Mathematics I
0%
Course Title: Mathematics I
Course No: MTH117
Nature of the Course: THEORY
Semester: 1
Full Marks: 60 + 40
Pass Marks: 24 + 16
Credit Hours: 3
Course Description
Course Objectives
Course Contents
1.1. Representation and Types of Functions
- Four ways of representing a function
- Linear mathematical model
- Polynomial
- Rational
- Trigonometric
- Exponential and Logarithmic functions
- Combination of functions
- Range and domain of functions and their Graphs
2.1. Limits and Asymptotes
- Precise definition of Limit
- Limits at infinity
- Continuity
- Horizontal asymptotes
- Vertical and Slant asymptotes
3. Derivatives
4 hrs
3.1. Derivative Concepts and Theorems
- Tangents and velocity
- Rate of change
- Review of derivative
- Differentiability of a function
- Mean value theorem
- Indeterminate forms and L'Hospital rule
4.1. Optimization and Analysis
- Curve sketching
- Review of maxima and minima of one variable
- Optimization problems
- Newton's method
5. Antiderivatives
5 hrs
5.1. Integration Concepts
- Review of antiderivatives
- Rectilinear motion
- Indefinite integrals and Net change
- Definite integral
- The Fundamental theorem of calculus
- Improper integrals
6.1. Geometric Applications of Integration
- Areas between the curves
- Volumes of cylindrical cells
- Approximate Integrations
- Arc length
- Area of surface of revolution
7.1. First Order Differential Equations
- Introduction
- Introduction to first order equations
- Separable equations
- Linear equations
7.2. Second Order Differential Equations
- Second order linear differential equations
- Non homogeneous linear equations
- Method of undetermined coefficients
8.1. Series and Convergence
- Infinite sequence and series
- Convergence tests and power series
- Taylor's and Maclaurin's series
9.1. Vector Operations and Applications
- Introduction
- Applications
- Dot product and cross Product
- Equations of lines and Planes
- Derivative and integrals of vector functions
- Arc length and curvature
- Normal and binormal vectors
- Motion in space
10.1. Multivariable Calculus
- Limit and continuity
- Partial derivatives
- Tangent planes
- Maximum and minimum values
- Multiple integrals
Text Books
- 1.Calculus Early Transcendentals, James Stewart, 7E, CENGAGE Learning
Reference Books
- 1.Calculus Early Transcendentals, Thomas, 12th Editions, Addision Wesley