# Mathematics I Syllabus - BCA (TU)

### Course Description

#### Course Description

This course includes several topics from algebra and analytical geometry such as set theory and real & complex number; relation, functions and graphs;  sequence and series; matrices and determinants; permutation & combination; conic section and vector in space which are essential as mathematical foundation for computing.

#### Course Objectives

The general objective of this course is to provide the students with basic mathematical skills required to understand Computer Application Courses.

### Unit Contents

#### 1. Set theory and Real & Complex Number : 7 hrs

Concept, Notation and Specification of Sets, Types of Sets, Operations on Sets (Union, Intersection, Difference, Complement) and their Venn Diagrams, Laws of Algebra of Sets(without proof), Cardinal number of Set and Problems Related to Sets. Real Number System, Intervals, Absolute Value of Real Number, Introduction of Complex Number, Geographical Representation of Complex Number, Simple Algebraic Properties of Complex Numbers (Addition, Multiplication, Inverse, Absolute Value)

#### 2. Relation, Functions and Graphs : 8 hrs

Ordered pairs, Cartesian product, Relation, Domain and Range of a relation, Inverse of a relation; Types of relations: reflective, symmetric, transitive, and eqivalence relations. Definition of function, Domain and Range of a function, Inverse function, Special functions (Identity, Constant), Algebraic(linear, Quadratic, Cubic), Trigonometric and their graphs. Definition of exponential and logarithmic functions, Composite function.(Mathematical)

#### 3. Sequence and Series : 7 hrs

Sequence and Series (Arithmetic, Geometric, Harmonic), Properties of Arithmetic, Geometric, Harmonic sequences, A. M., G. M., and H, M. and relation among them. Sum of Infinite Geometric Series. Taylor's Theorem(without proof), Taylor's series, Exponential series.

#### 4. Matrices and Determinants : 8 hrs

Introduction of Matrices, Types of Matrices, Equality of Matrices, Algebra of Matrices, Determinant, Transpose, Minors and Cofactors of Matrix, Properties of determinants(with out proof), Singular and non-singular matrix, adjoin and inverse of matrices. Linear transformations, orthogonal transformations; rank of matrices.(Matlab)

#### 5. Analytical Geometry : 8 hrs

Conic Sections: Definitions ( Circle, Parabola, Ellipse, Hyperbola and Related Terms), Examples to Explain The Defined Terms, Equations and Graphs of The Conic Sections Defined Above, Classifying The Defined Conic Sections by Eccentricity and Related Problems, Polar Equations of Lines, Circles, Ellipse, Parabolas, and Hyperbolas.(Mathematica/ Matlab)

Vectors in Space: Vectors in Space, Algebra of Vectors in Space, Length, Distance Between Two Points, Unit Vector, Null Vector, Scalar Product of Two and Three Vectors and Their Geomatrical Inerpretations and Related Examples.(Matlab)

#### 6. Permutation and Combination : 7 hrs

Basic Principle of Counting, Permutation of a. Set of Objects All Different b. Set of Objects Not All Different c. Circular Arrangement d. Repeated Use of The Same Object. Combination of Things All Different, Properties of Combination.

### Text and Reference Books

#### Text Book

1. 1. Thomas, G. B, Finney, R. S., “Calculus with Analytic Geometry”, Addison -Wesley, 9th Edition.

#### Reference Books

1. Bajracharya D. R., Shreshtha, R. M. & et al, “Basic Mathematics I, II” Sukunda Pustak Bhawan, Nepal
2. Budnick, F. S., “Applied Mathematics for Business, Economics and the Social Sciences”, McGraw-Hill Ryerson Limited.