Mathematics-with-Business

Degree Type: 

Bachelor of Science

Department: 

Department of Mathematics

Programme Duration: 

4 years (Standard Entry)

Modes of Study: 

Regular

About Programme: 

Our B.Sc Mathematics with Business programme will prepare you for interesting career opportunities in business and industry. It also qualifies you for advanced studies and professions in fields such as actuary, banking, insurance etc. 

9 READING LIST 

                             

  1. Adams,  A. R. (2003). Calculus, A Complete Course, 6th Ed. Addison Wesley Longman.

  2. Ahlfors,  L. (1979).  Complex Analysis, McGraw-Hill.

  3. Allan, J. (2002). Advanced Engineering Mathematics, Harcourt/Academic Press, USA.

  4. Allen L, J.S. (2007). An Introduction to Mathematical Biology,  Pearson Education, New Jersey, USA

  5. Anderson, A. & May, R.  (1991). Infectious Diseases of Humans: Dynamics and Control,  Oxford University Press, London. United Kingdom.

  6. Anderson, D. R., Sweeney, D. J. & Williams, T. A. (1988). An Introduction to Management Science: Quantitative Approaches to Decision Making; 5 Ed., West Pub. Co., USA.

  7. Anton, H. & Rorres, C. (1988 ). Elementary Linear Algebra, Applications Version, John Wiley, New York, USA.

  8. Axler, S. (1997).  Linear Algebra Done Right, Springer. 

  9. Bak, J. & Newman, D. J. (2010). Complex Analysis, Springer-Verlag, New York.                             

  10. Betts, J. T. (2001). Practical Methods for Optimal Control Using Nonlinear   

      Programming, SIAM, Philadelphia, USA.

  1.  Berenstein, C. A. (1985). Complex Analysis; Springer-Verlag, New York.

  2. Bick, T. A. (1971 ). Introduction to Abstract Mathematics; Academic Press.

  3. Birkhoff, G. and Rota, G. (1989).  Ordinary Differential Equations; John Wiley and Sons.

  4. Boyce, W. E. & DiPrima, R. C. (2006).  Elementary Differential Equations And Boundary Value Problems, Prentice Hall, New Jersey, USA.

  5.   Brauer, F. (2006).  Some Simple Epidemic Models, Mathematical biosciences and  

  6. Brauer, F., Castillo-Chavez, C. (2012). Mathematical Models for Communicable 

  7. Brian D, Hahn, (2007). Essential MATLAB for Scientists and Engineers, Pearson Education, South Africa.

  8. Broman, A. (1970). Introduction to Partial Differential Equations; Dover, USA.

  9. Brown, J. & Churchill, R. (1996). Complex variables and applications, 7th Ed. 

  10. Brown, J. W. & Sherbert, D. R. (1984). Introductory Linear Algebra with Applications, PWS, Boston.

  11. Bryson, A. E. & Ho, Y. (1975).  Applied optimal control: Optimization, Estimation  

  12. Budak, B. M., & Fomin S. (1973). Multiple Integrals, Field Theory and Series; Mir Publishers, Moscow.

  13. Burden, R. & Faires, J. D.  (2006), Numerical Analysis, PWS Publishers

Diseases, SIAM, Philadelphia, USA.  

  1. Capinski, M. &  Kopp, E. (2005), Measure, Integral and Probability,   Springer-Verlage London Limited.                

  2. Christian, P., Nagy, J. G.  Dianne & O’Leary, D., (2006), Deblurring Images, Matrices, Spectra, and Filtering. SIAM , Philadelphia, USA.

  3. Churchill, R. V. & Brown, J. W (1990 ). Complex Variables and Applications; McGraw Hill Inc., USA.

  4. Coddington, E.A. & Levinson, N. (1983), Theory of Ordinary Differential Equations; Robert Krieger Publishing Company, Malabar, Florida.

  5. Courant, R., & John, F. (1974). Introduction to Calculus and Analysis; Vol. 2, John Wiley and Sons, USA.                         

  6. Daellenbach, H. G., George, J. A. & McNicke, D.C. (1983). Introduction to Operations Research Techniques; 2 Ed., Allyn and Bacon, Inc., USA.

