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 Marks | 32 + 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
