University of Michigan Robotics Department
ROB 201 is an innovative approach to teaching calculus that integrates mathematical theory with computational tools and real-world engineering applications. This course breaks away from traditional calculus education by emphasizing the practical application of mathematical concepts through programming and numerical methods using Julia.
Instructor: Jessy Grizzle
Department: Robotics, University of Michigan, Ann Arbor
Semester: Winter 2025
This course recognizes that modern engineering requires both mathematical understanding and computational proficiency. Rather than treating calculus as an abstract mathematical exercise, ROB 201 demonstrates how calculus serves as the foundation for solving complex engineering problems, particularly in robotics and control systems.
The following schedule shows lectures, assignments, and due dates:
| Lecture | Topic | Lecture Notes | Chapter | YouTube | Assignments Due |
|---|---|---|---|---|---|
| 01 | Pre-Calculus and Calculus Foundations | Notes | 1-2 | Video | |
| 02 | Limits at Infinity and Real Numbers | Notes | 2 | Video | |
| 03 | Algebra of Limits and Geometric Sums | Notes | 2 | Video | HW01 |
| 04 | Definite Integration and Riemann Sums | Notes | 3 | Video | |
| 05 | Area Between Functions and Simpson's Rule | Notes | 3 | Video | HW02 |
| 06 | Center of Mass and Function Properties | Notes | 3-4 | Video | |
| 07 | Limits and Continuity | Notes | 4 | Video | HW03 |
| 08 | Advanced Limits and Function Analysis | Notes | 4 | Video | |
| 09 | Introduction to Differentiation | Notes | 5 | Video | Project 1 |
| 10 | Advanced Differentiation and Taylor Series | Notes | 5 | Video | |
| 11 | Multivariable Calculus and Arc Length | Notes | 5-6 | Video | HW04 |
| 12 | Root Finding and Optimization | Notes | 6 | Video | |
| 13 | Constrained Optimization and Lagrangian Dynamics | Notes | 6 | Video | HW05 |
| 14 | Energy and Antiderivatives | Notes | 6-7 | Video | |
| 15 | Fundamental Theorems of Calculus | Notes | 7 | Video | |
| 16 | Integration Techniques | Notes | 7 | Video | HW06 |
| 17 | Improper Integrals | Notes | 8 | Video | |
| 18 | Introduction to ODEs | Notes | 9 | Video | HW07 |
| 19 | Systems of ODEs and Matrix Exponentials | Notes | 9 | Video | |
| 20 | Matrix Exponentials and Eigenvalues | Notes | 9 | Video | Project 2 |
| 21 | Introduction to Laplace Transforms | Notes | 10 | Video | |
| 22 | Inverse Laplace and Transfer Functions | Notes | 10 | Video | |
| 23 | Transfer Functions and Feedback Control | Notes | 10 | Video | |
| 24 | Controller Design and System Response | Notes | 10 | Video | HW08 |
| 25 | Advanced Control and Linearization | Notes | 10 | Video | |
| 26 | Bonus: Fourier Series | Notes | - | Video | |
| 27 | Final Exam Review | Notes | - | Video | Project 3 |
The course includes 8 homework sets, each containing both written problems and Julia programming exercises:
Written assignments (solutions included at end of each file):
- HW01: Pre-calculus and Approximation Principle
- HW02: Proofs and Finite Sums
- HW03: Definite Integration
- HW04: Function Properties and Continuity
- HW05: Differentiation
- HW06: Engineering Applications
- HW07: Antiderivatives and ODEs
- HW08: Laplace Transforms and Control
Julia programming assignments:
- Available in the Homework/Julia directory
- Setup instructions and requirements: Homework/Julia/README.md
The course features three major individual projects that apply calculus concepts to real engineering problems:
- Projects overview - General descriptions of all three projects
Note for faculty: Complete project files with detailed specifications, starter code, and solutions are available upon request. Please contact the University of Michigan Robotics Department for access to full project materials, as new versions for future iterations cannot be created at this time.
- Pre-calculus Foundations - Mathematical notation, functions, and the Approximation Principle
- Calculus Foundations - Proofs, limits, and geometric sums
- Definite Integration - Riemann sums, numerical integration, and engineering applications
- Function Properties - Continuity, boundedness, and optimization
- Differentiation - Theory and applications in engineering systems
- Engineering Applications - Optimization, dynamics, and Lagrangian mechanics
- Antiderivatives - Fundamental theorems and integration techniques
- Improper Integrals - Applications in probability and statistics
- Ordinary Differential Equations - First-order and linear systems
- Laplace Transforms - Control theory and feedback systems
By completing this course, students will:
- Master fundamental calculus concepts with computational proficiency
- Apply mathematical modeling to real-world engineering problems
- Develop skills in numerical methods and algorithmic thinking
- Understand the role of calculus in robotics and control systems
- Gain experience with Julia programming for mathematical computation
- Design and analyze feedback control systems
- Computational integration: Heavy use of Julia programming throughout
- Engineering focus: Real-world applications in robotics and control
- Project-based learning: Substantial individual projects with practical applications
- Modern approach: Emphasis on numerical methods and computational thinking
- Student Teaching Evaluations - Student feedback and course assessment results
- "Calculus for the Modern Engineer: An Open-Source Approach Integrating Julia Programming" - ArXiv preprint describing the pedagogical approach and course design
- Michigan Robotics - The Robotics Department at the University of Michigan
The HW sets included here were prepared by undergraduate Instructional Assistants Sydney Ragla, Kane Weng, Meiyi Yang, and Elvis Xiang. Sydney’s exceptional effort and attention to detail set a high standard for the materials and greatly enriched the final product. Additional thanks go to the undergraduate Instructional Assistants who collaborated in Winter and Summer 2024: Kaylee Johnson (lead), Advaith (Adi) Balaji, Madeline (Maddy) Bezzina, Justin Boverhof, Elaina Mann, Reina Mezher, and Maxwell (Max) West. They worked diligently to create homework sets, projects, and refine the initial draft of the textbook.