  7. Datta, B. N.  (2009), Numerical Linear Algebra and Applications, SIAM, Philadelphia, USA.

  8. David, C. L. (2002). Linear Algebra and its Applications, Addison-Wesley, New York, USA.

  9. De-Lillo, N. J. (1982). Advanced Calculus with Applications; Macmillan Pub., USA.

  10. Diekmann, O. & Heesterbeek, J.A. P.  (2000). Mathematical Epidemiology of Infectious Diseases, John Wiley & Sons, West Sussex.

  11. Edwards, C. H. & Penny, D. E. (2005).  Elementary Differential Equations With Boundary Value Problems, Prentice Hall, New Jersey, USA

  12. Edwards,  C. H. & Penney, D. E. (1999). Calculus With Analytic Geometry: Early Trancendentals; 5 Prentice Hall Inc., USA.

  13. Eisberg, R.M. (2000). Fundamentals of Modern Physics, John Wiley & Sons Inc. New York.      

  14. Evans, C. L. (2010). Partial Differential Equations, American Mathematical Society.                 

  15. Fiacco, A. V. &  McCormock, G. P. (1990). Nonlinear Programming, SIAM, Philadelphia, USA.

  16. Fraleigh, J. B. (1989). A First Course in Abstract Algebra.

  17. Froberg E. (1968). Introduction to Numerical Analysis, Addison and Wesley, USA.

 Philadelphia, USA.                        

  1. Gallian, J. A.  (1990), Contemporary Abstract Algebra; D. C. Heath and Company.

  2.  Gerald, C. F. & Wheatley (2001)  Applied Numerical Analysis; Addison &Wesley, USA.

  3.  Gibarg, D. & Trudinger, N. S. (1983). Elliptic Partial Differential Equations of Second  Order; Springer-Verlag, New York.

  4. Goldstein, H. (1986).  Classical Mechanics, Addison-Wesley Publishing Company.                  

  5. Haaser, N. B. & Sullivan, J. A. (1991). Real Analysis; Dover.

  6. Halmos, P.R. (1960), Measure Theory; Springer-Verlag, New York.

  7. Hertcote , H. W. (2000). The Mathematics of Infectious Disease, SIAM Review,  Amsterdam, The Netherlands.

  8. Higham , D. J.  (2005). MATLAB Guide, SIAM, Philadelphia, USA.

  9. Hilberland, F. B. (1962). Advanced Calculus for Application; Prentice Hall, USA.

  10. Hillier, F. S. (2012). Introduction to Operations Research, McGraw Hill, Inc., USA.

  11. Hirsch, M. W, Smale, S. & Devaney, R. L. (2004).  Differential Equations,         Dynamical Systems & An Introduction to CHAOS, Elsevier Academic Press,  

  12. Hocking, L. M. (1991), Optimal Control: An Introduction to the Theory with Applications, Clarendon Press, London.

  13. Hungerford, T. W. (1974). Algebra; Springer-Verlag, New York.

 Vol 42, No. 4, December 2000, pp. 599—653.         

  1. Igor G., Nash, S. G. & Sofer A., (2009). Linear and Nonlinear  Optimization, SIAM, Philadelphia, USA.

  2. Kaufmann, J. E. (1987). College Algebra and Trigonometry; PWS Publishers, USA.

  3. Kirk , D. E., (2004), Optimal control theory: An Introduction, Dover Publications.

  4. Klages, R. & Howard, P. (2008),  Introduction to Dynamical Systems, (Lecture         Notes Version 1.2), Queen Mary University of London.

  5. Kofinti, N. K. (1997). Mathematics Beyond the Basic; Vol. 1, City Printers, Accra.

  6. Kolman, B. (1984). Introductory Linear Algebra with Applications; Macmillan Publishing Company.

  7. Kreyszig, E. (1978 ). Introductory Functional Analysis with Applications; John Wiley and Sons,  New York, U.S.A.

  8. Kudryavtsev, V. A. (1981). A Brief Course of Higher Mathematics; Mir Publishers, Moscow.  

  9. La Salle, J. P.  (1976), The Stability of Dynamical Systems, SIAM, Philadelphia, USA.

  10. Lang, S. (2012). Calculus of Several Variables, Springer-Verlag, New York.

  11.  Lenhart S., & Workman J. T., (2007), Optimal Control Applied to Biological         Systems, Chapman & Hall, New York, USA.

