Mathematics I - BCA 1st Semester, Tribhuvan University

Unit 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) Unit 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) Unit 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. Unit 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) Unit 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) Unit 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.