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Applied Mathematics 1A-MATH132

Applied Mathematics 1A-MATH132. Lecture 1 Course Syllabus Warm welcome to everybody. Dr Jean 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

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Applied Mathematics 1A-MATH132

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

  2. 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 Applied Mathematics 1A-MATH132 Dr Jean Medard T Ngnotchouye

  3. Subject • Grads: • Tests 20% • Final exam 80% • 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 Dr Jean Medard T Ngnotchouye

  4. 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 Dr Jean Medard T Ngnotchouye

  5. 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 Dr Jean Medard T Ngnotchouye

  6. 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 Applied Mathematics 1A-MATH132 Dr Jean Medard T Ngnotchouye

  7. 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 Dr Jean Medard T Ngnotchouye

  8. 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 Dr Jean Medard T Ngnotchouye

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