ROCKVIEW UNIVERSITY

SCHOOL OF NATURAL SCIENCE

DEPARTMENT OF MATHEMATICS AND NATURAL SCIENCES

M I11: FOUNDATION MATHEMATICS

COURSE OUTLINE
AIM
The aim of this course is to equip the students with a good foundation in mathematics
that will enable them do higher mathematics; enable students acquire the knowledge,
skills, and attitudes to solve some real life problems which require mathematical
skills.
PREREQUISITE KNOWLEDGE
Better in Mathematics at Grade 12 or ‘O’ Level.
LEARNING OBJECTIVES
By the end of this course students should be able to:
 Describe and apply the Set operations, Binary operations, relations, and
functions
 Describe the sets of numbers.
 Describe the domain and range of Polynomial, Rational, Modulus, Radical and
Trigonometric functions, simplify expression and solve the equation and
inequalities involving these functions.
 Define the limits, continuity and derivatives of functions.
 Differentiate polynomial, rational and trigonometric functions and their
composite.
COURSE CONTENT
1. SETS
a. Sets Theory:
 Definitions
 Subsets
 Set operations
  De Morgan’s laws,
b. Sets of numbers:
 Natural numbers
 Integers
 Rational Numbers
 Complex Numbers
1) Arithmetic operations on Complex Numbers
2) Surds
3) Complex
2. FUNCTIONS
a. Binary operations
b. Relations
c. Functions
 Domain
 Range
 Many-to-one functions
 One-to-one functions
 Inverse functions
 Composed functions
 Even and odd functions
d. Linear and Quadratic functions:
 Completing the square
 Maximum and minimum values of quadratic functions
 Graphs of quadratic functions, applications.
e. Polynomials Functions:
 Polynomials
 Addition
 Multiplication
 Division
 Remainder theorem
 Factor theorem
 Factorization
 Graphs.
f. Rational functions
 Domains
 Range
 Graphs
g. Modulus Functions
 Domain
  Range
 Graphs
h. Radical functions
 Domain
 Range
 Graphs
i. Exponential and logarithmic functions:
 Domain and range
 Graphs
 Theorem properties
 Inverse, equations.
3. EQUATIONS AND INEQUALITIES
a. Equations:
 Quadratic
 Polynomials
 Involving radicals
 Quotients and absolute value
 System of equations in two and three unknowns.
b. Inequalities:
 Linear
 Quadratic
 Polynomials
 Involving quotients and absolute value.
4. Partial Fractions
a. Denominator with:
 Linear factors none of which is repeating
 Linear factors of which some are repeating, quadratic factors
none of which is repeating
 Quadratic factors of which some are repeating.
5. COMPLEX NUMBERS
 Definition
 Geometrical representation
 Identity
 Equality of complex numbers
 Operations:
1) Addition
2) Subtraction
3) Multiplication
 4) Division
 Complex numbers in Polar form
 Modulus and argument
 De-Moivres theorem
 Roots of a complex number
6. SEQUENCES, SERIES AND MATHEMATICAL INDUCTION
 Introduction to series
 Arithmetic sequence
 Geometric sequence
 Mathematical induction
7. BINOMIAL EXPANSIONS
 Pascal’s triangle
 Factorials
 Binomial coefficients
 Binomial expansions
 Binomial series
 Binomial formula for positive integral
 Binomial formula for rational exponents
8. Transcendental Functions
a. Trigonometric functions
 Trigonometric ratios
 Special ratios
 Ratios of angles
 Degrees and radian measure
 Exact values of trigonometric functions
 Trigonometric functions, domain,
b. Graphs of trigonometric functions
 Period
 Amplitude
 Phase shift
 Vertical shift
c. Trigonometric identities
 Reciprocal identities
 Quotient identities
 Pythagoras identities
 Sum and Difference/Compound identities
 Double-angle identities
 Half-angle identities
 Product and sum identities
 d. Trigonometric equations.
e. Inverse trigonometric functions
 Domain
 Range
 Graphs of Inverse trigonometric functions
f. t-substitution
9. COORDINATE GEOMETRY
 Distance between two points
 Division of a straight line into a ratio
 Equation of a straight line, parallel and perpendicular lines
 Equation of a circle, tangent and normal lines to a circle.
 Conic sections:
1) Parabolas
2) Ellipses
3) Hyperbolas
 Polar coordinate systems
10. VECTORS
 Definition and properties
 Vector addition
 Position vectors
 Vectors operations
 Vectors in 3-dimension
 Dot product
 Vector (cross) product
 Direction cosines
 Vectors equations in two dimensions
 Application to perpendicular and parallel vectors and areas
11. DIFFERENTIAL CALCULUS
a. Limits
 Limits of a function
 Continuity of a function
 Differentiation of function from first principle
 Differentiation by formula:
1) Sum
2) Product rule
3) Quotient rule
4) Chain rule
 Implicit differentiation
 Derivative of Exponential and Logarithmic functions
  Derivatives of Inverse trigonometric functions
12. FURTHER DIFFERENTIAL CALCULUS
 Tangents and normal lines to a curve
 Increasing and decreasing functions
 Stationary points (critical points)
 Point of inflexion
 Relative maximum and minimum
 Related rates
 Curve sketching and asymptotes of functions
13. INTEGRAL CALCULUS
 Definite and Indefinite integrals
 Methods of integration:
1) Substitution
2) Integration by parts
 Change of variable
 Partial fraction
 Definite integrals
 Application to areas
14. MATRICES
 Sum
 Product
 Transpose
 Determinants
 Factorization of determinants
 Inverse matrix
 Applications:
1) Solutions of system of linear equations by inverse matrix
method
2) Cramer’s rule

TEACHING METHOD
 3 lectures
 1 Clinic per week
 1 tutorial per week

ASSESSMENT STRUCTURE
 Continuous assessment 50%
6 Assignments 20%
2 Tests 20%
 Presentations/Quizzes 10%
 Final examination 50%
Total 100%
PRESCRIBED READINGS
1. Backhouse, J., Wouldsworth, S., Horril, P.J.F., & Wood, J.R., (1991).
Essential Pure Mathematics, Single Volume Edition, Longman Group ISBN:
058206681.

2. Wylie, C.R. & Barrett, L.C. (1982). Advanced Engineering Mathematics,

McGraw-Hill Book Company.

RECOMMENDED READINGS
1. Aufmann, R.N, Barker V.C. Nation R.D., College Algebra and Trigonometry
7th Ed. (2001). Brooks/Cole Cengage Learning. ISBN: 1439049396.
2. Larson R. Hodgkins, A. (2013). College Algebra and Calculus, 2ND Edition.
Brooks/Cole Cengage Learning. ISBN: 11331055183.
3. Kreyszig, E. (1988). Advanced Engineering Mathematics, John Wiley and
Sons.