  12.  Lenhart, S., & Workman, J. T. (2007). Optimal Control Applied to Biological, John Wiley & Sons, New York, USA.   

  13.  Levine, I.N.  (1991). Quantum Chemistry, 4th Ed., Prentice Hill.

  14.  Levy, A. B.  (2009). The Basics of Practical Optimization, SIAM, Philadelphia,            USA.

  15. Levy, A. B. (2009). The Basics of Practical Optimization and Control, SIAM, Philadelphia, USA.

  16.  Linz, P. &  Wang, R. (2002). Exploring Numerical Methods: An Introduction to Scientific Computing Using MATLAB, Jones & Bartlett Publishers, London.

  17. Lipschuts, S.  (1975), General Topology; McGraw-Hill Book Company.

  18. Liu, J. H. (2003). A First Course in the Qualitative Theory of Differential Equations, Pearson Education, Inc., New Jersey.

  19.  Luenberger, D. G., (1996). Optimization by Vector Space Methods, John Wiley & Sons, New York, USA.    

  20. Marion, J.B. & Thornton, S.T. (1995).  Classical Dynamics of Particles and Systems, Saunder College Publishers.

  21. Marsden, J.E. (1970). Basic Complex Analysis; W.H. Freeman and Co.

  22. McCann, R. C. Introduction to Ordinary Differential Equations; Harcourt Brace Janovich, USA.

  23. McCoy, N. H. (1968). Introduction to Modern Algebra; Allyn and Bacon Inc.,

  24. Merzbacher, E.  (1986). Quantum Mechanics, 2nd Ed. John Wiley & Son Inc.

  25. Morash, R. P. (1987). A Bridge to Abstract Mathematics; Random House Inc., New York.

  26. Munem, M. A. (1989). After Calculus: Analysis; Collier Macmillan Pub. , London.

  27. Nicholson, K. W. (1986). Elementary Linear Algebra with Applications; PWS-KENT.

  28.  Ortega, J. M. (1990), Numerical Analysis, SIAM, Philadelphia, USA.

 Philadelphia, USA.

  1.  Offei, D.N.  (1970), The use of boundary condition functions for non-self-adjoint boundary value problems; I

  2.  Offei, D. N. (1969). Some asymptotic expansions of a third-order differential equations; Journal of London Mathematical Society, 44 71-87.

