BSc CSIT · Semester I
Mathematics I syllabus
Official TU syllabus for Mathematics I (MTH117): 10 units, 53 topics, 3 credit hours. Every unit links to its notes and solved questions.
1
Function of One Variable
5h · 11 Q- 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
Limits and Continuity
4h · 8 Q- Precise definition of Limit
- Limits at infinity
- Continuity
- Horizontal asymptotes
- Vertical and Slant asymptotes
3
Derivatives
4h · 10 Q- Tangents and velocity
- Rate of change
- Review of derivative
- Differentiability of a function
- Mean value theorem
- Indeterminate forms and L'Hospital rule
4
Applications of Derivatives
4h · 8 Q- Curve sketching
- Review of maxima and minima of one variable
- Optimization problems
- Newton's method
5
Antiderivatives
5h · 7 Q- Review of antiderivatives
- Rectilinear motion
- Indefinite integrals and Net change
- Definite integral
- The Fundamental theorem of calculus
- Improper integrals
6
Applications of Antiderivatives
5h · 9 Q- Areas between the curves
- Volumes of cylindrical cells
- Approximate Integrations
- Arc length
- Area of surface of revolution
7
Ordinary Differential Equations
6h · 9 Q- Introduction
- Introduction to first order equations Separable equations
- Linear equations
- Second order linear differential equations
- Non homogeneous linear equations
- Method of undetermined coefficients
8
Infinite Sequence and Series
5h · 12 Q- Infinite sequence and series
- Convergence tests and power series
- Taylor's and Maclaurin's series
9
Plane and Space Vectors
4h · 11 Q- 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
Partial Derivatives and Multiple Integrals
3h · 14 Q- Limit and continuity
- Partial derivatives
- Tangent planes
- Maximum and minimum values
- Multiple integrals
Textbooks and references
- Calculus Early Transcendentals, James Stewart, 7E, CENGAGE Learning.
- Calculus Early Transcendentals, Thomas, 12th Editions, Addision Wesley.
Study MTH117 the smart way
Solved questions, flashcards & practice