Integral Calculus Course
Dive into advanced integral calculus covering improper integrals, Gamma and Gaussian forms, and heat-kernel methods. Tailored for maths experts seeking precise skills in probability theory, PDE solutions, and accurate computations of moments and transforms using rigorous tools.

from 4 to 360h 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, plus integration depending on parameters. You'll grasp dominated convergence, Fubini-Tonelli theorems, differentiation beneath the integral, and heat-kernel convolutions. Practical examples help you apply these to probability densities, expectations, variances, and moment-generating functions effectively.
Elevify advantages
Develop skills
- Master improper integrals using dominated convergence and Fubini theorems rigorously.
- Apply Gamma and Gaussian integrals to normalise densities and calculate moments swiftly.
- Analyse heat kernels through derivation, normalisation, and convolution for smoothing tasks.
- Differentiate under the integral sign to manage parameters and justify operation swaps.
- Evaluate expectations and variances via density integrals and recurrence relations.
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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