  3. Penny, J. & Lindfield, G.  (1995), Numerical Methods Using MATLAB, Ellis Horwood, New York.

  4. Petrovsky, I. G.(1954 ).  Lectures on Partial Differential Equations; Dover, USA.

  5. Pinchover, Y. & Rubinstein, J. (2005). An Introduction to Partial Differential Equation, Cambridge University Press.

  6. Piskunov, N. (1981). Differential and Integral Calculus; 4 Ed., Mir Publishers, Moscow.

  7.  Pliska, S. R.  (2002). Introduction to mathematical finance: Discrete time models, Blackwell Publishers Inc. 

  8.  Poole, D. (2014). Linear Algebra: A Modern Introduction, Dover, USA.

  9. Priestley, H. A. (2003). Introduction to Complex Analysis, 2nd  Ed., OUP.

  10. Redheffer, R. (1992). Introduction to Differential Equations; Jones & Bartlett Pub., Inc.

  11.  Roberts, A. J.  (2009), Elementary Calculus of Financial Mathematics, SIAM, Philadelphia, USA.

  12.  Rofman, J. J. (2015). Advanced Modern Algebra, American Mathematical Society.

  13. Roman, S. (2005), Advanced Linear Algebra, 2nd edn; Springer-Verlag, New York.

  14. Ross, S. L. (1984). Differential Equations; 3 Ed., John Wiley & Sons, USA.

  15. Rudin, W. (1974), Principles of Mathematical Analysis; McGraw-Hill Book Company.

  16. Savin, A. & Sternin, B. (2017). Introduction to Complex Theory of Differential Equations, Birkhauser.

  17.  Scheid, F.  (1988). Numerical Analysis (Schaum Series); McGraw Hill, USA.

  18. Schiff, L.I. (1988). Quantum Mechanics, 3rd Ed., McGraw Hill, New York.

  19. Simmon, G.F. (1973), Introduction to Topology and Modern analysis; McGraw-Hill. 

  20. Smith, K. L. (1988). College Mathematics and Calculus With Applications to Management, Life and Social Sciences; Brooks/Cole Publishing Co., California, USA.

  21. Speyer,  J. L. & Jacobson, D. H. (2010). Primer on Optimal Control Theory, SIAM.

  22. Spiegel, M. R. (1991 ). Complex Variables (Schaum Outline Series); McGraw Hill Inc.

  23. Spiegel, M.R. (1992), Real Variables:  Lebesque Measure and Integration with Applications to Fourier Series; MacGraw-Hill  

  24. Spiegle, M. R. (1991). Advanced Calculus; McGraw Hill, USA.

  25. Stewart J. (1983). Single Variable Calculus; PWS, USA.

  26. Stewart, J. (1987). Calculus; Wadsworth Inc.

  27. Stewart, J. (2003). Calculus (Early Transcendental), 6th Ed. Thomson Brooks/Cole.

  28. Strang, G. (2006). Linear algebra and Its Applications, Thomson Brookes/Cole,  

California, USA.

  1. Strauss, W. A. (1992). Partial Differential Equations, an Introduction; John Wiley &  

Sons Inc. New York. 

  1. Sun, W. & Yuan, Y. (2006), Optimization Theorey and Methods: Nonlinear  

Programming, Springer, New York, USA. 

  1. Swokowski, E. W. (1984). Calculus With Analytic Geometry; 3 Ed. Prindle, Weber 

  and Schmidt, Boston, USA.

  1. Symon, K.R.  (1973). Mechanics, Addison-Wesley Publishing Company

      Systems, Chapman & Hall, New York, USA.

  1. Taylor, A.E. & Lay, D.C.  (1988), Introduction to Functional  analysis; John Wiley 

 and Sons.

  1. Teschle, G., (2010). Ordinary Differential Equations and Dynamical Systems:  

 Graduate Studies in Mathematics, AMS Vol 140, Providence, Rhode Island, USA

  1. Thomas, G. B. and Finney, R. L. (1996). Calculus and Analytic Geometry; 9 Ed. 

 Addison-Wesley Pub., Reading, USA.

  1. Titchmarsh, E.C. (1972), Eigenfunction expansions associated with second-order 

 differential equations; Oxford University Press.

  1. Trefethen, L. N., &  Bau, D. ( 1997). Numerical Linear algebra ,SIAM, Philadelphia, 

USA.

  1. Winston, W. L. (1994). Operations Research: Applications and Algorithms; 3rd Ed., 

Duxbury Press, Belmont, USA.

  1. Winter, R.G. (1986).  Quantum Physics, 2nd Ed., Faculty Publishing Inc.

Zill, G. D. (2012). A First Course in Differential Equations with Modelling Applications, John Wiley and Sons.

Entry Requirements: 

Applicants pass Elective Mathematics, Economics and any one (1) of the following elective subjects: Physics, Chemistry Business Management, Principles of Costing and Accounting or Geography.

Career Opportunities: 

Mathematics is a challenging and an exciting science of exactness that plays a central role in many aspects of modern life including business. This degree programme combines mathematical concepts, techniques and models with a particular focus on its application to the world of business. It bridges the divide that exists between the two disciplines.     Students will therefore develop a working understanding of business enriched with mathematical perspectives, enhancing their dynamism and perspectives with regards to their professional expertise and intellectual capacities. 

