1. Eng. Malek Abuwarda Applied Mathematics 1A-MATH132 Lecture 1 Course Syllabus Warm welcome to everybody Applied Mathematics 1A-MATH132 1 Dr Jean Medard T Ngnotchouye

2. Eng. Malek Abuwarda 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 12 th February: Lecture & Thursday 28 th March: Tutorial.  Lecturer:  Dr Jean Medard T Ngnochouye  www.maths.unp.ac.za/coursework/Math132 Applied Mathematics 1A-MATH132 2 Dr Jean Medard T Ngnotchouye

3. Eng. Malek Abuwarda Subject  Grads:  Tests 20%  Final exam80%  DP cut off mark 35%  Course Materials  Lecture notes  Power points slides  Handout sheets  Textbooks  Engineering Applied Mathematics 1: Statics&Dynamics, Pearson Applied Mathematics 1A-MATH132 3 Dr Jean Medard T Ngnotchouye

4. Eng. Malek Abuwarda 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 Applied Mathematics 1A-MATH132 4 Dr Jean Medard T Ngnotchouye

5. Eng. Malek Abuwarda 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 Applied Mathematics 1A-MATH132 5 Dr Jean Medard T Ngnotchouye

6. Eng. Malek Abuwarda  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 Introduction to Mechanics Mechanics StaticsDynamics Kinematics Kinatics Applied Mathematics 1A-MATH132 6 Dr Jean Medard T Ngnotchouye

7. Eng. Malek Abuwarda 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 Dr Jean Medard T Ngnotchouye

8. Eng. Malek Abuwarda 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. Applied Mathematics 1A-MATH132 8 Dr Jean Medard T Ngnotchouye