This is the first mathematics course you will be studying in the Bachelor’s Degree Programme. The aim of this course is to develop an understanding of basic mathematical concepts and techniques that you will require for studying other mathematics courses of the programme, as well as any further study and work you undertake in mathematics. Calculus is divided into two broad areas, differential calculus and integral calculus. Broadly speaking, differential calculus is the study of change and integral calculus is about adding up the parts. Differential calculus helps you to find, for example, the effect of changing conditions on a system being investigated, and hence to gain control over the system. The process of this mathematical investigation uses the powerful technique of modelling the phenomena concerned. The models usually involve differential equations. Differential calculus is useful in formulating models and integral calculus is used to solve the differential equations associated with the model. Apart from well known applications in physics, mathematical models based on calculus are used for the study of population ecology, cybernetics, management practices, economics and medicine.
In this course on differential equations, we shall be dealing with both ordinary as well as partial differential equations. For a better understanding of the concepts in the course a good knowledge of calculus is essential. The knowledge of our calculus course BMTC-131 will more or less fulfill your this requirement. Since BMTC-131only deals with a function of one variable, to fill up the gaps, we have added contents on functions of two and more variables in this course. Accordingly, we have divided the material in this course into four blocks.
Real Analysis is the branch of mathematics that studies the structure of real numbers and the behavior of functions defined on the set of real numbers. You already have some idea of the structure of the set of real numbers, and of functions defined on it, from the 1st semester course, Calculus. In that course you were introduced to many concepts such as limit, continuity, differentiability and integrability for real-valued functions, though more from an algorithmic and computational aspect. However, when you apply the algorithms, it is important to know the logic behind them. The study of analysis provides the reasons behind these computation rules. The study will also help you to develop “analytical thinking” and the ability to apply mathematics more precisely and confidently.
Algebra is a word that you are familiar with. You may also know that it is derived from the Arabic word ‘Al-jabr’. Classically, algebra was concerned with obtaining solutions of equations. Then came ‘modern algebra’, a term used to describe detailed investigations within classical algebra. In Block 1 of the course, Calculus, you have studied some of the concepts of modern algebra – sets and operations on them, functions, a binary operation on a set, an algebraic way of studying plane geometry, properties of complex numbers, what a polynomial over R is, and solutions of some polynomial equations. In this course, we shall build on this learning, and take you much further. In this course, we will focus on ‘abstract algebra’, a generalisation of modern algebra. In abstract algebra we study algebraic systems that are defined by axioms alone. These axioms normally evolve from concrete situations. In this course, comprising four blocks, you will study three basic algebraic systems, namely, groups, rings and fields.
Linear algebra is a fundamental area in mathematics, focusing on the efficient solution of systems of linear equations. The course material introduces matrices, vector spaces, subspaces, basis and dimension, linear transformations, eigenvalues, and inner product spaces. Linear algebra deals with solving systems of linear equations, which is essential in various fields such as optimization and statistics. The concept of linearity is also crucial in differential equations, difference equations, and geometric transformations
This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods.
