Mathematics - 1
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Mathematics - 1 Syllabus — Unit-wise Content
The official GTU curriculum for Mathematics - 1 (subject code 3110014) as prescribed for Common · Semester 2 divides the course into 6 units, covering 55 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 (3110014)Unit 1 Indeterminate Forms and L’Hôspital’s Rule. 01
- 15 % Improper Integrals
- Convergence and divergence of the integrals
- Beta and Gamma functions and their properties. 03 Applications of definite integral
- Volume using cross-sections
- Length of plane curves
- Areas of Surfaces of Revolution
Unit 2 Convergence and divergence of sequences, The Sandwich Theorem for
- The Continuous Function Theorem for Sequences
- Bounded Monotonic Sequences
- Convergence and divergence of an infinite series
- geometric series
- telescoping series
- 𝑛𝑛𝑛 term test for divergent series
- Combining series
- Harmonic Series
- Integral test
- The p - series
- The Comparison test
- The Limit Comparison test
- Ratio test
- Raabe’s Test
- Root test
- Alternating series test
- Absolute and Conditional convergence
- Power series
- Radius of convergence of a power series
- Taylor and Maclaurin series
Unit 3 Fourier Series of 2𝑛 periodic functions, Dirichlet’s conditions for
- representation by a Fourier series
- Orthogonality of the trigonometric system
- Fourier Series of a function of period 2 𝑛
- Fourier Series of even and odd functions
- Half range expansions
Unit 4 Functions of several variables, Limits and continuity, Test for non
- existence of a limit
- Partial differentiation
- Mixed derivative theorem
- Chain rule
- Implicit differentiation
- Directional derivative
- tangent plane and normal line
- total differentiation
- Local extreme values
- Method of Lagrange Multipliers
Unit 5 Multiple integral, Double integral over Rectangles and general regions,
- double integrals as volumes
- Change of order of integration
- double integration in polar coordinates
- Area by double integration
- Triple integrals in rectangular
- cylindrical and spherical coordinates
- multiple integral by substitution
Unit 6 Elementary row operations in Matrix, Row echelon and Reduced row
- echelon forms
- Rank by echelon forms
- Inverse by Gauss-Jordan method
- Solution of system of linear equations by Gauss elimination and Gauss- Jordan methods
- Eigen values and eigen vectors
- Cayley-Hamilton theorem
- Diagonalization of a matrix
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