Mathematics-I
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Follow on Instagram for UpdatesMathematics-I Syllabus — Unit-wise Content
The official GTU curriculum for Mathematics-I (subject code BE01000041) as prescribed for Rubber · Semester 1 divides the course into 5 units, covering 32 listed topics. The unit-wise breakdown below is read from the GTU syllabus document for this subject code, so you can check what the course actually covers before deciding which papers to attempt.
Download the official syllabus PDF (BE01000041)Unit 1 Basic Calculus
- Evaluation of improper integrals of Type-I and Type-II
- Beta and Gamma functions and their properties
- Applications of definite integrals to evaluate surface areas and volumes of revolutions
Unit 2 Single-variable Calculus (Differentiation)
- Taylor’s and Maclaurin’s theorem for a function of one variable
- Taylor’s and Maclaurin’s series of a function using statement of the theorems
- Extreme values of functions
- Indeterminate forms and L' Hospital's rule
Unit 3 Sequences and series
- Sequence of numbers and its convergence
- Infinite series
- Tests for convergence (Telescoping series
- Geometric series test
- Integral test
- comparison test
- D’ Alembert’s ratio test
- Cauchy’s root test)
- Alternating series test
- Power series
- Radius and interval of convergence
- Conditional and Absolute convergence of a power series
Unit 4 Multivariable Calculus (Differentiation)
- Continuity and Differentiation for function of two or more variables
- total derivative
- directional derivatives
- Tangent plane and Normal line to the surface 𝑓(𝑥
- Extreme values for function of two variables (Maxima
- minima and saddle points)
- Method of Lagrange multipliers
Unit 5 Multivariable Calculus (Integration)
- Multiple Integration: Double integrals (Cartesian
- change of order of integration in double integrals
- Change of variables (Cartesian to polar)
- Applications: areas and volumes
- Center of mass and Gravity (constant and variable densities)
- Triple integrals (Cartesian
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