Integral Calculus Course
This Integral Calculus Mastery Course equips math professionals with essential tools for improper integrals, Gamma and Gaussian integrals, and heat-kernel convolutions. Learners gain proficiency in dominated convergence, Fubini-Tonelli theorems, differentiation under integrals, and practical computations for probability densities, expectations, variances, and moment-generating functions, ideal for probability, PDEs, and rigorous analysis.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
Build expertise 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. Apply heat-kernel convolutions and solve real-world problems in probability densities, expectations, variances, and moment-generating functions through practical 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 effects.
- Differentiate under the integral sign to justify swaps and manage parameters effectively.
- Compute expectations and variances through density integrals and 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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