Transcript Engineering Mechanics

Applied Mathematics 1A-MATH132
Lecture 1
Course Syllabus
Warm welcome to everybody
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Applied Mathematics 1A-MATH132
Malek
Abuwarda
Dr Jean Eng.
Medard
T Ngnotchouye
Subject
 Course: Applied Mathematics 1A
Statics-Mechanics of rigid bodies at rest
Linear algebra
 Shedule: in Room F15, this room.
Mondays: Lecture, 7:45-8:30
Tuesdays: Tutorial, 14:10-17:10
Thursdays: Lecture, 10:30-12:30
Friday: Lecture, 8:40-9:25
Note: Tuesday 12th February: Lecture & Thursday 28th March: Tutorial.
 Lecturer:
Dr Jean Medard T Ngnochouye
www.maths.unp.ac.za/coursework/Math132
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Applied Mathematics 1A-MATH132
Malek
Abuwarda
Dr Jean Eng.
Medard
T Ngnotchouye
Subject
 Grads:
Tests
Final exam
20%
80%
DP cut off mark
35%
 Course Materials
Lecture notes
Power points slides
Handout sheets
Textbooks
Engineering Applied Mathematics 1: Statics&Dynamics, Pearson
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Applied Mathematics 1A-MATH132
Malek
Abuwarda
Dr Jean Eng.
Medard
T Ngnotchouye
Instructional Objectives
 After completing the course, you should be able to:
Analyze vectors, add vectors using the parallelogram rule of addition of
vectors, know to do operations on vectors
Analyze forces and find out the resultant forces in two and three
dimension
Draw free-body-diagram and solve the equilibrium equations for the
unknown forces
 Solve simultaneously a system of linear equations using row operations
on the augmented matrix
Manipulate matrices and the algebra of matrices
Compute the determinant of a matrices using either row operations or the
method of cofactor
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Applied Mathematics 1A-MATH132
Malek
Abuwarda
Dr Jean Eng.
Medard
T Ngnotchouye
Course Outline
 Part 1, Statics
 Vectors, dot product and cross product
 Force System
Two-dimensional force systems
Three-dimensional force systems
 Equilibriums
Equilibrium in two dimensions
Equilibrium in three dimensions
 Part2, Linear algebra
System of linear equations
Matrix algebra
Determinants
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Applied Mathematics 1A-MATH132
Malek
Abuwarda
Dr Jean Eng.
Medard
T Ngnotchouye
Introduction to Mechanics
 What is mechanics?
Physical science deals with the
state of rest or motion of bodies
under the action of force
 Why we study mechanics?
This science form the
groundwork for further study in
the design and analysis of
structures
Mechanics
Statics
Dynamics
Kinematics
Kinatics
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Applied Mathematics 1A-MATH132
Malek
Abuwarda
Dr Jean Eng.
Medard
T Ngnotchouye
Basic Terms
 Essential basic terms to be understood
Statics: dealing with the equilibrium of a rigid-body at rest
Rigid body: the relative movement between its parts are negligible
Dynamics: dealing with a rigid-body in motion
Length: applied to the linear dimension of a strait line or curved line
Area: the two dimensional size of shape or surface
Volume: the three dimensional size of the space occupied by substance
Force: the action of one body on another whether it’s a push or a pull
force
Mass: the amount of matter in a body
Weight: the force with which a body is attracted toward the centre of
the Earth
Particle: a body of negligible dimension
Applied Mathematics 1A-MATH132
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Malek
Abuwarda
Dr Jean Eng.
Medard
T Ngnotchouye
Introduction to Linear algebra
 Solving systems of linear equations
 Matrix form of the equation
 Elementary row and columns operations
 Geometric interpretation of the solutions
 Operation on matrices
Addition and substraction of matrices
Scalar multiplication of matrices
 Invertible matrices and how to compute the inverse of a matrix
 Determinants
Square matrices
 Computation of the determinant of a matrix using row operations
Computation of a determinant using Laplace’s expansion
Application: Cramer’s rule for the solution of systems of linear equations.
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Applied Mathematics 1A-MATH132
Malek
Abuwarda
Dr Jean Eng.
Medard
T Ngnotchouye