Integral Calculus Course
This Integral Calculus Course equips mathematics professionals with advanced techniques for improper integrals, Gamma and Gaussian integrals, and heat-kernel convolutions. Participants will develop rigorous skills in dominated convergence, Fubini and Tonelli theorems, differentiation under the integral sign, and practical computations for probability densities, expectations, variances, and moment-generating functions, ideal for applications in probability theory and partial differential equations.

4 to 360 hours flexible workload
valid certificate in your country
What will I learn?
This course develops expertise in improper integrals, Gamma and Gaussian integrals, and integration depending on parameters. Learners will master theorems including dominated convergence, Fubini and Tonelli, alongside differentiation under the integral sign and heat-kernel convolutions. Practical examples provide tools for probability densities, expectations, variances, and moment-generating functions.
Elevify advantages
Develop skills
- Master improper integrals by applying dominated convergence and Fubini theorems rigorously.
- Employ Gamma and Gaussian integrals to normalise probability densities and compute moments efficiently.
- Analyse heat kernels by deriving, normalising, and applying convolution for smoothing operations.
- Differentiate under the integral sign to justify interchanges and manage parameters effectively.
- Calculate expectations and variances using 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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