Programme Structure

Level 100

First Semester

CMS 107: Communicative Skills I
3 Credit(s)

Engaging in academic work at the university is challenging. This course is aimed at equipping fresh students to make the transition from pre-university level to the university level. It assists them in engaging and succeeding in complex academic tasks in speaking, listening, reading and writing. It also provides an introduction to university studies by equipping students with skills that will help them to engage in academic discourse with confidence and fluency.
MAT 101: Algebra and Trigonometry
3 Credit(s)
Pre-requisite: WASSCE/SSSCE Elective Mathematics

This course seeks to prepare students for advanced courses in Mathematics. Students will have a better appreciation of how to perform basic operations on sets, real numbers and matrices and to prove and apply trigonometric identities. The specific topics that will be covered are: commutative, associative and distributive properties of union and intersection of sets.  DeMorgan’s laws. Cartesian product of sets. The real number system; natural numbers, integers, rational and irrational numbers. Properties of addition and multiplication on the set of real numbers. Relation of order in the system of real numbers. Linear, quadratic and other polynomial functions, rational algebraic functions, absolute value functions, functions containing radicals and their graphical representation. Inequalities in one and two variables. Application to linear programming. Indices and logarithms, their laws and applications. Binomial theorem for integral and rational indices and their application. Linear and exponential series. Circular functions of angles of any magnitude and their graphs. Trigonometric formula including multiple angles, half angles and identities. Solution to trigonometric equations.

Second Semester

CMS 108: Communicative Skills II
3 Credit(s)

This is a follow-up course on the first semester one. It takes students through writing correct sentences, devoid of ambiguity, through the paragraph and its appropriate development to the fully-developed essay. The course also emphasizes the importance and the processes of editing written work.

Level 200

First Semester

MAT 201: Introduction to Abstract Algebra
3 Credit(s)
Pre-requisite: MAT 102

This course aims to provide a first approach to the subject of algebra, which is one of the basic pillars of modern mathematics. The focus of the course will be the study of certain structures called groups, rings, fields and some related structures. Abstract algebra gives to student a good mathematical maturity and enable learners to build mathematical thinking and skill. The topics to be covered are injective, subjective and objective mappings.  Product of mappings, inverse of a mapping. Binary operations on a set. Properties of binary operations (commutative, associative and distributive properties).  Identity element of a set and inverse of an element with respect to a binary operation. Relations on a set. Equivalence relations, equivalence classes. Partition of set induced by an equivalence relation on the set.  Partial and total order relations on a set. Well-ordered sets. Natural numbers; mathematical induction. Sum of the powers of natural numbers and allied series. Integers; divisors, primes, greatest common divisor, relatively prime integers, the division algorithm, congruencies, the algebra of residue classes.  Rational and irrational numbers. Least upper bound and greatest lower bound of a bounded set of real numbers. Algebraic structures with one or two binary operations. Definition, examples and simple properties of groups, rings, integral domains and fields.
MAT 203: Further Calculus
3 Credit(s)
Pre-requisite: MAT 102

This course is designed to develop advanced topics of differential and integral calculus. Emphasis is placed on the applications of definite integrals, techniques of integration, indeterminate forms, improper integrals and functions of several variables. The topics to be covered are differentiation of inverse, circular, exponential, logarithmic, hyperbolic and inverse hyperbolic functions.  Leibnitz’s theorem. Application of differentiation to stationary points, asymptotes, graph sketching, differentials, L’Hospital rule.  Integration by substitution, by parts and by use of partial fractions. Reduction formulae. Applications of integration to plane areas, volumes and surfaces of revolution, arc length and moments of inertia.  Functions of several variables, partial derivatives.

Second Semester

MAT 202: Vector Algebra and Differential Equations
3 Credit(s)
Pre-requisite: MAT 102

The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. The course will demonstrate the usefulness of ordinary differential equations for modeling physical and other phenomena. Complementary mathematical approaches for their solution will be presented. The topics to be covered are vector algebra with applications to three-dimensional geometry. First order differential equations; applications to integral curves and orthogonal trajectories.  Ordinary linear differential equations with constant coefficients and equation reducible to this type. Simultaneous linear differential equations. Introduction to partial differential equations.
MAT 206: Complex Numbers and Matrix Algebra
3 Credit(s)
Pre-requisite: MAT 101

