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Basic Mathematics syllabus

MTH 1039 units · 66 topicsAcademic year 2083/84
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Basic Mathematics

9 units

1. Set Theory and Real Number System (6 LHs)

  1. Concept
    1. Concept
  2. Notation and specification of sets
    1. notation and specification of sets
    2. Types of sets
  3. Relation between sets
    1. Relation between sets
    2. Venn diagrams
  4. Operations on sets. Laws of algebra of sets (without proof)
    1. Operations on sets. Laws of algebra of sets (without proof)
  5. Number of elements in a set and the problems relating up to three sets
    1. Number of elements in a set and the problems relating up to three sets. Sets of numbers (Natural numbers, Integers, Rational numbers, Irrational numbers, Real numbers)
  6. Representation of real numbers on the real line
    1. Representation of real numbers on the real line. Properties (addition multiplication, cancellation, distributive, order) of real numbers (without proof)
  7. Inequalities and their properties. Intervals
    1. Inequalities and their properties. Intervals
  8. Modulus of a real number and its properties
    1. Modulus of a real number and its properties.

2. Complex Numbers (4 LHs)

  1. Definition of a complex number
    1. Definition of a complex number
  2. Integral powers of i
    1. Integral powers of i
  3. Algebra of complex numbers (sum, difference, multiplication, division)
    1. Algebra of complex numbers (sum, difference, multiplication, division)
  4. Properties of complex numbers
    1. Properties of complex numbers
  5. Conjugate of a complex number and its properties
    1. Conjugate of a complex number and its properties
  6. Modulus of a complex number and its properties
    1. Modulus of a complex number and its properties
  7. Representation of a complex number by a point in a plane (Argand's diagram)
    1. Representation of a complex number by a point in a plane (Argand's diagram)
  8. Polar representation of a complex number
    1. Polar representation of a complex number
  9. Square roots of a complex number
    1. Square roots of a complex number
  10. De-Moivre's theorem
    1. De-Moivre's theorem (statement only) and its application to find up to cube roots of a complex number.

3. Functions, Limits and Continuity (6 LHs)

  1. Constant and variable
    1. Constant and variable
  2. Concept of functions
    1. Concept of functions
    2. Types of functions
  3. Graphic representation of algebraic
    1. Graphic representation of algebraic
  4. Logarithmic and exponential functions
    1. logarithmic and exponential functions
  5. Computation of functional values
    1. Computation of functional values
  6. Domain and range of a function
    1. Domain and range of a function. Application of functions to business and economics. Idea of a limit
  7. Limit of a function at a particular point and at infinity
    1. Limit of a function at a particular point and at infinity
  8. Properties of limits
    1. Properties of limits (without proof) and use in evaluating limits involving algebraic functions. Concept of continuity and discontinuity
  9. Test of continuity and discontinuity for simple algebraic functions
    1. Test of continuity and discontinuity for simple algebraic functions.

4. Differentiation and Its Application (8 LHs)

  1. Average rate of change
    1. Average rate of change
  2. Definition of derivative
    1. Definition of derivative
  3. Derivative as a slope of tangent to the curve
    1. Derivative as a slope of tangent to the curve
  4. Differentiation by the first principle of algebraic
    1. Differentiation by the first principle of algebraic
  5. Logarithmic and exponential functions
    1. logarithmic and exponential functions
  6. Methods of differentiation (power rule, sum rule, product rule, quotient rule chain rule)
    1. Methods of differentiation (power rule, sum rule, product rule, quotient rule chain rule)
  7. Differentiation of implicit and parametric functions
    1. Differentiation of implicit and parametric functions
  8. Increasing and decreasing function
    1. Increasing and decreasing function
    2. Stationary point
    3. Point of inflection
  9. Higher order derivatives
    1. Higher order derivatives (up to 3rd order). Economic applications of derivatives for maximum and minimum points.

5. Integration and Its Application (6 LHs)

  1. Concept of integration
    1. Concept of integration
  2. Techniques of integration (Standard forms, Substitution method, Integration by parts)
    1. Techniques of integration (Standard forms, Substitution method, Integration by parts)
  3. Integration of algebraic
    1. Integration of algebraic
    2. logarithmic
  4. And exponential functions. Definite integral
    1. and exponential functions. Definite integral
  5. Methods of evaluating definite integrals
    1. Methods of evaluating definite integrals
    2. Area under a curve
  6. Application of integration in business and economics
    1. Application of integration in business and economics (including consumer's surplus and producer’s surplus).

6. Differential Equations (5 LHs)

  1. Introduction to differential equations
    1. Introduction to differential equations
  2. Order and degree of a differential equation
    1. Order and degree of a differential equation
  3. Solution of a differential equation
    1. Solution of a differential equation
  4. General and particular solutions. Equations of the first order and first degree
    1. General and particular solutions. Equations of the first order and first degree: a) variables separated from b) homogeneous equations
  5. C) linear equations (without involving trigonometric functions)
    1. c) linear equations (without involving trigonometric functions).

7. Vectors (5 LHs)

  1. Definition of a vector in a plane and space
    1. Definition of a vector in a plane and space
  2. Directed line segment
    1. Directed line segment
  3. Magnitude of a vector
    1. Magnitude of a vector
    2. Types of vectors
  4. Multiplication of a vector by a scalar
    1. Multiplication of a vector by a scalar
    2. Addition of vectors
  5. Parallelogram law of addition of vectors
    1. Parallelogram law of addition of vectors
  6. Collinear and coplanar vectors
    1. Collinear and coplanar vectors
  7. Linearly dependent and independent vectors
    1. Linearly dependent and independent vectors
  8. Scalar product of two vectors
    1. Scalar product of two vectors
    2. Orthogonal vectors
  9. Vector product of two vectors. Numerical Exercises
    1. Vector product of two vectors. Numerical Exercises

8. Matrices and Determinants (6 LHs)

  1. Introduction of matrices
    1. Introduction of matrices
    2. Types of matrices
  2. Equality of matrices
    1. Equality of matrices
    2. Algebra of matrices
  3. Transpose of a matrix. Determinant of a Square matrix
    1. Transpose of a matrix. Determinant of a Square matrix
  4. Minors and cofactors of matrix
    1. Minors and cofactors of matrix
  5. Singular and non-singular matrix
    1. Singular and non-singular matrix
  6. Adjoint and inverse of matrices
    1. Adjoint and inverse of matrices. Solution of a system of linear equations up to three variables (Cramer's rule, Inverse matrix method, Gaussian elimination method).

9. Least Square Method (2 LHs)

  1. Introduction to the least square method
    1. Introduction to the least square method
  2. Line of best fit (two variables only)
    1. Line of best fit (two variables only)
  3. Measurement of trends
    1. Measurement of trends
  4. Method of least square for time series analysis
    1. Method of least square for time series analysis.