Integral Calculus Course
This Integral Calculus course equips maths professionals with advanced techniques for improper integrals, Gamma and Gaussian integrals, and heat-kernel convolutions. Ideal for precise computations in probability, partial differential equations, moments, and transforms, featuring rigorous theorems like dominated convergence, Fubini-Tonelli, and differentiation under the integral sign.

4 to 360 hours flexible workload
valid certificate in your country
What will I learn?
Gain expertise in improper integrals, Gamma and Gaussian integrals, and parameter-dependent integration. Master dominated convergence, Fubini-Tonelli theorems, differentiation under the integral sign, and heat-kernel convolutions. Apply these through practical examples to compute probability densities, expectations, variances, and moment-generating functions effectively.
Elevify advantages
Develop skills
- Master improper integrals using dominated convergence and Fubini-Tonelli rigorously.
- Apply Gamma and Gaussian integrals to normalise densities and compute moments efficiently.
- Analyse heat kernels through derivation, normalisation, and convolution for smoothing.
- Differentiate under the integral sign to justify parameter swaps cleanly.
- Compute expectations and variances via 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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