This course is designed to give an introduction to complex numbers and matrix algebra, which are very important in science and technology, as well as mathematics. The topics to be covered are complex numbers and algebra of complex numbers. Argand diagram, modulus-argument form of a complex number. Trigonometric and exponential forms of a complex number.  De Moivre’s theorem, roots of unity, roots of a general complex number, nth roots of a complex number. Complex conjugate roots of a polynomial equation with real coefficients.  Geometrical applications, loci in the complex plane. Transformation from the z-plane to the w-plane. Matrices and algebra of matrices and determinants, Operations on matrices up to . inverse of a matrix and its applications in solving  systems of equation. Gauss-Jordan method of solving systems of equations. Determinants and their use in solving systems of linear equations. Linear transformations and matrix representation of linear transformations. 

Level 300

First Semester

MAT 303: Introductory Analysis
3 Credit(s)
Pre-requisite: MAT 201 and MAT 203

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. The topics to be covered include

limit of a sequence of real numbers, standard theorems on limits, bounded and monotonic sequences of real numbers, infinite series of real numbers, tests for convergence, power series, limit, continuity and differentiability of functions of one variable,  Rolle’s theorem, mean value theorems, Taylor’s theorem, definition and simple properties of the Riemann integral.
MAT 305: Linear Algebra I
3 Credit(s)
Pre-requisite: MAT 101

This course introduces more algebraic methods needed to understand real world questions. It develops fundamental algebraic tools involving matrices and vectors to study linear systems of equations and Gaussian elimination, linear transformations, orthogonal projection, least squares, determinants, eigenvalues and eigenvectors and their applications.  The topics to be covered are axioms for vector spaces over the field of real and complex numbers. Subspaces, linear independence, bases and dimension. Row space, Column space, Null space, Rank and Nullity.  Inner Products Spaces. Inner products, Angle and Orthogonality in Inner Product Spaces, Orthogonal Bases, Gram-Schmidt orthogonalization process. Best Approximation. Eigenvalues and Eigenvectors. Diagonalization. Linear transformation, Kernel and range of a linear transformation. Matrices of Linear Transformations.
MAT301: Advanced Calculus I
3 Credit(s)
Pre-requisite: MAT 202 and 203

Limit and continuity of functions of several variables; partial derivatives, differentials, composite, homogenous and implicit functions; Jacobians, orthogonal curvilinear coordinates; multiple integral, transformation of multiple integrals; Mean value and Taylor’s Theorems for several variables; maxima and minima with applications.

Second Semester

MAT302: Advanced Calculus II
3 Credit(s)
Pre-requisite: MAT 301 and MAT 303

 

 

This course covers vector valued functions. It introduces students to the concept of change and motion and the manner in which quantities approach other quantities.  Topics include limits, continuity,  derivatives of vector functions, gradient, divergence, curl, formulae involving gradient, divergence, laplacian, orthogonal curvilinear coordinates,  line integrals, Green’s theorem in the plane, surface integrals. Other topics are the divergence theorem, improper integrals, Gamma functions, Beta functions, the Riemann Stieltjes Integral,  pointwise and uniform convergence of sequence and series, integration and differentiation term by term.

Limits, continuity and derivatives of vector functions; gradient, divergence and curl; formulae involving gradient, divergence, curl and laplacian and orthogonal curvilinear coordinates; line integrals; Green’s theorem in the plane; surface integrals; the divergence theorem; improper integrals; Gamma and Beta functions; The Riemann Stieltjes integral; pointwise and uniform convergence of sequence and series; integration and differentiation term by term.
MAT 306: Linear Algebra II
3 Credit(s)
Pre-requisite: MAT 305

This course introduces more algebraic methods needed to understand real world questions. It develops fundamental algebraic tools involving direct sum of subspaces, complement of subspace in a vector space and dimension of the sum of two subspaces. Other topics to be covered are one-to one, onto and bijective linear transformations, isomorphism of vector spaces, matrix of a linear transformation relative to a basis, orthogonal transformations, rotations and reflections, real quadratic forms, and positive definite forms.
MAT 310: Abstract Algebra I
3 Credit(s)
Pre-requisite: MAT 201 and MAT 202

This course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics. The topics to be covered are: axioms for groups with examples, subgroups, simple  properties of groups, cyclic groups, homomorphism and isomorphism, axioms for rings, and fields, with examples, simple properties of rings, cosets and index of a subgroup, Lagrange’s theorem, normal subgroups and quotient groups, the residual class ring, homomorphism and isomorphism of rings, subrings.

