Calculus
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Calculus Syllabus — Unit-wise Content
The official GTU curriculum for Calculus (subject code 2110014) as prescribed for Production · Semester 1 divides the course into 6 units, covering 22 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 (2110014)Unit 1 Infinite Sequences and Series
- Introduction of Convergence
- Divergence of Sequences and Infinite Series The nth term test for Divergence
- Integral Test Comparison Test
- Ratio Test
- Root Test Alternating Series
- Absolute convergence
- Conditional convergence Power Series & Radius of convergence Taylor’s series Maclaurin’s series 7 20-22%
Unit 2 Curve Sketching
- Concavity Curve sketching Polar co-ordinates
- Relation between Polar and Cartesian 4 10-12% Co-ordinates Graphs in Polar co-ordinates
Unit 3 Indeterminate Forms
- Indeterminate form , 0, 0 0 Indeterminate form 1, 0 0 0 Improper Integral Improper integrals of Type- I and Type - II Convergence and divergence of improper integrals 4 10-12%
Unit 4 Applications of Integration
- Volume by slicing Volume of solids of revolution by disk method Volume of solids of revolutions by washer method Volume by cylindrical shell. 4 10-12%
Unit 5 Partial Derivatives
- Function of 2-variables
- level curves Limit
- continuity of function of several variables Partial derivatives and Clairauts’ theorem Tangent plane
- Normal line Linear approximation
- Total differential Chain rule
- implicit differentiation Euler’s theorem for homogeneous function Maximum and minimum values by second derivative test Lagrange multipliers Taylor’s formula for two variables 10 30-32%
Unit 6 Multiple Integrals
- Double integrals over rectangles and Fubini’s theorem
- Properties of double integrals Double integrals over general region Double integrals in polar co-ordinates Triple Integrals
- Triple integrals in cylindrical co- ordinates Triple integrals in spherical co-ordinates Change of Order of Integration Jacobian of several variables
- Change of variable in multiple integrals 7 20-22% Note: Teachers are advised to encourage students to perform the projects in group of 4 students for conceptual understanding by geometrically
- numerically and algebraically
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