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Mathematics I

This course provides the "logical" foundation for "instructional materials" by covering calculus of one variable, including limits, differentiation, and integration. It focuses on the "technical clarity" needed to formulate real-world problems into mathematical statements and demonstrate solutions numerically or graphically.

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TabFlux . Mathematics I . TU . BCA-OLD

Mathematics I

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Course Title: Mathematics I

Course No: CACS104

Nature of the Course: Theory + Lab

Semester: 1

Full Marks: 20 + 20 + 60

Pass Marks: 8 + 8 + 24

Credit Hours: 3

Course Description

Course Objectives

Course Contents

1. Unit 1: Set Theory and Real & Complex Number

7 hrs

1.1. Concept, Notation and Specification of Sets, Types of Sets, Operations on Sets (Union, Intersection, Difference, Complement) and their Venn diagrams

1.2. Laws of Algebra of Sets (without proof), Cardinal Number of Set and Problems Related to Sets

1.3. Real Number System, Intervals, Absolute Value of Real Number

1.4. Introduction of Complex Number, Geometrical Representation of Complex Number

1.5. Simple Algebraic Properties of Complex Numbers (Addition, Multiplication, Inverse, Absolute Value)

2. Unit 2: Relation, Functions and Graphs

8 hrs

2.1. Ordered pairs, Cartesian product, Relation, Domain and Range of a relation

2.2. Inverse of a relation; Types of relations: reflective, symmetric, transitive, and equivalence relations

2.3. Definition of function, Domain and Range of a function, Inverse function, Special functions (Identity, Constant), Algebraic (linear, Quadratic, Cubic), Trigonometric and hyperbolic functions

2.4. Definition of exponential and logarithmic functions, Composite function

3. Unit 3: Sequence and Series

7 hrs

3.1. Sequence and Series (Arithmetic, Geometric, Harmonic)

3.2. Properties of Arithmetic, Geometric, Harmonic sequences

3.3. A. M., G. M., and H. M. and relation among them

3.4. Sum of Infinite Geometric Series, Taylor’s Theorem (without proof), Taylor’s series, Exponential series

4. Unit 4: Matrices and Determinants

8 hrs

4.1. Introductions of Matrices, Types of Matrices, Equality of Matrices

4.2. Determinant, Transpose, Minors and Cofactors of Matrix

4.3. Properties of determinants (with out proof), Singular and non-singular matrix, adjoint and inverse of matrices

4.4. Linear transformations, orthogonal transformations; rank of matrices

5. Unit 5: Analytical Geometry

8 hrs

5.1. Conic Sections: Definitions (Circle, Parabola, Ellipse, Hyperbola) and Related Terms

5.2. Examples to Explain The Defined Terms, Equations and Graphs of The Conic Sections Defined Above

5.3. Classifying The Defined Conic Sections by Eccentricity and Related Problems

5.4. Polar Equations of Lines, Circles, Ellipse, Parabolas, and Hyperbolas

5.5. Vectors in Space: Vectors in Space, Algebra of Vectors in Space, Length, Distance Between Two Points, Unit Vector, Null Vector, Scalar Product, Cross Product of Two and Three Vectors and Their Geometrical Interpretations and Related Examples

6. Unit 6: Permutation and Combination

7 hrs

6.1. Basic Principle of Counting

6.2. Permutation of a. Set of Objects All Different b. Set of Objects Not All Different

6.3. c. Circular Arrangement d. Repeated Use of The Same Object

6.4. Combination of Things All Different, Properties of Combination

Laboratory Works

Text Books

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

Reference Books

1.Bajracharya D. R., Shreshtha, R. M. & et al, “Basic Mathematics I, II” Sukunda Pustak Bhawan, Nepal
2.New ReferenceBudnick, F. S., “Applied Mathematics for Business, Economics and the Social Sciences”, McGraw-Hill Ryerson Limited.
3.New RefeMonga, G. S., “Mathematics for Management and Economics”, Vikas Publishing House Pvt. Ltd., New Delhi.rence
4.New RefePaudel, K. C., GC. F. B., and et. al, “Higher Secondary Mathematics”, Asmita Publication & Distributors Pvt. Ltd, Nepal.rence
5.New ReferenUpadhayay, H. P., Paudel, K.C & et al, “Elements of Business Mathematics”, Pinnacle Publication.ce
6.New RefereYamane, T. “Mathematics for Economist”, Prentice-hall of India.nce

Notes:

Source:

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.

Upon the conclusion of the course, students should be able to:

- Provide the students with basic mathematical skills required to understand Computer Application Courses.

Mathematics and/or Matlab should be used for above mentioned topics.

Suggested Practical Works:

- Set operations and Venn diagrams

- Plotting functions and graphs

- Matrices and Determinants operations

- Conic sections and their graphs

- Vector operations in space

- Permutation and Combination problems

This syllabus follows the official BCA curriculum of Tribhuvan University. In case of any doubt or revision, the university's published syllabus shall be considered authoritative.