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## Basic Mathematics (BCS-012)

This course fosters mathematical maturity and readies students for computer science courses like discrete mathematics. It covers algebra, calculus, vectors, and 3D geometry, building crucial analytical and problem-solving skills.

Live Course

Live Class: Tuesday, 26 Mar

Duration: 16 Hours

Enrolled: 8

Offered by: IGNOU Guidance

### \$12

Objectives:

The primary objective of this course is to introduce students some of the mathematics through which they can develop some mathematical maturity, that is enhance their ability to understand and create mathematical arguments. The secondary objective of this course is to prepare students for mathematical oriented courses in computer science such as discrete mathematics, database theory, analysis of algorithms etc.

• BLOCK-1: Algebra-I (Unit-1: Determinants, Unit-2: Matrices-1, Unit-3: Matrices-2, Unit-4: Mathematical Induction)
• BLOCK 2 : Algebra II (Unit 1: Sequence and Series, Unit 2: Complex Number, Unit 3: Equations, Unit 4: Inequalities)
• BLOCK 3: Calculus (Without Trigonometry) {Unit 1: Differential Calculus, Unit 2: Simple Application of Differential Calculus, Unit 3: Integration, Unit 4: Application of Integration}
• BLOCK 4: Vectors and Three-Dimensional Geometry (Unit 1: Vector-1, Unit 2: Vector-2, Unit 3: Three & Dimensional Geometry-1, Unit 4: Linear Programming)

The course is divided into four distinct blocks, each addressing essential topics with a systematic and progressive approach.

The first block, Algebra I, introduces determinants, matrices, and mathematical induction, covering fundamental concepts and their practical applications.

The second block, Algebra II, delves into sequences, series, complex numbers, equations, and inequalities, offering a well-rounded exploration of algebraic structures and their properties.

Moving on to the third block, Calculus (Without Trigonometry), the course navigates through the core concepts of differential calculus, its applications, and integral calculus. This block emphasizes real-world applications, providing a bridge between abstract mathematical concepts and their practical implications.

The final block, Vectors and Three-Dimensional Geometry, introduces vectors, scalars, and three-dimensional geometry, culminating in the exploration of linear programming. This section bridges the gap between algebra and geometry, showcasing the interdisciplinary nature of advanced mathematical concepts.

Throughout the course, students gain proficiency in mathematical reasoning, problem-solving, and critical thinking. The sequential structure of the units ensures a logical progression of difficulty and complexity, allowing learners to build a solid understanding before moving on to more advanced topics. The inclusion of real-world applications and practical examples enhances the relevance of the course, demonstrating the applicability of mathematical concepts in various fields.

In essence, this course equips students with a strong mathematical foundation, fostering analytical skills and preparing them for more advanced studies in mathematics or its applications in diverse professional fields. The well-organized curriculum and comprehensive coverage make it a valuable resource for individuals seeking a robust understanding of algebra, calculus, vectors, and three-dimensional geometry.

## Skills You Will Gain

Mathematics Database theory Analysis of algorithms Algebra Determinants Matrices Equations Inequalities Calculus Vectors Problem-solving Critical thinking Real-world applications Logical progression Analytical skills Advanced studies Comprehensive coverage

### Course Offerings

• Prepare You for the Examination
• Assignment Preparation Guidance
• Last Year Exam Questions Discussion
• Study Learning Material (Soft Copy)
• Provision of Notes if Required
• Interactive Classes Led by Teachers
• Clarification of Doubts During Class
• Access Recordings of Live Classes
• Accessible on all Devices
• Community Based Discussion Forum
• Topics
• Instructor (1)
• Unit-1: Determinants-Determinants of order 2 and 3, properties of determinants
• evaluation of determinants. Area of triangles using determinants, cramer’s rule. Unit-2: Matrices-1 Definition, equality, addition and multiplication of matrices. Adjoint and inverse of a matrix. Solution of a system of linear equations – homogeneous and nonhomogeneous. Unit-3: Matrices-2 Elementary row operations
• rank of a matrix, reduction to normal form,Inverse of a matrix using elementary row operations. Unit-4: Mathematical Induction Principle of mathematical induction 1 and 2.
• Unit 1: Sequence and Series Definition of sequence and series
• A.P, G.P, H.P and A.G.P., Idea of limit of a sequence. Unit 2: Complex Number Complex number in the form of a+ib. Addition, multiplication, division of complex numbers. Conjugate and modulus of complex numbers. De Moivre’s Theorem. Unit 3: Equations Quadratic, cubic and biquadratic equations. Relationship between roots and co-efficient. Symmetric functions of roots. Unit 4: Inequalities Solution of linear and quadratic inequalities.
• Unit 1: Differential Calculus Concept of limit and continuity
• differentiation of the sum, difference, product and quotient of two functions, chain rule. Differentiation of parametric functions. 2nd order derivatives. Unit 2: Simple Application of Differential Calculus Rate of change
• monotoncity-increasing and decreasing
• maxima and minima. Unit 3: Integration Integration as an anti-derivative. Integration by substitution and by parts. Unit 4: Application of Integration Finding area under a curve. Rectification.
• Unit 1: Vector-1 Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratio of vectors. Addition of two vectors. Multiplication of a vector by a scalar. Position vector of a point and section formula. Unit 2: Vector-2 Scalar (Dot) product of vectors, Vector (Cross) product of vectors. Scalar triple product and vector triple product. Unit 3: Three & Dimensional Geometry-1 Introduction, Distance formula. Direction cosines/ratio of a line passing through two points. Equations of a line in different forms
• angle between two lines
• Coplanar and skew lines. Distance between skew lines. Unit 4: Linear Programming Introduction, definition and related terminology such as constrains, objective function, optimization. Mathematical Formulation of LPP. Graphical method of solving LPP in two variables. Feasible and inferring solution (up to three non-trivial constraints).