Integral Calculus Course
Dive into advanced integral calculus with this course tailored for maths pros seeking precise tools in probability, PDEs, and rigorous computations of moments and transforms. Conquer improper integrals, Gamma functions, Gaussian integrals, and heat-kernel convolutions using theorems like dominated convergence, Fubini, Tonelli, and differentiation under the integral sign.

from 4 to 360h flexible workload
certificate valid in your country
What will I learn?
This course equips you with essential skills in improper integrals, Gamma and Gaussian integrals, and integration depending on parameters. Master dominated convergence, Fubini and Tonelli theorems, differentiation under the integral sign, and heat-kernel convolutions. Gain practical expertise through examples for probability densities, expectations, variances, and moment-generating functions.
Elevify advantages
Develop skills
- Master improper integrals using dominated convergence and Fubini rigorously.
- Apply Gamma and Gaussian integrals to normalise densities and compute moments swiftly.
- Analyse heat kernels: derive, normalise, and convolve for smoothing applications.
- Differentiate under the integral sign to justify swaps and manage parameters effectively.
- Compute expectations and variances via density integrals with 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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