# Mathematics I Syllabus: B.Sc. CSIT 1st Semester 2080

B.Sc.CSIT Mathematics I syllabus covers various mathematical concepts, including functions, limits, continuity, differentiation, and integration.

Mathematics I B.Sc. CSIT Syllabus covers a range of topics in mathematics, including functions, limits, continuity, differentiation, integration, and more. The course is designed to provide students with a strong foundation in the principles of mathematics and prepare them for further study in the field.

The syllabus is divided into 10 units, each focusing on a specific topic. Students will learn about functions of one variable, limits and continuity, derivatives, applications of derivatives, antiderivatives, applications of antiderivatives, ordinary differential equations, infinite sequences and series, plain and space vectors, and partial derivatives and multiple integration.

Through this course (Mathematics I), students will develop the skills and knowledge necessary to understand and solve real-world problems using mathematical concepts and techniques.

## Mathematics I Syllabus

General Information

Course B.SC. CSIT
Course Title Mathematics I
Course No MTH112
Nature of the course Theory
Semester I (First)
Full Marks 80 + 20
Pass Marks32 + 8
Credit Hrs. 3

CHAPTER LIST: Mathematics I

S.N. Chapter
Unit 1 Function of One Variable
Unit 2 Limits and Continuity
Unit 3 Derivatives
Unit 4 Applications of Derivatives
Unit 5 Antiderivatives
Unit 6 Applications of Antiderivatives
Unit 7 Ordinary Differential Equations
Unit 8 Infinite Sequence and Series
Unit 9 Plain and Space Vectors
Unit 10 Partial Derivatives and Multiple Integration

Course Description : This course covers the concepts of functions, limit, continuity, differentiation, integration of function of one variable; logarithmic, exponential, applications of derivatives and antiderivatives, differential equations, vector and applications, partial derivatives and multiple integration.

Course Objective : The objective of this course is to make student able to understand and formulate real world problems into mathematical statements, develop solutions to mathematical problems at the level appropriate to the course and describe mathematical solutions either numerically or graphically.

## Course Contents

### Unit 1: Function of One Variable

Course Duration: 5 Hours
Representing function of one variables, Polynomial, Trigonometric, Exponential and Logarithmic functions, Range and domain of functions and their graphs.

### Unit 2: Limits and Continuity

Course Duration: 4 Hours

Precise definition of Limits and Continuity, Limits at infinity, Continuity, Horizontal asymptotes, Vertical and Slant asymptotes

### Unit 3: Derivatives

Course Duration: 4 Hours

Tangents and velocity, Rate of change, Review of Derivative, Differentiability of a function, Mean value theorem, Indeterminate forms and L-Hospital Rule

### Unit 4: Applications of Derivatives

Course Duration: 4 Hours

Curve sketching, Review of maxima and minima of one variable, Optimization problems, Newton's method

### Unit 5: Antiderivatives

Course Duration: 5 Hours

Review of Antiderivatives, Rectilinear motion, Indefinite integrals and Net change, Definite integral, The fundamental theorem of calculus, Improper integrals

### Unit 6: Applications of Antiderivatives

Course Duration: 5 Hours

Areas between the curves, Volume of cylindrical cells, Approximate Integrations, Arc length, Area of surface of revolution

### Unit 7: Ordinary Differential Equations

Course Duration: 6 Hours

Introduction, Introduction to first order equations separable equations, Linear equations, Second Order linear differential equations, Non homogenous linear equations, Method of undetermined coefficients

### Unit 8: Infinite Sequence and Series

Course Duration: 5 Hours

Infinite Sequence and Series, Convergence tests and power series, Taylor's and Maclaurin's series

### Unit 9: Plain and Space Vectors

Course Duration: 4 Hours

Introduction, Applications, Dot product and cross Product, Equations of lines and Planes, Derivatives and integrals of vector functions, Arc length and curvature, Normal and binomial vectors, Motion in space

### Unit 10: Partial Derivatives and Multiple Integration

Course Duration: 3 Hours

Limit and Continuity, Partial Derivatives, Tangent planes, Maximum and minimum values, Multiple integrals.

## Mathematics I Books

### Text Books:

• Calculus Early Transcendentals, James Stewart, 7E, CENGAGE Learning

### Reference Books:

• Calculus Early Transcendentals, Thomas, 12th Editions, Addison Wesle

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