mathematics and Computer Science agree that the present course’s content is far too specialized for a Level I mathematics course.  This also takes away from presenting the fundamentals of classical applied mathematics in more common areas of interest.  Finally, we wish to align the syllabus more closely with the classical part of CAPE Applied Mathematics.  The reason for this is so that those majoring in mathematics, having done this course and entering into the teaching profession, will be well-prepared to handle this aspect of CAPE Applied Mathematics more confidently.  This new syllabus may also assist those students doing some physics courses, as well as those who may branch across to the field of engineering.  At present, there is no other course on any of UWI’s campuses that handles classical applied mathematics in this manner. Thus there is a great need to expose students to this aspect of the field, which provides the necessary tools, with illustrations, on the usefulness and power of mathematics in working out simplified real world problems.

 

Course Description

 

This course will cover the basic concepts and techniques of Dynamics, mostly particle dynamics.  It will provide students with a good understanding of the laws and associated applications of particles in motion, as well as supply the necessary tools used in solving elementary common problems in the field.

Prior knowledge of CAPE Pure Mathematics Units 1 and 2 (or its equivalent) will be assumed.

Assessment is designed to encourage students to work continuously with the course materials. Active learning will be achieved through weekly assignments and problem sheets allowing continuous feedback and guidance on problem solving techniques in tutorials and lectures. Assessment will be based on the weekly assignments and in-course tests (40%),  followed by a final examination (60%) based on the whole course.

 

Learning Outcomes

 

 On successful completion of this course, students will be able to:

  • Apply the laws associated with the motion of particles subject to a constant or variable acceleration, and so work out problems related to such.
  • Define Work, Energy and Power. 
  • Solve problems involving the behaviour of connected particles, including pulley systems.
  • Derive and apply the equations that define Simple Harmonic Motion.
  • Analyze the motion of bodies connected to elastic strings.
  • Apply Impulse and conservation of momentum to collision type problems.
  • Derive and apply the laws of motion of particles projected in a medium, with and without a resistance.
  • Use the equations for circular motion to solve applied problems.

 

 

Content

 

  • Newton’s laws of motion, (including a particle moving on an inclined smooth/rough plane).
  • Motion in a straight line with variable acceleration.
  • Work, Energy, (Kinetic, Potential & Mechanical Energy, conservation of & work-energy principle), and Power.
  • Connected particles, including pulley systems.
  • Simple Harmonic Motion.
  • Elasticity, (Hooke’s law).
  • Impulse.
  • Conservation of momentum.
  • Collisions, (direct impact, impact with a wall, coefficient of restitution).
  • Projectiles in a vacuum.
  • Vertical motion in a resisting medium.
  • Circular motion.

Teaching Methodology

 

Lectures: Two (2) lectures each week (50 minutes each).

Tutorial: One (1) weekly tutorial session (50 minutes).

 

 

Assessment

 

Coursework will be worth 50%.  This will generally be made up of at least two coursework examinations, worth 40% in total, and 10% will be drawn from six of the ten assignments given. The six assignments to be assessed will be determined by the lecturer.

 

Final Examination (one 2-hour written paper) – 50%

 

 

Course Calendar

 

Week

Lecture subjects

Tutorials

1

Introduction/Course Overview

Newton’s laws of motion, (including a particle moving on an inclined smooth/rough plane).

None

2

Motion in a straight line with variable acceleration. 

Assignment # 1

3

Work, Energy, (Kinetic, Potential & Mechanical Energy, conservation of & work-energy principle), and Power.

Assignment # 2

4

Connected particles, including pulley systems.

Assignment # 3

5

Simple Harmonic Motion.

Assignment # 4

6

Simple Harmonic Motion, (continued).

First coursework examination

7

Elasticity, (Hooke’s law). 

Assignment # 5

8

Impulse.  Conservation of momentum.

Assignment # 6

9

Collisions, (direct impact, impact with a wall, coefficient of restitution).

Assignment # 7

10

Projectiles in a vacuum.

Second coursework examination

11

Vertical motion in a resisting medium.

Assignment # 8

12

Circular motion.

Assignment # 9

13

Revision.

Assignment # 10

 

 

Required Reading

 

Reference Texts (No essential textbook. Lecture notes will be prepared and made available for the students).

 

  • Applied Mathematics (Vols. 1 & 2) – C. Bostock & S. Chandler (Stanley Thomas Ltd.).
  • Mathematics – Mechanics and Probability – L. Bostock, S. Chandler.
  • Further Mechanics and Probability – L. Bostock, S. Chandler.