Mathematics
Advanced Calculus Masterclass — From Fundamentals to Applications
Master differentiation, integration, and real-world problem solving
westvelocity1@gmail.com
Instructor
About This Course
A comprehensive calculus course designed for engineering students, professionals, and anyone seeking to master mathematical analysis. Covers limits, derivatives, integrals, series, and their applications in physics, engineering, and data science.
What You'll Learn
- Understand limits and continuity rigorously
- Master differentiation techniques including chain rule, implicit, and parametric
- Apply integration methods: substitution, by parts, partial fractions, trigonometric
- Solve real-world optimization and rate-of-change problems
- Work with sequences, series, and convergence tests
- Apply calculus to physics, engineering, and data science problems
- Understand multivariable calculus fundamentals
Prerequisites
- Basic algebra and trigonometry
- Understanding of functions and graphs
- Comfort with mathematical notation
Target Audience
- Engineering and science students
- Working professionals needing mathematical upskilling
- Anyone preparing for competitive exams
- Data science learners needing calculus foundations
1
Foundations: Limits & Continuity
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2
Foundations: Limits & Continuity
What is Calculus? — Historical Context
Understanding Limits — Formal Definition
Continuity and Intermediate Value Theorem
Squeeze Theorem and Special Limits
3
Differentiation
The Derivative — Definition and Meaning
Power, Product, Quotient, Chain Rules
Implicit Differentiation and Related Rates
Higher-Order Derivatives and Curve Sketching
Optimization Problems in Engineering
4
Integration
Definite Integral and Area Under Curves
Antiderivatives and Substitution
Integration by Parts and Partial Fractions
Applications — Volume, Work, Arc Length
Numerical Integration Methods
5
Series and Sequences
Sequences — Convergence and Bounds
Infinite Series and Convergence Tests
Power Series and Taylor Expansions
Applications of Series in Engineering
6
Multivariable Calculus Introduction
Functions of Several Variables
Gradient and Directional Derivatives
Double and Triple Integrals
Course Summary and Next Steps
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