Basic Mathematics

 

  1.   Course Title: MTH 102- BASIC MATHEMATICS
  2. Subject Status: Elective
  • Credit Rating:             9 Credits
  1. Total hours spent: 90 hours

                                        Lectures                             40 hrs

                                                Tutorials                                 20 hrs

                                                Practical                                 0 hrs

                                                Assignments              10  hrs

                                                Independent Study               20 hrs                         

             Prerequisites:                        None

 

  1. Course Expected Learning Outcomes:

By the end of the course students should be able to:

  • use vector algebra
  • use matrix algebra
  • solve calculus of one variable
  • solve ordinary differential equation
  • use Laplace Transforms

 

  1. Course Contents:

Algebra:  Indices and logarithms; simultaneous equations; quadratic equations; coordinate geometry of a straight line; Applications of the straight line law to experimental data. Vector algebra. Trigonometry: Trigonometric formulas and equations. Matrices and determinants: operations on matrices; inverse of a matrix and properties of determinants. Systems of linear equations – Gaussian elimination method, Cramer’s rule.

Calculus: Functions – including polynomial, trigonometric, exponential, logarithmic functions. General idea of limits and continuity. Differentiation – properties of derivatives. Techniques of differentiation including implicit and logarithmic.Application of differentiation – e.g. tangents and normals, rates of change, approximations, maxima and minima. Integration – anti-derivatives (indefinite integrals). The definite integral.Techniques of integration. Applications of integration – including areas, volumes, arc lengths.

First order differential equations: solutions of some first order differential equations-namely: separable variables type, those reducible to separable variables type, linear differential equations, exact types.

Application of first order differential equations to practical problems, e.g. Chemical reactions problems, carbon dating, exponential decay problems, emission and pollution problems.

               

  • Reading List:

Bondi, C. (ed.). (1991). New Applications of Mathematics. Penguin. New York

Courant, R., Robbins, H. and Stewart, I. (1996). What is Mathematics (2nded.). OUP. New York.

Gardner, M. (2004). The Colossal Book of Mathematics. Norton. New York/ London.

Körner, T. W. (2014). Calculus of the Ambitious. CUP. London.

Terence, T. (2006). Solving Mathematical Problems. OUP. New York.

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