Engineering Mechanics
Download
Report
Transcript Engineering Mechanics
Applied Mathematics 1A-MATH132
Lecture 1
Course Syllabus
Warm welcome to everybody
1
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
2
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
3
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
4
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
5
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
6
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
7
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.
8
Applied Mathematics 1A-MATH132
Malek
Abuwarda
Dr Jean Eng.
Medard
T Ngnotchouye