Level 400

First Semester

MAT 405: Ordinary Differential Equations
3 Credit(s)
Pre-requisite: MAT 301

The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. The course will demonstrate the usefulness of ordinary differential equations for modelling physical and other phenomena. Complementary mathematical approaches for their solution will be presented. Topics  covered include linear differential equation of order n with coefficients continuous on some interval J,  existence-uniqueness theorem for linear equations of order n, determination of a particular solution of non-homogeneous equations by the method of variation of parameters,  Wronskian matrix of n independent solutions of a homogeneous linear equation,  ordinary and singular points for linear equations of the second order,  solution near a singular point, method of Frobenius, singularities at infinity, simple examples of  Boundary value problems for ordinary linear equation of the second order, Green’s functions, eigenvalues, eigenfunctions, Sturm-Liouville systems, properties of the gamma and beta functions, definition of the gamma function for negative values of the argument; Legendre, Bessel, Chebyshev, Hypergeometic functions and  orthogonality properties.
MAT 405: Ordinary Differential Equations
3 Credit(s)

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MAT 406: Partial Differential Equations
3 Credit(s)
Pre-requisite: MAT 405

This course introduces students to the theory of boundary value and initial value problems for partial differential equations with emphasis on linear equations. Topics covered include first and second order partial differential equations, classification of second order linear partial differential equations, derivation of standard equation, methods of solution of initial and boundary value problems, separation of variables, Fourier series and their applications to boundary value problems in partial differential equation of engineering and physics, internal transform methods; Fourier and Laplace transforms and their application to boundary value problems.
MAT 415: Financial Mathematics
3 Credit(s)

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STA 403: Statistical Method II
3 Credit(s)

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Second Semester

MAT 404: Complex Analysis
3 Credit(s)
Pre-requisite: MAT 302 and MAT 303

This course provides an introduction to complex analysis which is the theory of complex functions of a complex variable. The topics to be covered in the course are: complex numbers, sequences and series of complex numbers, limits and continuity of functions of complex variables, elementary functions of a complex variable, Cauchy-Riemann criterion for differentiability,  analytic functions, complex integrals, Taylor’s and Laurent’s series, calculus of residues, contour integration and conformal mapping.
MAT 407: Numerical Analysis I
3 Credit(s)
Pre-requisite: MAT 302 and MAT 307

This course is designed to equip students with the basic techniques for the efficient numerical solution of problems in science and engineering. Topics covered include round off errors and floating-point arithmetic,  solution of non-linear equations, bracketing, fixed point methods, secant method, Newton's method, zeros of polynomials, Polynomial interpolation, orthogonal polynomial, least squares approximations, approximation by rational function, numerical differentiation, numerical integration, and  adaptive quadrature.
MAT 408: Introductory Functional Analysis
3 Credit(s)
Pre-requisite: MAT 401

This course is intended to introduce the student to the basic concepts and theorems of functional analysis and its applications. Topics covered include linear spaces, topological spaces, normed linear spaces & Banach Spaces, inner product spaces,  Hilbert spaces, linear functional and the Hahn-Banach theorem.
MAT 416: Dynamical Systems
3 Credit(s)

 

The course offers an introduction to Dynamical Systems from an applied and practical point of view. It will offer students the opportunity to learn how to compute the behaviour of differential equations as parameters varies. Topics include: linear  dynamical systems and their stability, Routh-Hurwitz conditions, autonomous Systems, non-linear dynamical systems, equilibrium points and their stability, almost linear systems, phase plane analysis: direction fields and phase portraits, Lyapunov stability (simple and damped pendulum), periodic solutions, limit cycles, bifurcation  theory, chaos and attractions. 

 
MAT 499: Project Work (Optional)
3 Credit(s)

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