BIT · Semester I
Basic Mathematics syllabus
Official TU syllabus for Basic Mathematics (MTH104): 10 units, 89 topics. Every unit links to its notes and solved questions.
1
Functions and Their Properties
6 Q- Definition and notation of functions
- Domain and range of functions
- Even and odd functions
- Absolute value functions
- Function composition
- Piecewise defined functions
- Graph transformations and shifts
- Symmetry properties
2
Limits and Continuity
9 Q- Limit definition and notation
- Limit evaluation techniques
- Limits at infinity
- Infinite limits and vertical asymptotes
- Continuity definition
- Discontinuity types
- Continuous extension of functions
- Epsilon-delta definition
3
Asymptotes and Curve Behavior
3 Q- Horizontal asymptotes
- Vertical asymptotes
- Oblique asymptotes
- Asymptotic behavior analysis
4
Derivatives and Differentiation
7 Q- Derivative definition and interpretation
- Derivative as slope of tangent line
- Power rule and basic differentiation rules
- Product and quotient rules
- Chain rule
- Implicit differentiation
- Derivatives of trigonometric functions
- Derivatives of inverse trigonometric functions
- Derivatives of exponential and logarithmic functions
- Higher order derivatives
- Partial derivatives
5
Applications of Derivatives
13 Q- Tangent and normal lines to curves
- Average and instantaneous rates of change
- Related rates problems
- Optimization and extrema
- Absolute maximum and minimum values
- Local extrema and critical points
- First derivative test
- Second derivative test
- Concavity and inflection points
- Curve sketching
- Rolle's theorem
- Mean value theorem
- L'Hospital's rule
6
Integration and Antiderivatives
8 Q- Indefinite integral definition
- Basic integration rules
- Integration by substitution
- Integration by parts
- Partial fraction decomposition
- Trigonometric integrals
- Definite integral definition
- Fundamental theorem of calculus
- Improper integrals
7
Applications of Integration
8 Q- Area between curves
- Area under curves
- Volume of solids of revolution
- Disk and washer methods
- Shell method
- Arc length of curves
- Surface area of revolution
- Trapezoidal rule for numerical integration
8
Series and Sequences
11 Q- Convergence and divergence of series
- Geometric series
- Harmonic series
- Integral test
- Comparison tests
- Ratio test
- Root test
- Alternating series test
- Power series
- Taylor series
- Maclaurin series
- Taylor polynomials
9
Multivariable Calculus
10 Q- Partial derivatives
- Second order partial derivatives
- Gradient vector
- Directional derivatives
- Chain rule for multivariable functions
- Implicit differentiation in multiple variables
- Local extrema of multivariable functions
- Critical points and classification
10
Differential Equations
8 Q- First order differential equations
- Separable differential equations
- Linear differential equations
- Initial value problems
- Second order linear differential equations
- Homogeneous differential equations
- Phase lines and qualitative analysis
- Newton's method for root finding
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