Course description

Advanced Calculus extends the principles of basic calculus to more complex and multidimensional problems, focusing on rigorous mathematical reasoning and applications. It covers topics like multivariable calculus, including partial derivatives, multiple integrals, and vector calculus concepts such as gradient, divergence, and curl. Fundamental theorems like Green's, Stokes', and the Divergence Theorem are explored in detail.

The subject also delves into real analysis, emphasizing sequences, series, and the rigorous study of continuity and differentiability in higher dimensions. Advanced integration techniques, such as improper and Lebesgue integration, are introduced to handle complex scenarios.

Differential equations—both ordinary and partial—play a significant role, along with their solutions and applications in physics and engineering. Differential geometry, which studies curves, surfaces, and manifolds, further expands the scope to abstract spaces and real-world modeling.

Applications of advanced calculus are vast, ranging from physics and engineering to optimization, machine learning, and economics. Mastery of this subject provides a deeper understanding of mathematics and its role in solving real-world, multidimensional problems.

What will i learn?

• CO1 Knowledge in transforming double integral to line integrals, triple integrals to surface integrals, surface integrals to line integrals and vice versa.
• CO2 Determine the important analytical quantities associated with scalar and vector fields.
• CO3 Solving line integral, double integral and applying these knowledge to find out work done by a force, volume of regions in space, center of gravity of a mass etc.