Integral Calculus Course
This Integral Calculus Mastery Course equips you with essential skills in improper integrals, Gamma and Gaussian integrals, and parameter-dependent integration. Master key theorems like dominated convergence, Fubini, Tonelli, and differentiation under the integral sign. Explore heat-kernel convolutions and apply them to probability densities, expectations, variances, and moment-generating functions through practical examples for real-world math applications in PDEs and probability.

flexible workload from 4 to 360h
valid certificate in your country
What will I learn?
Gain expertise in improper integrals, Gamma and Gaussian integrals, plus integration depending on parameters. Learn dominated convergence, Fubini, Tonelli theorems, differentiation under integrals, and heat-kernel convolutions. Build tools for probability densities, expectations, variances, and moment-generating functions with worked examples.
Elevify advantages
Develop skills
- Master improper integrals using dominated convergence and Fubini rigorously.
- Apply Gamma and Gaussian integrals to normalise densities and compute moments quickly.
- Analyse heat kernels by deriving, normalising, and convolving for smoothing.
- 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 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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