MMU Elearning

Purpose:

To provide students with basic mathematical tools and abilities of algebra, trigonometry, permutation and combinations, series and complex numbers

Learning outcomes:

At the end of this course, the student should be able to:

1. Form and solve quadratic equations
2. Solve mathematical problems involving series and trigonometry
3. Perform mathematical operations involving complex numbers

Course description:

Surds, logarithms and indices; Determination of linear laws from experimental data; Quadratic functions, equations and inequalities; Remainder theorem and its application to solution of factorisable polynomial equations and inequalities; Permutations and combinations; Series: finite, infinite, arithmetic, geometric and binomial, and their applications such as compound interest, approximations, growth and decay; The principle of induction and examples such as formulae for summation of series and properties of divisibility; Trigonometry;   trigonometric functions,  their  graphs  and  inverses  for degree and  radian  measure,  addition,  multiple  angle  and  factor  formulae,  trigonometric identities and equations;  Sine and cosine formulae; their application to solution of triangles, trigonometric identities; Complex numbers: Argand diagrams, arithmetic operations and their geometric representation;   Modulus and argument; De Moivre’s theorem and its applications to trigonometric identities and roots of complex numbers.

Teaching methodology:  Lectures, tutorials; and group discussions

Instruction materials/equipment:

1. Liquid Crystal Displays.
2. White boards/black boards
3. Flip  charts

Course Assessment:

Continuous Assessment                      30%

End of Semester Examination            70%

LECTURE/WEEK	COURSE CONTENT	REMARKS
	Surds, logarithms and indices;
	Determination of linear laws from experimental data; Quadratic functions, equations and inequalities
	Remainder theorem and its application to solution of factorisable polynomial equations and inequalities;
	Permutations and combinations;
	Series: finite, infinite, arithmetic, geometric and
	Binomial, and their applications such as compound interest, approximations, growth and decay;
	The principle of induction and examples such as formulae for summation of series and properties of divisibility;
	Trigonometry; trigonometric functions, their graphs and inverses for degree and radian measure, addition, multiple angle and factor formulae, trigonometric identities and equations;
	Sine and cosine formulae; their application to solution of triangles, trigonometric identities;
	Complex numbers: Argand diagrams, arithmetic operations and their geometric representation; Modulus and argument;
	De Moivre’s theorem and its applications to trigonometric identities and roots of complex numbers.

 

 

Core Reading Materials:

Course Textbooks

1. Uppal S.M. and Humphreys H.M. (2008). Mathematics for Science, (2^nd Ed.). New Delhi, India: New Age International Pvt Ltd Publishers. ISBN-13: 978-8122409949
2. Backhouse J.K. (2007). Pure Mathematics 1 (4^th Ed.). NY, USA: Longman. ISBN-13: 978-0582353879
3. Sullivan M. (2011). Algebra and Trigonometry (9^th Ed.). Canada: Pearson Education. ISBN-13: 978-0321716569

Course Journals

1. IMA Journal of Applied Mathematics, Oxford University Press. ISSN 0272-4960.
2. American Journal of Mathematics, The Johns Hopkins University Press. ISSN: 0002-9327
3. Advances in Theoretical and Mathematical Physics, International Press. ISSN: 1095-0761.

Reference Materials:

Reference Textbooks

1. McKeague C.M. (2011). Elementary Algebra, (9^th Ed.). New Delhi, India: Cengage Learning. ISBN-13: 978-0840064219
2. McKeague C.M. (2009). Basic Mathematics, (7^th Ed.). New Delhi, India: Cengage Learning. ISBN-13:978-0534378929
3. Aufmann R.N., Barker V.C. and Nation R.D. (2007). College Algebra and Trigonometry (6^th Ed.). Boston, USA: Houghton Mifflin. ISBN-13: 978-0618825158

Reference Journals

1. ActaNumerica. Cambridge University Press. ISSN: 0962-4929
2. European Journal of Applied Mathematics. Cambridge University Press. ISSN: 0956-7925
3. Communications on Pure and Applied Mathematics Journal. Wiley Periodicals. ISSN: 1097-0312