Integral Calculus Course
Dive into advanced integral calculus, mastering improper integrals, Gamma and Gaussian functions, parameter differentiation, and heat-kernel methods. Tailored for maths pros seeking precise tools for probability, PDEs, and rigorous computations of moments and transforms in real-world applications.

4 to 360 hours flexible workload
valid certificate in your country
What will I learn?
This course equips you with essential techniques for improper integrals, Gamma and Gaussian integrals, and integration with parameters. You'll gain expertise in dominated convergence, Fubini-Tonelli theorems, differentiation under the integral, and heat-kernel convolutions, applying them to probability densities, expectations, variances, and moment-generating functions via practical examples.
Elevify advantages
Develop skills
- Master improper integrals using dominated convergence and Fubini theorems rigorously.
- Apply Gamma and Gaussian integrals to normalise densities and compute moments efficiently.
- Analyse and utilise heat kernels for derivation, normalisation, and convolution smoothing.
- Differentiate under the integral sign to handle parameters and justify operations cleanly.
- Calculate expectations and variances through density integrals and recurrence methods.
Suggested summary
Before starting, you can change the chapters and the workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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